Research Article Constraints on the Nonstandard...

Research ArticleConstraints on the Nonstandard Interaction inPropagation from Atmospheric Neutrinos

Shinya Fukasawa and Osamu Yasuda

Department of Physics Tokyo Metropolitan University Minami-Osawa Hachioji Tokyo 192-0397 Japan

Correspondence should be addressed to Osamu Yasuda yasudaphyssetmuacjp

Received 3 May 2015 Accepted 5 August 2015

Academic Editor Vincenzo Flaminio

Copyright copy 2015 S Fukasawa and O Yasuda This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited The publication of this article was funded by SCOAP3

The sensitivity of the atmospheric neutrino experiments to the nonstandard flavor-dependent interaction in neutrino propagationis studied under the assumption that only nonvanishing components of the nonstandard matter effect are the electron and tauneutrino components 120598

119890119890 and 120598

119890120591 120598120591120591and that the tau-tau component satisfies the constraint 120598

120591120591= |120598119890120591|2

(1+120598119890119890)which is suggested

from the high energy behavior for atmospheric neutrino data It is shown that the Super-Kamiokande (SK) data for 4438 daysconstrains |tan120573| equiv |120598

119890120591(1 + 120598

119890119890)| ≲ 08 at 25120590 (988) CL whereas the future Hyper-Kamiokande experiment for the same period

of time as SK will constrain as |tan120573| ≲ 03 at 25120590CL from the energy rate analysis and the energy spectrum analysis will give eventighter bounds on 120598

119890119890and |120598

119890120591|

1 Introduction

From the experiments with solar atmospheric reactor andaccelerator neutrinos it is now established that neutrinos havemasses and mixing [1] Neutrino oscillations in the standardthree-flavor scheme are described by threemixing angles 120579

12

12057913 and 120579

23 one CP phase 120575 and two independent mass-

squared differences Δ119898221and Δ1198982

31 The sets of the param-

eters (Δ119898221 12057912) and (|Δ1198982

31| 12057923) were determined by the

solar neutrino experiments and the KamLAND experimentand by atmospheric and long baseline neutrino experimentsrespectively 120579

13was determined by the reactor experiments

and the long baseline experiments [1] The only oscillationparameters which are still undetermined are the value of theCP phase 120575 and the sign of Δ1198982

31(the mass hierarchy) In

the future neutrino long-baseline experiments with intenseneutrino beams the signs of Δ1198982

31and 120575 are expected to be

determined [2 3] As in the case of B factories [4 5] such highprecisionmeasurements will enable us to search for deviationfrom the standard three-flavor oscillations (see eg [6])Among such possibilities in this paper we will discuss

the effective nonstandard neutral current flavor-dependentneutrino interaction with matter [7ndash9] given by

LNSIeff = minus2radic2120598

119891119875

120572120573119866119865(]120572120574120583119875119871]120573) (119891120574120583

1198751198911015840

) (1)

where119891 and1198911015840 stand for fermions (the only relevant ones areelectrons 119906 and 119889 quarks)119866

119865is the Fermi coupling constant

and 119875 stands for a projection operator that is either 119875119871equiv

(1 minus 1205745)2 or 119875

119877equiv (1 + 120574

5)2 If the interaction (1) exists

then the standard matter effect [7 10] is modified We willdiscuss atmospheric neutrinos which go through the Earthso we make an approximation that the number densities ofelectrons (119873

119890) protons and neutrons are equal (this assump-

tion is not valid in other environments eg in the Sun)Defining 120598

120572120573equiv sum119875(120598119890119875

120572120573+ 3120598119906119875

120572120573+ 3120598119889119875

120572120573) the Hermitian 3 times 3

matrix of the matter potential becomes

A equiv 119860(

1 + 120598119890119890

120598119890120583

120598119890120591

120598120583119890

120598120583120583

120598120583120591

120598120591119890

120598120591120583

120598120591120591

) (2)

Hindawi Publishing CorporationAdvances in High Energy PhysicsVolume 2015 Article ID 820941 13 pageshttpdxdoiorg1011552015820941

2 Advances in High Energy Physics

where 119860 equiv radic2119866119865119873119890stands for the matter effect due to the

charged current interaction in the standard case With thismatter potential the Dirac equation for neutrinos in matterbecomes

119894

119889

119889119909

(

]119890(119909)

]120583(119909)

]120591(119909)

)

= [119880diag (0 Δ11986421 Δ11986431) 119880minus1

+A](

]119890(119909)

]120583(119909)

]120591(119909)

)

(3)

where 119880 is the leptonic mixing matrix defined by

119880

equiv (

1198881211988813

1199041211988813

11990413119890minus119894120575

minus1199041211988823minus 119888121199042311990413119890119894120575

1198881211988823minus 119904121199042311990413119890119894120575

1199042311988813

1199041211990423minus 119888121198882311990413119890119894120575

minus1198881211990423minus 119904121198882311990413119890119894120575

1198882311988813

)

(4)

and Δ119864119895119896equiv Δ119898

2

1198951198962119864 equiv (119898

2

119895minus 1198982

119896)2119864 119888

119895119896equiv cos120579

119895119896 and

119904119895119896equiv sin120579

119895119896

Constraints on 120598120572120573

have been discussed by many authorsfrom atmospheric neutrinos [11ndash15] from 119890

+

119890minus colliders [16]

from the compilation of various neutrino data [17] from solarneutrinos [18ndash20] from ]

119890119890 or ]

119890119890 scatterings [21 22] from

solar and reactor neutrinos [23] and from solar reactor andaccelerator neutrinos [24] Since the coefficients 120598

120572120573in (2) are

given by 120598120572120573sim 120598119890

120572120573+3120598119906

120572120573+3120598119889

120572120573 considering the constraints in

these references we have the following limits [25] at 90CL

(

1003816100381610038161003816120598119890119890

1003816100381610038161003816lt 4 times 10

010038161003816100381610038161003816120598119890120583

10038161003816100381610038161003816lt 3 times 10

minus1 1003816100381610038161003816120598119890120591

1003816100381610038161003816lt 3 times 10

0

10038161003816100381610038161003816120598120583120583

10038161003816100381610038161003816lt 7 times 10

minus210038161003816100381610038161003816120598120583120591

10038161003816100381610038161003816lt 3 times 10

minus1

1003816100381610038161003816120598120591120591

1003816100381610038161003816lt 2 times 10

1

) (5)

From (5) we observe that the bounds on 120598119890119890 120598119890120591 and 120598

120591120591are

much weaker than those on 120598120572120583(120572 = 119890 120583 120591)

On the other hand the nonstandard interaction (NSI)with components 120598

120572120573(120572 120573 = 119890 120591)must be consistent with the

high-energy atmospheric neutrino data It was pointed out in[26 27] that the relation

1003816100381610038161003816120598119890120591

1003816100381610038161003816

2

≃ 120598120591120591(1 + 120598

119890119890) (6)

should hold for the matter potential (2) to be consistent withthe high-energy atmospheric neutrino data which suggestthe behavior of the disappearance oscillation probability

1 minus 119875 (]120583997888rarr ]120583) sim sin22120579atmsin

2

(

Δ1198982

atm119871

4119864

) prop

1

1198642 (7)

where sin22120579atm and Δ1198982atm are the oscillation parameters inthe two-flavor formalism In [28] it was shown that in thehigh-energy behavior of the disappearance oscillation prob-ability

1 minus 119875 (]120583997888rarr ]120583) ≃ 1198880+

1198881

119864

+ O(1

1198642) (8)

in the presence of the matter potential (2) |1198880| ≪ 1 and |119888

1| ≪

1 imply 120598119890120583≃ 120598120583120583≃ 120598120583120591≃ 0 and 120598

120591120591≃ |120598119890120591|2

(1 + 120598119890119890)

Taking into account the various constraints describedabove in the present paper we take the ansatz

A = 119860(

1 + 120598119890119890

0 120598119890120591

0 0 0

120598lowast

1198901205910

1003816100381610038161003816120598119890120591

1003816100381610038161003816

2

(1 + 120598119890119890)

) (9)

and analyze the sensitivity to the parameters 120598120572120573(120572 120573 =

119890 120591) of the atmospheric neutrino experiment at Super-Kamiokande and the futureHyper-Kamiokande (HK) facility[29] (as far as 120598

120591120591is concerned the ansatz (9) is believed to be

the best fit of the high energy atmospheric neutrino data atpresent So as long as the true value of 120598

120591120591satisfies the relation

(6) even if we analyze the data assuming that 120598120591120591

is a freeparameter the allowed region in (120598

119890119890 |120598119890120591|) and the sensitivity

to NSI are not expected to change very much because theregion of 120598

120591120591 which does not satisfy (6) gets an additional

contribution of 1205942 and is not supposed to contribute toenlarge the allowed region or to increase the sensitivity toNSI)

The constraints on 120598119890119890and 120598119890120591from the atmospheric neu-

trino have been discussed in [30] along with those from thelong-baseline experiments in [31] by the Super-KamiokandeCollaboration in [32ndash34] on the future extension of theIceCube experiment and in [35] in the global analysis withthe ansatz different from ours

The sensitivity of the ongoing accelerator experiments tothe nonstandard interaction in propagation was studied byvarious authorsThe constraints have been obtained from theMINOS experiment in [36] from the MINOS data using thesame ansatz as the present paper in [37 38] from theMINOSdata from the viewpoint of degeneracy of 120579

13and NSI in [39]

from ]119890appearance in MINOS and T2K in [40] from the

OPERA experiment in [41 42] and from the LHC experi-ment in [43] As for the future long-baseline experiments thesensitivity of the INO experiment was discussed in [44] thatof the reactor and superbeam experiments was discussed in[45] that of the T2KK experiment was studied in [28 46]and that of the LBNE experiment was discussed in [43 47]The sensitivity of neutrino factories [6] was studied invarious contexts the sensitivity toNSI [48ndash50] the confusionwith the effect of 120579

13[51] the optimization [52] resolving

degeneracy with two baselines [53 54] and the relation withnonunitary mixing [55]

The paper is organized as follows In Section 2 we analyzethe SK atmospheric neutrino data and give the constraints onthe parameters 120598

120572120573(120572 120573 = 119890 120591) from the SK atmospheric

neutrino data In Section 3 we discuss the sensitivity to120598120572120573(120572 120573 = 119890 120591) of the future Hyper-Kamiokande atmo-

spheric neutrino experiment In Section 4 we draw ourconclusions

Advances in High Energy Physics 3

2 The Constraint of the Super-KamiokandeAtmospheric Neutrino Experiment on120598119890119890

and |120598119890120591|

In this section we discuss the constraint of the SK atmo-spheric neutrino experiment on the nonstandard interactionin propagation with the ansatz (9) The independent degreesof freedom in addition to those in the standard oscillationscenario are 120598

119890119890 |120598119890120591| and arg(120598

119890120591)

The SK atmospheric neutrino data we analyze here isthose in [56] for 4438 days In [56] the contained eventsthe partially contained events and the upward going 120583 eventsare divided into a few categories Since we have been unableto reproduce all their results of the Monte Carlo simulationwe have combined the two sub-GeV 120583-like data set in onethe two multi-GeV 119890-like in one the two partially contained

event data set and the multi-GeV 120583-like in one and the threeupward going 120583 in one Reference [56] gives information onthe ten zenith angle bins while that on the energy bins is notgiven so we perform analysis with the ten zenith angle binsand one energy bin that is we perform the rate analysis as faras the energy is concerned

The analysis was performed with the codes which wereused in [57ndash59] 1205942 is defined as

1205942

= min12057923|Δ1198982

32|120575arg(120598

119890120591)

(1205942

sub-GeV + 1205942

multi-GeV + 1205942

upward) (10)

In (10) 1205942 for the sub-GeV multi-GeV and upward going 120583events are defined by

1205942

sub-GeV = min1205721199041205731015840119904

[

[

1205732

1199041

1205902

1205731199041

+

1205732

1199042

1205902

1205731199042

+

10

sum

119895=1

1

119899119904

119895(119890)

[120572119904(1 minus

1205731199041

2

+

1205731199042

2

)119873119904

119895(]119890997888rarr ]119890) + 120572119904(1 +

1205731199041

2

+

1205731199042

2

)119873119904

119895(]120583997888rarr ]119890) + 120572119904(1 minus

1205731199041

2

minus

1205731199042

2

)119873119904

119895(]119890997888rarr ]119890) + 120572119904(1 +

1205731199041

2

minus

1205731199042

2

)119873119904

119895(]120583997888rarr ]119890) minus 119899119904

119895(119890)]

2

+

1

119899119904

119895(120583)

[120572119904(1 minus

1205731199041

2

+

1205731199042

2

)119873119904

119895(]119890997888rarr ]120583) + 120572119904(1 +

1205731199041

2

+

1205731199042

2

)119873119904

119895(]120583997888rarr ]120583) + 120572119904(1 minus

1205731199041

2

minus

1205731199042

2

)119873119904

119895(]119890997888rarr ]120583) + 120572119904(1 +

1205731199041

2

minus

1205731199042

2

)119873119904

119895(]120583997888rarr ]120583) minus 119899119904

119895(120583)]

2

]

]

1205942

multi-GeV = min1205721198981205731015840119904

[

[

1205732

1198981

1205902

1205731198981

+

1205732

1198982

1205902

1205731198982

+

10

sum

119895=1

1

119899119898

119895(119890)

[120572119904(1 minus

1205731198981

2

+

1205731198982

2

)119873119898

119895(]119890997888rarr ]119890) + 120572119904(1 +

1205731198981

2

+

1205731198982

2

)119873119898

119895(]120583997888rarr ]119890) + 120572119904(1 minus

1205731198981

2

minus

1205731198982

2

)119873119898

119895(]119890997888rarr ]119890) + 120572119904(1 +

1205731198981

2

minus

1205731198982

2

)119873119898

119895(]120583997888rarr ]119890) minus 119899119898

119895(119890)]

2

+

1

119899119898

119895(120583)

[120572119904(1 minus

1205731198981

2

+

1205731198982

2

)119873119898

119895(]119890997888rarr ]120583) + 120572119904(1 +

1205731198981

2

+

1205731198982

2

)119873119898

119895(]120583997888rarr ]120583) + 120572119904(1 minus

1205731198981

2

minus

1205731198982

2

)119873119898

119895(]119890997888rarr ]120583) + 120572119904(1 +

1205731198981

2

minus

1205731198982

2

)119873119898

119895(]120583997888rarr ]120583) minus 119899119898

119895(120583)]

2

]

]

1205942

upward = min120572119906

1205722

119906

1205902

120572

+

10

sum

119895=1

1

119899119906

119895(120583)

[120572119906119873119906

119895(]119890997888rarr ]120583) + 120572119906119873119906

119895(]120583997888rarr ]120583) + 120572119906119873119906

119895(]119890997888rarr ]120583) + 120572119906119873119906

119895(]120583997888rarr ]120583) minus 119899119906

119895(120583)]

2

(11)

The summation on 119895 runs over the ten zenith angle bins foreach 1205942 119899119886

119895(120572) (119886 = 119904119898 119906 120572 = 119890 120583) stands for the neutrino

and antineutrino data of the numbers of the sub-GeV multi-GeV and upward going 120583 events 119873119886

119895(]120572rarr ]120573) (119873119886119895(]120572rarr

]120573)) stands for the theoretical prediction for the number of

ℓ120573-like events (ℓ

120573= 119890 120583) which is produced from ]

120573(]120573)

that originates from ]120572(]120572) through the oscillation process

]120572rarr ]120573(]120572rarr ]120573) and it is expressed as the product

of the oscillation probability 119875(]120572rarr ]120573) (119875(]

120572rarr ]120573))

the flux 119865(]120572) (119865(]

120572)) the cross section the number of the

targets and the detection efficiency 120572119886(119886 = 119904119898 119906) stands

for the uncertainty in the overall flux normalization for thesub-GeV multi-GeV and upward going 120583 events and 120573

1198861

(1205731198862) stands for the uncertainty in the relative normalization

between ]119890minus ]120583flux (] minus ] flux) for the sub-GeV (119886 = 119904) and

multi-GeV (119886 = 119898) events respectively It is understood that1205942 is minimized with respect to 120572

119904 120573119904119896(119896 = 1 2) 120572

119898 120573119898119896

(119896 = 1 2) and 120572119906 We have put the systematic errors

1205901205731199041

= 1205901205731198981

= 003

1205901205731199042

= 1205901205731198982

= 005

120590120572= 02

(12)

and we have assumed that 120572119904and 120572

119898for the contained

events are free parameters as in [60] We have omitted theother uncertainties like the 119864] spectral index the relativenormalization between PC and FC and up-down correlationand so forth for simplicity In (10) the sum of each 120594

2 isoptimized with respect to the mixing angle 120579

23 the mass

squared difference |Δ119898232| the Dirac CP phase 120575 and the

phase arg(120598119890120591) of the parameter 120598

119890120591 The other oscillation

parameters give little effect on 1205942 so we have fixed them assin22120579

12= 086 sin22120579

13= 01 and Δ1198982

21= 76 times 10

minus5 eV2The result for the Super-Kamiokande data for 4438 days is

given in Figure 1 The best-fit point for the normal (inverted)hierarchy is (120598

119890119890 |120598119890120591|) = (minus10 00) ((30 17)) and the value of

1205942 at this point is 790 (786) for 50 degrees of freedom and

goodness of fit is 28 (27) 120590CL respectivelyThe best-fit pointis different from the standard case (120598

119890119890 |120598119890120591|) = (0 0) and this

may be not only because we have been unable to reproducetheMonte Carlo simulation by the Super-Kamiokande groupbut also because we use only the information on the energy


05120590

1120590

15120590

2120590

25120590

3120590

minus3 minus2 minus1minus4 1 2 3 40120598ee

2

15

|120598e120591|

1

05

0

(a) SK 4438 days NH

05120590

1120590

15120590

2120590

25120590

3120590

minus4 minus3 minus2 minus1

120598ee

0 1 2 3 4

2

15

|120598e120591|

1

05

0

(b) SK 4438 days IH

Figure 1 The allowed region in the (120598119890119890 |120598119890120591|) plane from the SK atmospheric neutrino data for a normal mass hierarchy (a) and for an

inverted mass hierarchy (b) In the left panel the best-fit point is (120598119890119890 |120598119890120591|) = (minus10 00) although it is difficult to see from the figure that there

is a very narrow region with CL less than 05120590 near this point

rate and the sensitivity to NSI is lost due to the destructivephenomena between the lower and higher energy bins (seethe discussions in Section 31) The difference of the value of1205942 for the standard case and that for the best-fit point for the

normal (inverted) hierarchy is Δ1205942 = 27 (34) for 2 degreesof freedom (11120590CL (13120590CL)) respectively and the standardcase is certainly acceptable for the both mass hierarchies inour analysis From Figure 1 we can read off the allowed regionfor |tan120573| equiv |120598

119890120591||1 + 120598

119890119890| and we conclude that the allowed

region for |tan120573| is approximately

1003816100381610038161003816tan120573100381610038161003816

1003816equiv

1003816100381610038161003816120598119890120591

1003816100381610038161003816

10038161003816100381610038161 + 120598119890119890

1003816100381610038161003816

≲ 08 at 25120590CL (13)

3 Sensitivity of the Hyper-KamiokandeAtmospheric Neutrino Experiment to120598119890119890

and |120598119890120591|

In this section we discuss the potential sensitivity of HK to 120598119890119890

and |120598119890120591| Here we assume for simplicity that the the Hyper-

Kamiokande detector has the same detection efficiencies asthose of SK and that the fiducial volume ofHK is twenty timesas large as that of SK Since HK is a future experiment thesimulated numbers of events are used as ldquothe experimentaldatardquo and we vary 120598

119890119890and 120598

119890120591as well as the standard

oscillation parameters trying to fit to ldquothe experimental datardquoHere we perform an analysis on the assumption that we knowthe mass hierarchy because some hint on the mass hierarchy

is expected to be available at some confidence level by the timeHKwill accumulate the atmospheric neutrino data for twentyyears

Since ldquothe experimental datardquo are the simulated numbersof events we can perform a energy spectrum analysisassuming that the detection efficiency and so forth are allequal among neutrinos and antineutrinos Before we studythe sensitivity to NSI as a benchmark of our analysis we haveinvestigated the significance of the wrong mass hierarchywith our code assuming the standard oscillation scenario andusing different numbers of the energy bins By comparing ourresult with the one in [29] we have found that our analysis onthe mass hierarchy gives a result similar to that in [29] whenwe work with two energy bins in the contained events (thesub-GeV and multi-GeV events) and the systematic errorswhich are slightly different from those in [29] (when we havemore than two energy bins our results would lead to too largesignificance of the wrong mass hierarchy in the case of thestandard oscillation scenario compared with the one in [29]Also in the presence of NSI our study with more than twoenergy bins would give allowed regions which are smallerthan those by the two-energy-bin analysis So we will taketwo energy bins in the energy spectrum analysis to beconservative throughout this paper) We have checked thatthe sensitivity to NSI is not affected significantly by changingthe systematic errors As for the upward going 120583 events sinceour ansatz (9) is taken in such a way that the oscillationprobability with 120598

120572120573(120572 120573 = 119890 120591) approaches to the one with

the standard scenario in the high energy limit the upward


going 120583 events are expected to give a small contribution tothe significance of NSI So in the case of the energy spectrumanalysis we will work with two energy bins in the containedevents and a single energy bin in the upward going 120583 events

31 The Case with the Standard Oscillation Scenario First ofall let us discuss the case where ldquothe experimental datardquo isthe one obtained with the standard oscillation scenario Thevalues of the oscillation parameters which are used to obtainldquothe experimental datardquo are the following (to distinguishthe oscillation parameters for the ldquothe experimental datardquo(119899119886119860119895(ℓ) (119895 = 1 10 119860 = 119871119867 119886 = 119904119898 ℓ = 119890 120583) etc)

and those for the numbers of events (119873119886119860119895(]120572rarr ]120573) (119895 =

1 10 119860 = 119871119867 119886 = 119904119898 120572 120573 = 119890 120583) etc) for fittingthe parameters with a bar denote those for ldquothe experimentaldatardquo whereas those without a bar denote the parameters forthe numbers of events for fitting)

Δ1198982

31= 25 times 10

minus3 eV2

sin212057923= 05

120575 = 0

sin2212057912= 086

sin2212057913= 01

Δ1198982

21= 76 times 10

minus5 eV2

(14)

As in the case of the analysis of the SK data we vary theoscillation parameters 120579

23 |Δ119898232| 120575 and arg(120598

119890120591) while fixing

the other oscillation parameters sin2212057912= 086 sin22120579

13=

01 and Δ119898221= 76 times 10

minus5 eV2In the energy rate analysis1205942 is the same as (10) where the

numbers of events are calculatedwith the standard oscillationscenario with 120579

119895119896 Δ1198982119895119896 and 120575 given by (14) and we have

assumed that all the systematic errors except 1205901205731198982

are thesame as those in (12) in the analysis of SK data 120590

1205731198982=

016 which is the uncertainty in the relative normalizationbetween the ] minus ] flux was chosen because this value wasused in the energy spectrum analysis on the significance ofthe wrong mass hierarchy to give the result close to that in[29] (see the discussions below)

In the spectrum analysis on the other hand 1205942sub-GeV and1205942

multi-GeV are replaced by

1205942

sub-GeV

= min12057211990412057310158401199041205741015840119904

[

[

1205732

1199041

1205902

1205731199041

+

1205732

1199042

1205902

1205731199042

+

1205742

1198711

1205902

1205741198711

+

1205742

1198712

1205902

1205741198712

+

1205742

1198671

1205902

1205741198671

+

1205742

1198672

1205902

1205741198672

+ sum

119860=119871119867

10

sum

119895=1

1

119899119904

119860119895(119890)

sdot [120572119904(1 minus

1205731199041

2

+

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]119890997888rarr ]119890)

+ 120572119904(1 +

1205731199041

2

+

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]120583997888rarr ]119890)

+ 120572119904(1 minus

1205731199041

2

minus

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]119890997888rarr ]119890)

+ 120572119904(1 +

1205731199041

2

minus

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]120583997888rarr ]119890)

minus 119899119904

119860119895(119890)]

2

+

1

119899119904

119860119895(120583)

sdot [120572119904(1 minus

1205731199041

2

+

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731199041

2

+

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]120583997888rarr ]120583)

+ 120572119904(1 minus

1205731199041

2

minus

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731199041

2

minus

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]120583997888rarr ]120583)

minus 119899119904

119860119895(120583)]

2

]

]

(15)

1205942

multi-GeV

= min12057211989812057310158401199041205741015840119904

[

[

1205732

1198981

1205902

1205731198981

+

1205732

1198982

1205902

1205731198982

+

1205742

1

1205902

1205741

+

1205742

2

1205902

1205742

+ sum

119860=119871119867

10

sum

119895=1

1

119899119898

119860119895(119890)

sdot [120572119904(1 minus

1205731198981

2

+

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]119890997888rarr ]119890)

+ 120572119904(1 +

1205731198981

2

+

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]120583997888rarr ]119890)

+ 120572119904(1 minus

1205731198981

2

minus

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]119890997888rarr ]119890)


+ 120572119904(1 +

1205731198981

2

minus

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]120583997888rarr ]119890)

minus 119899119898

119860119895(119890)]

2

+

1

119899119898

119860119895(120583)

sdot [120572119904(1 minus

1205731198981

2

+

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731198981

2

+

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]120583997888rarr ]120583)

+ 120572119904(1 minus

1205731198981

2

minus

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731198981

2

minus

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]120583997888rarr ]120583)

minus 119899119898

119860119895(120583)]

2

]

]

(16)

In (16) we have introduced the relative normalization whichin general depends on the flavor and the energy of the eventsbetween the upward and downward going bins

120574119895

11986012=

12057411986012

(119895 le 119895th 119860 = 119871119867)

minus12057411986012

(119895 gt 119895th 119860 = 119871119867)

120574119895

12=

12057412

(119895 le 119895th)

minus12057412

(119895 gt 119895th)

(17)

and 119895th = 3 is the index which separates the upward anddownward bins The indices 119871 and 119867 stand for the lower(119864 lt 119864th) and higher (119864 gt 119864th) energy bins and the thresholdenergy 119864th is chosen so that the numbers of events for thelower and higher energy bins are approximately equal and inthe case of the sub-GeV events 119864th = 05GeV and in the caseof themulti-GeV events the threshold energy is119864th =32GeVrespectively for all the zenith angle bins We have put thesystematic errors as follows

1205901205731199041

= 1205901205731198981

= 003

1205901205731199042

= 005

1205901205731198982

= 016

120590120572= 02

(18)

1205901205741198711

= 0005

1205901205741198712

= 0008

1205901205741198671

= 0021

1205901205741198672

= 0018

1205901205741= 0015

1205901205742= 0025

(19)

All the systematic errors in (18) except 1205901205731198982

and 1205901205742

are thesame as those in (12) in Section 2 and those used in [60]1205901205731198982

= 016 is the uncertainty in the relative normalizationbetween the multi-GeV ] minus ] flux and it was 005 in (12)1205901205742= 0025 is the uncertainty in the relative normalization

between the upward and downward going multi-GeV 120583-likeevents and it was 0008 in the analysis of SK data [60] Thechoice of these systematic errors (18) and (19) and the index119895th = 3 has been made so that the result of our analysis on themass hierarchy is close to that in [29] and we have checkedthat the choice of (18) and (19) and the index 119895th = 3 donot affect the sensitivity to NSI significantly Notice that wehave included the systematic uncertainty for the up-downcorrelation unlike our analysis of the Super-Kamiokandedata in Section 2 We have omitted the other systematicuncertainties such as the119864] spectral index for simplicityThesystematic error for the spectral index affects all the numbersof events for each energy universally and it is not expected toaffect the sensitivity to NSI very much

The results from the energy rate (spectrum) analysis aregiven by the upper (lower) panel in Figure 2 From the energyrate analysis we have |120598

119890120591(1 + 120598

119890119890)| ≲ 03 at 25120590CL On the

other hand from the energy spectrum analysis we get minus01 ≲120598119890119890≲ 02 and |120598

119890120591| lt 008 at 25120590 (988) CL for the normal

hierarchy and to minus04 ≲ 120598119890119890≲ 12 and |120598

119890120591| lt 034 at 25120590

(988) CL for the inverted hierarchyFrom Figure 2 we note two things Firstly the allowed

regions from the energy spectrum analysis (the lower panel)are much smaller than those from the energy rate analysis(the upper panel) for both mass hierarchies Secondly theallowed regions (the right panel) for the inverted hierarchyare wider than those (the left panel) for the normal hierarchyfor both rate and spectrum analyses

To understand these phenomena we have plotted inFigure 3 1205942multi-GeV for the multi-GeV events which areexpected to be sensitive to the matter effect and therefore to120598119890119890 as a function of 120598

119890119890in the case of 120598

119890120591= 0 In plotting

the figures in Figure 3 we have taken into account only thestatistical errors for simplicity and we assume that the HKdetector could distinguish neutrinos and antineutrinos forboth 119890-like and 120583-like events in all the energy ranges of themulti-GeV events and that the detection efficiency is thesame for both neutrinos and antineutrinos Since the SKcollaboration distinguish neutrinos and antineutrinos onlyfor the multi-GeV 119890-like events [56] our assumption heremay not be realistic and the separate plots for neutrinos or forantineutrinos except for the 119890-like events should be regardedas information for theoretical consideration The two figures


05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

2

15

|120598e120591|

1

05

0

2

15

|120598e120591|

1

05

0

03

025

|120598e120591|

02

015

01

005

0

06

05

04

|120598e120591|

03

02

01

0

minus3 minus2 minus1 0 1 2 3 4minus4

120598ee


120598ee


120598ee

minus1 minus05minus15 05 1 150120598ee

HK 4438 days rate NH HK 4438 days rate IH

HK 4438 days 2 energy bins NH HK 4438 days 2 energy bins IH

Figure 2 Upper panel the allowed region in the (120598119890119890 |120598119890120591|) plane from the HK atmospheric neutrino data for a normal mass hierarchy (left

panel) and for an inverted mass hierarchy (right panel) from the energy-rate analysis Lower panel the same allowed region as the upperpanel from the two energy-bin analysis Notice that the vertical scales in the lower panel are different for both mass hierarchies from the onein the upper panel


0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

e120583

120583e + e120583 + 120583

e

(a) Rate NH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

e120583

120583e + e120583 + 120583

e

(b) Rate IH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

Le

L120583H120583

L120583H120583

Le HeHe

(c) 2bin NH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

Le

L120583H120583

L120583H120583

Le HeHe

(d) 2bin IH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

He + e

Le + e L120583 + 120583H120583 + 120583

(e) 2bin NH combined

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

He + e

Le + e L120583 + 120583H120583 + 120583

(f) 2bin IH combined

Figure 3 The behaviors of 1205942multi-GeV for 120598119890120591= 0 as a function of 120598

119890119890 ((a) (b)) Energy rate analysis for NH (a) and IH (b) ((c) (d)) Energy

spectrum analysis for NH (d) and IH (e) for the separate neutrino or antineutrino events ((e) (f)) Energy spectrum analysis for NH (e)and IH (f) using only the combined numbers of events of ]

119890+ ]119890and ]

120583+ ]120583 In (a) (b) (c) and (d) the plots for the separate neutrino or

antineutrino events are created based on the assumption that HK could distinguish neutrinos and antineutrinos


1

2En

ergy

bin

s

2 3 4 5 6 7 8 9 101Zenith angle bins

100

50

0

minus50

minus100

(a) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ119873

120583


1

2

Ener

gy b

ins

100

50

0

minus50

minus100

(b) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ119873

120583


1

2

Ener

gy b

ins

100

50

0

minus50

minus100

(c) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ(119873

120583+ 119873120583)

Figure 4 The behaviors of the difference of the numbers of the multi-GeV 120583-like events with the standard scenario and those with NSI(120598119890119890 |120598119890120591|) = (2 0) The vertical axis stands for the energy bin (1 for the lower energy and 2 for the higher energy) and the horizontal axis is

the zenith angle bin (1 for minus10 lt cosΘ lt minus08 10 for 08 lt cosΘ lt 10) (a) The difference of the numbers of the multi-GeV ]120583-like

events (b) The difference of the numbers of the multi-GeV ]120583-like events (c) The difference of the numbers of the multi-GeV ]

120583-like and

]120583-like events

((a) and (b)) in the top row are the results of the energy rateanalysis The two figures ((c) and (d)) in the middle row arethe results of the energy spectrum analysis with two energybins for the separate neutrino or antineutrino eventsThe twofigures ((e) and (f)) in the bottom row are the results of theenergy spectrum analysis with two energy bins of neutrinosand antineutrinos combined Comparing the figures ((a) and(b)) in the top row and those ((e) and (f)) in the bottomrow we see that even if some of the data set in the spectrumanalysis have a sensitivity to the effect of 120598

119890119890 the data in the

rate analysis does not necessarily have a sensitivity to 120598119890119890

particularly for 120598119890119890gt 0 for both mass hierarchies While it

is not clear to us why the sensitivity is lost only for 120598119890119890gt 0

we have found that if we try to fit the same data with thenumbers of events with the wrong mass hierarchy then theplot becomes left-right reversed that is the sensitivity is lostonly for 120598

119890119890lt 0 On the other hand by comparing the figures

((c) and (d)) in the middle row and those ((e) and (f)) inthe bottom row we see that in the case of the inverted masshierarchy even though the separate ]

120583data has a sensitivity

to 120598119890119890 the combined data ]

120583+ ]120583loses a sensitivity We could

not explain these phenomena using the analytic expressionfor the oscillation probability but we interpret this loss ofsensitivity as a destructive phenomenon between neutrinos

and antineutrinos in the rate analysis and between the lowerand higher energy bins in the spectrum analysis for theinverted mass hierarchy

To visualize how this destructive phenomenon happensin terms of the numbers of events we have plotted in Figure 4the difference of the numbers of the multi-GeV 120583-like eventswith standard scenario and those with NSI for a typical case(120598119890119890 |120598119890120591|) = (2 0) From Figure 4 we see that each positive

and negative contribution to the difference in the ]120583events

(Figure 4(a)) is almost cancelled by negative and positivecontribution in the ]

120583events in Figure 4(b) so significance

is reduced in the combined events (Figure 4(c))Although we have not thoroughly investigated according

to our investigation for a specific case (120598119890119890= 0) this destruc-

tive phenomenon does not happen for |120598119890120591| that is distinc-

tion between neutrinos and antineutrinos does not makemuch difference on the sensitivity to |120598

119890120591| This conclusion is

consistent with the result of [44] in which the sensitivity to|120598119890120591|was studied although they took a set of assumptions dif-

ferent from ours This destructive phenomenon seems to becharacteristic to the sensitivity to 120598

119890119890because of the asymme-

try between the cases for 120598119890119890+ 1 gt 0 and for 120598

119890119890+ 1 lt 0

It is expected that the HK experiment will be able to useinformation on the energy spectrum so we believe that the


2

15

|120598e120591|

1

05

0minus3 minus2 minus1 0 1 2 3 4minus4

120598ee

(a) NH

2

15

|120598e120591|

1

05


120598ee

(b) IH

Figure 5 The allowed region at 25120590CL around the point (120598119890119890 |120598119890120591|) = (0 0) where 120575 = arg(120598

119890120591) = 0 is assumed Most of the allowed regions

are connected but those around a few points have an isolated island and they are depicted in different colors In (a) the blue curves around(120598119890119890 |120598119890120591|) = (minus2 27) and (0 27) correspond to the degenerate allowed regions for the true values of (minus2 27) the green curves around (2

27) and (2 67) are the degenerate allowed regions for the true values of (2 27) and the brown curves around (minus3 67) and (minus4 87) are thedegenerate allowed regions for the true values of (minus3 67) In (b) the blue curves around (minus2 27) and (0 27) correspond to the degenerateallowed regions for the true values of (minus2 27)The allowed regions at 120598

119890119890= plusmn3 for the normal mass hierarchy and at 120598

119890119890= 2 3 for the inverted

mass hierarchy are much wider compared with other cases so their boundary is shown with dashed lines for 120598119890119890= 3 (NH and IH) and with

dotted lines for 120598119890119890= minus3 (NH) and 120598

119890119890= 2 (IH) Also these boundary and their centers are shown in different colors purple for |120598

119890120591| = 27

light blue for |120598119890120591| = 47 brown for |120598

119890120591| = 67 green for |120598

119890120591| = 87 orange for |120598

119890120591| = 107 and grey for |120598

119890120591| = 127

allowed region in the lower panel in Figure 2 with the energyspectrum analysis reflects the true HK sensitivity more thanthat in the upper panel does

32 The Case in the Presence of NSI Next let us discussthe case where ldquothe experimental datardquo is the one obtainedwith (120598

119890119890 120598119890120591) = (0 0) The analysis is the same as the one

in Section 31 except that the ldquothe experimental datardquo isproduced assuming the presence ofNSI and here we performonly an energy spectrum analysis with two energy bins Theresults are shown in Figure 5 where the allowed regions at25120590CL (Δ1205942 = 88 for 2 degrees of freedom) around the truepoints are depicted The straight lines |120598

119890120591| = 08 times |1 + 120598

119890119890| in

Figure 5 stand for the approximate bound from the SK atmo-spheric neutrinos in Figure 1 and we have examined only thepoints below these straight lines As seen from Figure 5 theerrors in 120598

119890119890and |120598

119890120591| are small for |120598

119890119890| ≲ 2 in the case of

the normal hierarchy and for minus3 ≲ 120598119890119890≲ 1 in the case of

the inverted hierarchy The errors are large otherwise andthe reason that the errors are large is because a sensitivity islost due to a destructive phenomenon between neutrinos andantineutrinos as was discussed in Section 31

We note in passing that there are a couple of points inFigure 5 where the allowed region has an additional isolatedisland This is regarded as so-called parameter degeneracy

which is classified into the intrinsic degeneracy [61] thesign degeneracy [62] and the octant degeneracy [63 64] inthe standard three-flavor framework in the presence of theNSI Since little is known about parameter degeneracy in thepresence of the new physics and since the study of the subjectis beyond the scope of this paper we do not discuss parameterdegeneracy here

4 Conclusions

In this paper we have studied the constraint of the SK atmo-spheric neutrino data on the nonstandard flavor-dependentinteraction in neutrino propagationwith the ansatz (9) Fromthe SK atmospheric neutrino data for 4438 days we haveobtained the bound |120598

119890120591||1 + 120598

119890119890| ≲ 08 at 25120590CL while we

have little constraint on 120598119890119890

We have also discussed the sensitivity of the future HKatmospheric neutrino experiment to NSI by analyses withthe energy rate and with the energy spectrum If nature isdescribed by the standard oscillation scenario then the HKatmospheric neutrino data will give us the bound |120598

119890120591||1 +

120598119890119890| ≲ 03 at 25120590CL from the energy rate analysis and from

the energy spectrum analysis it will restrict 120598119890119890

to minus01 ≲

120598119890119890≲ 02 and |120598



119890120591| lt 034 at 25120590

(988) CL for the inverted hierarchy On the other hand


if nature is described by NSI with the ansatz (9) then HKwill measure the NSI parameters 120598

119890119890and |120598

119890120591| relatively well

for |120598119890119890| ≲ 2 in the case of the normal hierarchy and for

minus3 ≲ 120598119890119890≲ 1 in the case of the inverted hierarchy

We have shown that it is important to use information onthe energy spectrum to obtain strong constraint because asensitivity toNSIwould be lost due to destructive phenomenabetween the low and high energy events If there is a way todistinguish between neutrinos and antineutrinos as is doneby the SK collaboration [56] for the 119890-like multi-GeV eventsalso for the multi-GeV 120583-like events then the sensitivityto NSI would be greatly improved because in this case wecan avoid destructive phenomena between neutrinos andantineutrinos

Finally let us discuss some prospects for the globalanalysis with these future atmospheric results and the solarneutrino results In [35] the global analysis was performedwith all the data presently available and the conclusion wasthat the constraints from the solar and KamLAND data arestronger than those from the atmospheric and long baselineexperiments Furthermore because of the slight differencebetween the best fit values for the solar and KamLAND datain the standard scenario their result may suggest a nonzerovalue for theNSI parameter 120598119891

119863 which is a function of 120598119891

119890120572(120572 =

119890 120583 120591) 120598119891120583120572

(120572 = 119890 120583 120591) and 120598119891120591120591 Fromour results in Section 3

if the mass hierarchy is normal then we see that the errorsof the parameters 120598

119890119890and |120598

119890120591| obtained in the future Hyper-

Kamiokande experiment may be comparable to or evensmaller than the present error of 120598119891

119863 So HK may be able to

contribute to give further constraints on the 120598119891119863parameter

although more detailed study will be required to be conclu-sive

While HK is expected to play an important role inmeasurement of 120575 in the standard three-flavor scenario usingthe JPARCbeamHKhas also a potential for newphysics withatmospheric neutrinos Search for NSI may lead to physicsbeyond the Standard Model and the effects of NSI at HKdeserves further studies

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research was partly supported by a Grant-in-Aid forScientific Research of the Ministry of Education Science andCulture under Grants no 24540281 and no 25105009

References

[1] Particle Data Group ldquoReview of particle physicsrdquo ChinesePhysics C vol 38 no 9 Article ID 090001 2014

[2] K Abe H Aihara C Andreopoulos et al ldquoA long baselineneutrino oscillation experiment using J-PARC neutrino beamandhyper-kamiokanderdquo httparxivorgabs14124673

[3] C Adams D Adams T Akiri et al ldquoThe long-baseline neu-trino experiment exploring fundamental symmetries of the-universerdquo httparxivorgabs13077335

[4] Belle experiment httpbellekekjp[5] Babar experiment httpwww-publicslacstanfordedubabar[6] A Bandyopadhyay S Choubey R Gandhi et al ldquoPhysics at

a future Neutrino Factory and super-beam facilityrdquo Reports onProgress in Physics vol 72 no 10 Article ID 106201 2009

[7] L Wolfenstein ldquoNeutrino oscillations in matterrdquo PhysicalReview D vol 17 no 9 pp 2369ndash2374 1978

[8] M M Guzzo A Masiero and S T Petcov ldquoOn the MSW effectwith massless neutrinos and no mixing in the vacuumrdquo PhysicsLetters B vol 260 no 1-2 pp 154ndash160 1991

[9] E Roulet ldquoMikheyev-Smirnov-Wolfenstein effect with flavor-changing neutrino interactionsrdquo Physical Review D vol 44Article ID R935(R) 1991

[10] S P Mikheev and A Y Smirnov ldquoResonance amplificationof oscillations in matter and spectroscopy of solar neutrinosrdquoSoviet Journal of Nuclear Physics vol 42 pp 913ndash917 1985Yadernaya Fizika vol 42 p 1441 1985

[11] M C Gonzalez-Garcia M M Guzzo P I Krastev et alldquoAtmospheric neutrino observations and flavor changing inter-actionsrdquo Physical Review Letters vol 82 no 16 pp 3202ndash32051999

[12] P Lipari andM Lusignoli ldquoExotic solutions of the atmosphericneutrino problemrdquo Physical Review D vol 60 Article ID013003 1999

[13] N Fornengo M C Gonzalez-Garcia and J W F Valle ldquoOnthe interpretation of the atmospheric neutrino data in terms offlavor changing neutrino interactionsrdquo Journal of High EnergyPhysics vol 2000 no 7 article 006 2000

[14] N Fornengo M Maltoni R Tomas and J W F Valle ldquoProbingneutrino nonstandard interactions with atmospheric neutrinodatardquo Physical Review D vol 65 Article ID 013010 2002

[15] M C Gonzalez-Garcia andMMaltoni ldquoAtmospheric neutrinooscillations and new physicsrdquo Physical Review D vol 70 ArticleID 033010 2004

[16] Z Berezhiani and A Rossi ldquoLimits on the non-standard intera-ctions of neutrinos from 119890

+

119890minus collidersrdquo Physics Letters B vol

535 pp 207ndash218 2002[17] S Davidson C Pena-Garay N Rius and A Santamaria

ldquoPresent and future bounds on non-standard neutrino interac-tionsrdquo Journal of High Energy Physics vol 2003 no 3 article 0112003

[18] A Friedland C Lunardini andC Pena-Garay ldquoSolar neutrinosas probes of neutrino-matter interactionsrdquo Physics Letters B vol594 no 3-4 pp 347ndash354 2004

[19] O G Miranda M A Tortola and J W F Valle ldquoAre solar neu-trino oscillations robustrdquo Journal of High Energy Physics vol2006 no 10 article 008 2006

[20] A Palazzo and J W F Valle ldquoConfusing nonzero 12057913

withnonstandard interactions in the solar neutrino sectorrdquo PhysicalReview D vol 80 Article ID 091301 2009

[21] J Barranco O G Miranda C A Moura and J W F ValleldquoConstraining nonstandard interactions in V

119890119890 or V

119890119890 scatter-

ingrdquo Physical Review D vol 73 Article ID 113001 2006[22] J Barranco O G Miranda C A Moura and J W F Valle

ldquoConstraining nonstandard neutrino-electron interactionsrdquoPhysical Review D vol 77 no 9 Article ID 093014 10 pages2008


[23] A Bolanos O G Miranda A Palazzo M A Tortola and J WF Valle ldquoProbing nonstandard neutrino-electron interactionswith solar and reactor neutrinosrdquo Physical Review D vol 79Article ID 113012 2009

[24] F J Escrihuela O G Miranda M A Tortola and J W F ValleldquoConstraining nonstandard neutrino-quark interactions withsolar reactor and accelerator datardquo Physical Review D vol 80Article ID 105009 2009 Erratum in Physical Review D vol 80Article ID 129908 2009

[25] C Biggio M Blennow and E Fernandez-Martinez ldquoGeneralbounds on non-standard neutrino interactionsrdquo Journal of HighEnergy Physics vol 2009 no 8 article 090 2009

[26] A Friedland C Lunardini and M Maltoni ldquoAtmosphericneutrinos as probes of neutrino-matter interactionsrdquo PhysicalReview D vol 70 Article ID 111301 2004

[27] A Friedland and C Lunardini ldquoTest of tau neutrino inter-actions with atmospheric neutrinos and K2K datardquo PhysicalReview D vol 72 Article ID 053009 2005

[28] H Oki and O Yasuda ldquoSensitivity of the T2KK experiment tothe nonstandard interaction in propagationrdquo Physical ReviewDvol 82 Article ID 073009 2010

[29] K Abe T Abe H Aihara et al ldquoLetter of intent the hyper-Kamiokande experimentmdashdetector design and physics poten-tialrdquo httparxivorgabs11093262

[30] M C Gonzalez-Garcia M Maltoni and J Salvado ldquoTestingmatter effects in propagation of atmospheric and long-baselineneutrinosrdquo Journal of High Energy Physics vol 2011 no 5 article075 2011

[31] G Mitsuka K Abe Y Hayato et al ldquoStudy of nonstandardneutrino interactions with atmospheric neutrino data in Super-Kamiokande I and IIrdquo Physical Review D vol 84 Article ID113008 2011

[32] T Ohlsson H Zhang and S Zhou ldquoEffects of nonstandardneutrino interactions at PINGUrdquo Physical Review D vol 88 no1 Article ID 013001 2013

[33] A Esmaili and A Y Smirnov ldquoProbing non-standard interac-tion of neutrinos with IceCube and DeepCorerdquo Journal of HighEnergy Physics vol 2013 no 6 article 026 2013

[34] S Choubey and T Ohlsson ldquoBounds on non-standard neutrinointeractions using PINGUrdquo Physics Letters B vol 739 pp 357ndash364 2014

[35] M C Gonzalez-Garcia and M Maltoni ldquoDetermination ofmatter potential from global analysis of neutrino oscillationdatardquo Journal of High Energy Physics vol 2013 no 9 article 1522013

[36] A Friedland and C Lunardini ldquoTwo modes of searching fornew neutrino interactions at MINOSrdquo Physical Review D vol74 Article ID 033012 2006

[37] O Yasuda ldquoNew physics effects in long baseline experimentsrdquoActa Physica Polonica B vol 38 pp 3381ndash3388 2007

[38] H Sugiyama ldquoMore on non-standard interaction at MINOSrdquoAIP Conference Proceedings vol 981 article 216 2008

[39] M Blennow T Ohlsson and J Skrotzki ldquoEffects of non-standard interactions in the MINOS experimentrdquo Physics Let-ters B vol 660 no 5 pp 522ndash528 2008

[40] J A B Coelho T Kafka W A Mann J Schneps and OAltinok ldquoConstraints for nonstandard interaction 120598

119890120591119881119890from

V119890appearance in MINOS and T2Krdquo Physical Review D vol 86

Article ID 113015 2012[41] A Esteban-Pretel JW F Valle and PHuber ldquoCanOPERAhelp

in constraining neutrino non-standard interactionsrdquo PhysicsLetters B vol 668 no 3 pp 197ndash201 2008

[42] M Blennow D Meloni T Ohlsson F Terranova and MWesterberg ldquoNon-standard interactions using the OPERAexperimentrdquoThe European Physical Journal C vol 56 no 4 pp529ndash536 2008

[43] A Friedland M L Graesser I M Shoemaker and L VecchildquoProbing nonstandard standard model backgrounds with LHCmonojetsrdquo Physics Letters B vol 714 no 2ndash5 pp 267ndash275 2012

[44] A Chatterjee P Mehta D Choudhury and R Gandhi ldquoTest-ing non-standard neutrino matter interactions in atmosphericneutrinopropagationrdquo httparxivorgabs14098472

[45] J KoppM Lindner T Ota and J Sato ldquoNon-standard neutrinointeractions in reactor and superbeam experimentsrdquo PhysicalReview D vol 77 no 1 Article ID 013007 23 pages 2008

[46] N C Ribeiro H Nunokawa T Kajita S Nakayama P Ko andH Minakata ldquoProbing nonstandard neutrino physics by twoidentical detectors with different baselinesrdquo Physical Review Dvol 77 Article ID 073007 2008

[47] A Friedland and I M Shoemaker ldquoSearching for novel neu-trino interactions at NOvA and beyond in light of large 120579

13rdquo

httparxivorgabs12076642[48] A M Gago M M Guzzo H Nunokawa W J C Teves

and R Zukanovich Funchal ldquoProbing flavor changing neutrinointeractions using neutrino beams from a muon storage ringrdquoPhysical Review D vol 64 Article ID 073003 2001

[49] T Ota J Sato and N-A Yamashita ldquoOscillation enhancedsearch for new interactions with neutrinosrdquo Physical Review Dvol 65 Article ID 093015 2002

[50] M Campanelli and A Romanino ldquoEffects of new physics inneutrino oscillations in matterrdquo Physical Review D vol 66Article ID 113001 2002

[51] P Huber T Schwetz and J W F Valle ldquoHow sensitive is aneutrino factory to the angle 120579

13rdquo Physical Review Letters vol

88 Article ID 101804 2002[52] J Kopp T Ota and W Winter ldquoNeutrino factory optimization

for non-standard interactionsrdquo Physical Review D vol 78 no 5Article ID 053007 17 pages 2008

[53] N C Ribeiro H Minakata H Nunokawa S Uchinamiand R Zukanovich-Funchal ldquoProbing non-standard neutrinointeractions with neutrino factoriesrdquo Journal of High EnergyPhysics vol 2007 no 12 article 002 2007

[54] A M Gago H Minakata H Nunokawa S Uchinami andR Z Fun-chal ldquoResolving CP violation by standard and non-standard interactions and parameter degeneracy in neutrinooscillationsrdquo Journal of High Energy Physics vol 2010 no 1article 49 2010

[55] D Meloni T Ohlsson W Winter and H Zhang ldquoNon-standard interactions versus non-unitary lepton flavor mixingat a neutrino factoryrdquo Journal of High Energy Physics vol 2010no 4 article 041 2010

[56] K Abe Y Haga Y Hayato et al ldquoLimits on sterile neutrinomixing using atmospheric neutrinos in Super-KamiokanderdquoPhysical Review D vol 91 no 5 Article ID 052019 22 pages2008

[57] R Foot R R Volkas and O Yasuda ldquoComparing and contrast-ing the ]

120583rarr ]120591and ]

120583rarr ]119904solutions to the atmospheric

neutrino problem with SuperKamiokande datardquo PhysicalReview D vol 58 Article ID 013006 1998

[58] O Yasuda ldquoThree flavor neutrino oscillation analysis of theSuperKamiokande atmospheric neutrino datardquo Physical ReviewD vol 58 Article ID 091301 1998


[59] O Yasuda ldquoFour neutrino oscillation analysis of the Superka-miokande atmospheric neutrinodatardquo httparxivorgabshep-ph0006319

[60] Y Ashie J Hosaka K Ishihara et al ldquoMeasurement of atmo-spheric neutrino oscillation parameters by Super-KamiokandeIrdquo Physical Review D vol 71 Article ID 112005 2005

[61] J Burguet-Castell M B Gavela J J Gomez Cadenas PHernandez and O Mena ldquoOn the measurement of leptonicCP violationrdquo Nuclear Physics B vol 608 no 1-2 Article ID0103258 pp 301ndash318 2001

[62] H Minakata and H Nunokawa ldquoExploring neutrino mixingwith low energy superbeamsrdquo Journal of High Energy Physicsvol 2001 no 10 article 001 2001

[63] G L Fogli and E Lisi ldquoTests of three-flavor mixing in long-baseline neutrino oscillation experimentsrdquo Physical Review Dvol 54 no 5 pp 3667ndash3670 1996

[64] V Barger D Marfatia and K Whisnant ldquoBreaking eightfolddegeneracies in neutrino CP violation mixing and masshierarchyrdquo Physical Review D vol 65 Article ID 073023 2002

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


FluidsJournal of

Atomic and Molecular Physics

Journal of



Advances in Condensed Matter Physics

OpticsInternational Journal of



AstronomyAdvances in

International Journal of


Superconductivity


Statistical MechanicsInternational Journal of


GravityJournal of


AstrophysicsJournal of


Physics Research International


Solid State PhysicsJournal of

Computational Methods in Physics

Journal of



Soft MatterJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

AerodynamicsJournal of

Volume 2014


PhotonicsJournal of


Journal of

Biophysics


ThermodynamicsJournal of


where 119860 equiv radic2119866119865119873119890stands for the matter effect due to the

charged current interaction in the standard case With thismatter potential the Dirac equation for neutrinos in matterbecomes

119894

119889

119889119909

(

]119890(119909)

]120583(119909)

]120591(119909)

)

= [119880diag (0 Δ11986421 Δ11986431) 119880minus1

+A](

]119890(119909)

]120583(119909)

]120591(119909)

)

(3)

where 119880 is the leptonic mixing matrix defined by

119880

equiv (

1198881211988813

1199041211988813

11990413119890minus119894120575

minus1199041211988823minus 119888121199042311990413119890119894120575

1198881211988823minus 119904121199042311990413119890119894120575

1199042311988813

1199041211990423minus 119888121198882311990413119890119894120575

minus1198881211990423minus 119904121198882311990413119890119894120575

1198882311988813

)

(4)

and Δ119864119895119896equiv Δ119898

2

1198951198962119864 equiv (119898

2

119895minus 1198982

119896)2119864 119888

119895119896equiv cos120579

119895119896 and

119904119895119896equiv sin120579

119895119896

Constraints on 120598120572120573

have been discussed by many authorsfrom atmospheric neutrinos [11ndash15] from 119890

+

119890minus colliders [16]

from the compilation of various neutrino data [17] from solarneutrinos [18ndash20] from ]

119890119890 or ]

119890119890 scatterings [21 22] from

solar and reactor neutrinos [23] and from solar reactor andaccelerator neutrinos [24] Since the coefficients 120598

120572120573in (2) are

given by 120598120572120573sim 120598119890

120572120573+3120598119906

120572120573+3120598119889

120572120573 considering the constraints in

these references we have the following limits [25] at 90CL

(

1003816100381610038161003816120598119890119890

1003816100381610038161003816lt 4 times 10

010038161003816100381610038161003816120598119890120583

10038161003816100381610038161003816lt 3 times 10

minus1 1003816100381610038161003816120598119890120591

1003816100381610038161003816lt 3 times 10

0

10038161003816100381610038161003816120598120583120583

10038161003816100381610038161003816lt 7 times 10

minus210038161003816100381610038161003816120598120583120591

10038161003816100381610038161003816lt 3 times 10

minus1

1003816100381610038161003816120598120591120591

1003816100381610038161003816lt 2 times 10

1

) (5)

From (5) we observe that the bounds on 120598119890119890 120598119890120591 and 120598

120591120591are

much weaker than those on 120598120572120583(120572 = 119890 120583 120591)

On the other hand the nonstandard interaction (NSI)with components 120598

120572120573(120572 120573 = 119890 120591)must be consistent with the

high-energy atmospheric neutrino data It was pointed out in[26 27] that the relation

1003816100381610038161003816120598119890120591

1003816100381610038161003816

2

≃ 120598120591120591(1 + 120598

119890119890) (6)

should hold for the matter potential (2) to be consistent withthe high-energy atmospheric neutrino data which suggestthe behavior of the disappearance oscillation probability

1 minus 119875 (]120583997888rarr ]120583) sim sin22120579atmsin

2

(

Δ1198982

atm119871

4119864

) prop

1

1198642 (7)

where sin22120579atm and Δ1198982atm are the oscillation parameters inthe two-flavor formalism In [28] it was shown that in thehigh-energy behavior of the disappearance oscillation prob-ability

1 minus 119875 (]120583997888rarr ]120583) ≃ 1198880+

1198881

119864

+ O(1

1198642) (8)

in the presence of the matter potential (2) |1198880| ≪ 1 and |119888

1| ≪

1 imply 120598119890120583≃ 120598120583120583≃ 120598120583120591≃ 0 and 120598

120591120591≃ |120598119890120591|2

(1 + 120598119890119890)

Taking into account the various constraints describedabove in the present paper we take the ansatz

A = 119860(

1 + 120598119890119890

0 120598119890120591

0 0 0

120598lowast

1198901205910

1003816100381610038161003816120598119890120591

1003816100381610038161003816

2

(1 + 120598119890119890)

) (9)

and analyze the sensitivity to the parameters 120598120572120573(120572 120573 =

119890 120591) of the atmospheric neutrino experiment at Super-Kamiokande and the futureHyper-Kamiokande (HK) facility[29] (as far as 120598

120591120591is concerned the ansatz (9) is believed to be

the best fit of the high energy atmospheric neutrino data atpresent So as long as the true value of 120598

120591120591satisfies the relation

(6) even if we analyze the data assuming that 120598120591120591

is a freeparameter the allowed region in (120598

119890119890 |120598119890120591|) and the sensitivity

to NSI are not expected to change very much because theregion of 120598

120591120591 which does not satisfy (6) gets an additional

contribution of 1205942 and is not supposed to contribute toenlarge the allowed region or to increase the sensitivity toNSI)

The constraints on 120598119890119890and 120598119890120591from the atmospheric neu-

trino have been discussed in [30] along with those from thelong-baseline experiments in [31] by the Super-KamiokandeCollaboration in [32ndash34] on the future extension of theIceCube experiment and in [35] in the global analysis withthe ansatz different from ours

The sensitivity of the ongoing accelerator experiments tothe nonstandard interaction in propagation was studied byvarious authorsThe constraints have been obtained from theMINOS experiment in [36] from the MINOS data using thesame ansatz as the present paper in [37 38] from theMINOSdata from the viewpoint of degeneracy of 120579

13and NSI in [39]

from ]119890appearance in MINOS and T2K in [40] from the

OPERA experiment in [41 42] and from the LHC experi-ment in [43] As for the future long-baseline experiments thesensitivity of the INO experiment was discussed in [44] thatof the reactor and superbeam experiments was discussed in[45] that of the T2KK experiment was studied in [28 46]and that of the LBNE experiment was discussed in [43 47]The sensitivity of neutrino factories [6] was studied invarious contexts the sensitivity toNSI [48ndash50] the confusionwith the effect of 120579

13[51] the optimization [52] resolving

degeneracy with two baselines [53 54] and the relation withnonunitary mixing [55]

The paper is organized as follows In Section 2 we analyzethe SK atmospheric neutrino data and give the constraints onthe parameters 120598

120572120573(120572 120573 = 119890 120591) from the SK atmospheric

neutrino data In Section 3 we discuss the sensitivity to120598120572120573(120572 120573 = 119890 120591) of the future Hyper-Kamiokande atmo-

spheric neutrino experiment In Section 4 we draw ourconclusions



and |120598119890120591|


119890119890 |120598119890120591| and arg(120598

119890120591)




1205942

= min12057923|Δ1198982

32|120575arg(120598

119890120591)

(1205942

sub-GeV + 1205942

multi-GeV + 1205942

upward) (10)


1205942

sub-GeV = min1205721199041205731015840119904

[

[

1205732

1199041

1205902

1205731199041

+

1205732

1199042

1205902

1205731199042

+

10

sum

119895=1

1

119899119904

119895(119890)

[120572119904(1 minus

1205731199041

2

+

1205731199042

2

)119873119904

119895(]119890997888rarr ]119890) + 120572119904(1 +

1205731199041

2

+

1205731199042

2

)119873119904

119895(]120583997888rarr ]119890) + 120572119904(1 minus

1205731199041

2

minus

1205731199042

2

)119873119904

119895(]119890997888rarr ]119890) + 120572119904(1 +

1205731199041

2

minus

1205731199042

2

)119873119904

119895(]120583997888rarr ]119890) minus 119899119904

119895(119890)]

2

+

1

119899119904

119895(120583)

[120572119904(1 minus

1205731199041

2

+

1205731199042

2

)119873119904

119895(]119890997888rarr ]120583) + 120572119904(1 +

1205731199041

2

+

1205731199042

2

)119873119904

119895(]120583997888rarr ]120583) + 120572119904(1 minus

1205731199041

2

minus

1205731199042

2

)119873119904

119895(]119890997888rarr ]120583) + 120572119904(1 +

1205731199041

2

minus

1205731199042

2

)119873119904

119895(]120583997888rarr ]120583) minus 119899119904

119895(120583)]

2

]

]

1205942

multi-GeV = min1205721198981205731015840119904

[

[

1205732

1198981

1205902

1205731198981

+

1205732

1198982

1205902

1205731198982

+

10

sum

119895=1

1

119899119898

119895(119890)

[120572119904(1 minus

1205731198981

2

+

1205731198982

2

)119873119898

119895(]119890997888rarr ]119890) + 120572119904(1 +

1205731198981

2

+

1205731198982

2

)119873119898

119895(]120583997888rarr ]119890) + 120572119904(1 minus

1205731198981

2

minus

1205731198982

2

)119873119898

119895(]119890997888rarr ]119890) + 120572119904(1 +

1205731198981

2

minus

1205731198982

2

)119873119898

119895(]120583997888rarr ]119890) minus 119899119898

119895(119890)]

2

+

1

119899119898

119895(120583)

[120572119904(1 minus

1205731198981

2

+

1205731198982

2

)119873119898

119895(]119890997888rarr ]120583) + 120572119904(1 +

1205731198981

2

+

1205731198982

2

)119873119898

119895(]120583997888rarr ]120583) + 120572119904(1 minus

1205731198981

2

minus

1205731198982

2

)119873119898

119895(]119890997888rarr ]120583) + 120572119904(1 +

1205731198981

2

minus

1205731198982

2

)119873119898

119895(]120583997888rarr ]120583) minus 119899119898

119895(120583)]

2

]

]

1205942

upward = min120572119906

1205722

119906

1205902

120572

+

10

sum

119895=1

1

119899119906

119895(120583)

[120572119906119873119906

119895(]119890997888rarr ]120583) + 120572119906119873119906

119895(]120583997888rarr ]120583) + 120572119906119873119906

119895(]119890997888rarr ]120583) + 120572119906119873119906

119895(]120583997888rarr ]120583) minus 119899119906

119895(120583)]

2

(11)




119895(]120572rarr ]120573) (119873119886119895(]120572rarr




120573(]120573)




120572rarr ]120573))

the flux 119865(]120572) (119865(]




1198861




119904 120573119904119896(119896 = 1 2) 120572

119898 120573119898119896


1205901205731199041

= 1205901205731198981

= 003

1205901205731199042

= 1205901205731198982

= 005

120590120572= 02

(12)





23 the mass





12= 086 sin22120579

13= 01 and Δ1198982

21= 76 times 10






119890119890 |120598119890120591|) = (0 0) and this



05120590

1120590

15120590

2120590

25120590

3120590


2

15

|120598e120591|

1

05

0

(a) SK 4438 days NH

05120590

1120590

15120590

2120590

25120590

3120590


120598ee

0 1 2 3 4

2

15

|120598e120591|

1

05

0

(b) SK 4438 days IH






119890120591||1 + 120598



1003816100381610038161003816tan120573100381610038161003816

1003816equiv

1003816100381610038161003816120598119890120591

1003816100381610038161003816

10038161003816100381610038161 + 120598119890119890

1003816100381610038161003816

≲ 08 at 25120590CL (13)


and |120598119890120591|




119890119890and 120598












Δ1198982

31= 25 times 10

minus3 eV2

sin212057923= 05

120575 = 0

sin2212057912= 086

sin2212057913= 01

Δ1198982

21= 76 times 10

minus5 eV2

(14)


23 |Δ119898232| 120575 and arg(120598



13=

01 and Δ119898221= 76 times 10






1205731198982=




1205942

sub-GeV

= min12057211990412057310158401199041205741015840119904

[

[

1205732

1199041

1205902

1205731199041

+

1205732

1199042

1205902

1205731199042

+

1205742

1198711

1205902

1205741198711

+

1205742

1198712

1205902

1205741198712

+

1205742

1198671

1205902

1205741198671

+

1205742

1198672

1205902

1205741198672

+ sum

119860=119871119867

10

sum

119895=1

1

119899119904

119860119895(119890)

sdot [120572119904(1 minus

1205731199041

2

+

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]119890997888rarr ]119890)

+ 120572119904(1 +

1205731199041

2

+

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]120583997888rarr ]119890)

+ 120572119904(1 minus

1205731199041

2

minus

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]119890997888rarr ]119890)

+ 120572119904(1 +

1205731199041

2

minus

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]120583997888rarr ]119890)

minus 119899119904

119860119895(119890)]

2

+

1

119899119904

119860119895(120583)

sdot [120572119904(1 minus

1205731199041

2

+

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731199041

2

+

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]120583997888rarr ]120583)

+ 120572119904(1 minus

1205731199041

2

minus

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731199041

2

minus

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]120583997888rarr ]120583)

minus 119899119904

119860119895(120583)]

2

]

]

(15)

1205942

multi-GeV

= min12057211989812057310158401199041205741015840119904

[

[

1205732

1198981

1205902

1205731198981

+

1205732

1198982

1205902

1205731198982

+

1205742

1

1205902

1205741

+

1205742

2

1205902

1205742

+ sum

119860=119871119867

10

sum

119895=1

1

119899119898

119860119895(119890)

sdot [120572119904(1 minus

1205731198981

2

+

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]119890997888rarr ]119890)

+ 120572119904(1 +

1205731198981

2

+

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]120583997888rarr ]119890)

+ 120572119904(1 minus

1205731198981

2

minus

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]119890997888rarr ]119890)


+ 120572119904(1 +

1205731198981

2

minus

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]120583997888rarr ]119890)

minus 119899119898

119860119895(119890)]

2

+

1

119899119898

119860119895(120583)

sdot [120572119904(1 minus

1205731198981

2

+

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731198981

2

+

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]120583997888rarr ]120583)

+ 120572119904(1 minus

1205731198981

2

minus

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731198981

2

minus

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]120583997888rarr ]120583)

minus 119899119898

119860119895(120583)]

2

]

]

(16)


120574119895

11986012=

12057411986012

(119895 le 119895th 119860 = 119871119867)

minus12057411986012

(119895 gt 119895th 119860 = 119871119867)

120574119895

12=

12057412

(119895 le 119895th)

minus12057412

(119895 gt 119895th)

(17)


1205901205731199041

= 1205901205731198981

= 003

1205901205731199042

= 005

1205901205731198982

= 016

120590120572= 02

(18)

1205901205741198711

= 0005

1205901205741198712

= 0008

1205901205741198671

= 0021

1205901205741198672

= 0018

1205901205741= 0015

1205901205742= 0025

(19)


and 1205901205742





119890120591(1 + 120598

119890119890)| ≲ 03 at 25120590CL On the




119890120591| lt 034 at 25120590




119890119890in the case of 120598

119890120591= 0 In plotting



05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

2

15

|120598e120591|

1

05

0

2

15

|120598e120591|

1

05

0

03

025

|120598e120591|

02

015

01

005

0

06

05

04

|120598e120591|

03

02

01

0


120598ee


120598ee


120598ee







0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

e120583

120583e + e120583 + 120583

e

(a) Rate NH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

e120583

120583e + e120583 + 120583

e

(b) Rate IH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

Le

L120583H120583

L120583H120583

Le HeHe

(c) 2bin NH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

Le

L120583H120583

L120583H120583

Le HeHe

(d) 2bin IH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

He + e

Le + e L120583 + 120583H120583 + 120583


0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

He + e

Le + e L120583 + 120583H120583 + 120583





119890+ ]119890and ]




1

2En

ergy

bin

s


100

50

0

minus50

minus100

(a) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ119873

120583


1

2

Ener

gy b

ins

100

50

0

minus50

minus100

(b) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ119873

120583


1

2

Ener

gy b

ins

100

50

0

minus50

minus100

(c) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ(119873

120583+ 119873120583)




120583-like and

]120583-like events



























119890119890+ 1 lt 0



2

15

|120598e120591|

1

05


120598ee

(a) NH

2

15

|120598e120591|

1

05


120598ee

(b) IH










119890120591| = 27


119890120591| = 67 green for |120598

119890120591| = 87 orange for |120598

119890120591| = 107 and grey for |120598

119890120591| = 127





119890120591| = 08 times |1 + 120598

119890119890| in


119890119890and |120598

119890120591| are small for |120598

119890119890| ≲ 2 in the case of





4 Conclusions


119890120591||1 + 120598

119890119890| ≲ 08 at 25120590CL while we



119890120591||1 +



to minus01 ≲

120598119890119890≲ 02 and |120598



119890120591| lt 034 at 25120590




119890119890and |120598







119890120572(120572 =

119890 120583 120591) 120598119891120583120572



119890119890and |120598









Acknowledgment


References
















+









119890119890 or V

119890119890 scatter-






















119890120591119881119890from










13rdquo














120583rarr ]120591and ]
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics





and |120598119890120591|


119890119890 |120598119890120591| and arg(120598

119890120591)




1205942

= min12057923|Δ1198982

32|120575arg(120598

119890120591)

(1205942

sub-GeV + 1205942

multi-GeV + 1205942

upward) (10)


1205942

sub-GeV = min1205721199041205731015840119904

[

[

1205732

1199041

1205902

1205731199041

+

1205732

1199042

1205902

1205731199042

+

10

sum

119895=1

1

119899119904

119895(119890)

[120572119904(1 minus

1205731199041

2

+

1205731199042

2

)119873119904

119895(]119890997888rarr ]119890) + 120572119904(1 +

1205731199041

2

+

1205731199042

2

)119873119904

119895(]120583997888rarr ]119890) + 120572119904(1 minus

1205731199041

2

minus

1205731199042

2

)119873119904

119895(]119890997888rarr ]119890) + 120572119904(1 +

1205731199041

2

minus

1205731199042

2

)119873119904

119895(]120583997888rarr ]119890) minus 119899119904

119895(119890)]

2

+

1

119899119904

119895(120583)

[120572119904(1 minus

1205731199041

2

+

1205731199042

2

)119873119904

119895(]119890997888rarr ]120583) + 120572119904(1 +

1205731199041

2

+

1205731199042

2

)119873119904

119895(]120583997888rarr ]120583) + 120572119904(1 minus

1205731199041

2

minus

1205731199042

2

)119873119904

119895(]119890997888rarr ]120583) + 120572119904(1 +

1205731199041

2

minus

1205731199042

2

)119873119904

119895(]120583997888rarr ]120583) minus 119899119904

119895(120583)]

2

]

]

1205942

multi-GeV = min1205721198981205731015840119904

[

[

1205732

1198981

1205902

1205731198981

+

1205732

1198982

1205902

1205731198982

+

10

sum

119895=1

1

119899119898

119895(119890)

[120572119904(1 minus

1205731198981

2

+

1205731198982

2

)119873119898

119895(]119890997888rarr ]119890) + 120572119904(1 +

1205731198981

2

+

1205731198982

2

)119873119898

119895(]120583997888rarr ]119890) + 120572119904(1 minus

1205731198981

2

minus

1205731198982

2

)119873119898

119895(]119890997888rarr ]119890) + 120572119904(1 +

1205731198981

2

minus

1205731198982

2

)119873119898

119895(]120583997888rarr ]119890) minus 119899119898

119895(119890)]

2

+

1

119899119898

119895(120583)

[120572119904(1 minus

1205731198981

2

+

1205731198982

2

)119873119898

119895(]119890997888rarr ]120583) + 120572119904(1 +

1205731198981

2

+

1205731198982

2

)119873119898

119895(]120583997888rarr ]120583) + 120572119904(1 minus

1205731198981

2

minus

1205731198982

2

)119873119898

119895(]119890997888rarr ]120583) + 120572119904(1 +

1205731198981

2

minus

1205731198982

2

)119873119898

119895(]120583997888rarr ]120583) minus 119899119898

119895(120583)]

2

]

]

1205942

upward = min120572119906

1205722

119906

1205902

120572

+

10

sum

119895=1

1

119899119906

119895(120583)

[120572119906119873119906

119895(]119890997888rarr ]120583) + 120572119906119873119906

119895(]120583997888rarr ]120583) + 120572119906119873119906

119895(]119890997888rarr ]120583) + 120572119906119873119906

119895(]120583997888rarr ]120583) minus 119899119906

119895(120583)]

2

(11)




119895(]120572rarr ]120573) (119873119886119895(]120572rarr




120573(]120573)




120572rarr ]120573))

the flux 119865(]120572) (119865(]




1198861




119904 120573119904119896(119896 = 1 2) 120572

119898 120573119898119896


1205901205731199041

= 1205901205731198981

= 003

1205901205731199042

= 1205901205731198982

= 005

120590120572= 02

(12)





23 the mass





12= 086 sin22120579

13= 01 and Δ1198982

21= 76 times 10






119890119890 |120598119890120591|) = (0 0) and this



05120590

1120590

15120590

2120590

25120590

3120590


2

15

|120598e120591|

1

05

0

(a) SK 4438 days NH

05120590

1120590

15120590

2120590

25120590

3120590


120598ee

0 1 2 3 4

2

15

|120598e120591|

1

05

0

(b) SK 4438 days IH






119890120591||1 + 120598



1003816100381610038161003816tan120573100381610038161003816

1003816equiv

1003816100381610038161003816120598119890120591

1003816100381610038161003816

10038161003816100381610038161 + 120598119890119890

1003816100381610038161003816

≲ 08 at 25120590CL (13)


and |120598119890120591|




119890119890and 120598












Δ1198982

31= 25 times 10

minus3 eV2

sin212057923= 05

120575 = 0

sin2212057912= 086

sin2212057913= 01

Δ1198982

21= 76 times 10

minus5 eV2

(14)


23 |Δ119898232| 120575 and arg(120598



13=

01 and Δ119898221= 76 times 10






1205731198982=




1205942

sub-GeV

= min12057211990412057310158401199041205741015840119904

[

[

1205732

1199041

1205902

1205731199041

+

1205732

1199042

1205902

1205731199042

+

1205742

1198711

1205902

1205741198711

+

1205742

1198712

1205902

1205741198712

+

1205742

1198671

1205902

1205741198671

+

1205742

1198672

1205902

1205741198672

+ sum

119860=119871119867

10

sum

119895=1

1

119899119904

119860119895(119890)

sdot [120572119904(1 minus

1205731199041

2

+

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]119890997888rarr ]119890)

+ 120572119904(1 +

1205731199041

2

+

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]120583997888rarr ]119890)

+ 120572119904(1 minus

1205731199041

2

minus

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]119890997888rarr ]119890)

+ 120572119904(1 +

1205731199041

2

minus

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]120583997888rarr ]119890)

minus 119899119904

119860119895(119890)]

2

+

1

119899119904

119860119895(120583)

sdot [120572119904(1 minus

1205731199041

2

+

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731199041

2

+

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]120583997888rarr ]120583)

+ 120572119904(1 minus

1205731199041

2

minus

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731199041

2

minus

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]120583997888rarr ]120583)

minus 119899119904

119860119895(120583)]

2

]

]

(15)

1205942

multi-GeV

= min12057211989812057310158401199041205741015840119904

[

[

1205732

1198981

1205902

1205731198981

+

1205732

1198982

1205902

1205731198982

+

1205742

1

1205902

1205741

+

1205742

2

1205902

1205742

+ sum

119860=119871119867

10

sum

119895=1

1

119899119898

119860119895(119890)

sdot [120572119904(1 minus

1205731198981

2

+

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]119890997888rarr ]119890)

+ 120572119904(1 +

1205731198981

2

+

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]120583997888rarr ]119890)

+ 120572119904(1 minus

1205731198981

2

minus

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]119890997888rarr ]119890)


+ 120572119904(1 +

1205731198981

2

minus

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]120583997888rarr ]119890)

minus 119899119898

119860119895(119890)]

2

+

1

119899119898

119860119895(120583)

sdot [120572119904(1 minus

1205731198981

2

+

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731198981

2

+

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]120583997888rarr ]120583)

+ 120572119904(1 minus

1205731198981

2

minus

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731198981

2

minus

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]120583997888rarr ]120583)

minus 119899119898

119860119895(120583)]

2

]

]

(16)


120574119895

11986012=

12057411986012

(119895 le 119895th 119860 = 119871119867)

minus12057411986012

(119895 gt 119895th 119860 = 119871119867)

120574119895

12=

12057412

(119895 le 119895th)

minus12057412

(119895 gt 119895th)

(17)


1205901205731199041

= 1205901205731198981

= 003

1205901205731199042

= 005

1205901205731198982

= 016

120590120572= 02

(18)

1205901205741198711

= 0005

1205901205741198712

= 0008

1205901205741198671

= 0021

1205901205741198672

= 0018

1205901205741= 0015

1205901205742= 0025

(19)


and 1205901205742





119890120591(1 + 120598

119890119890)| ≲ 03 at 25120590CL On the




119890120591| lt 034 at 25120590




119890119890in the case of 120598

119890120591= 0 In plotting



05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

2

15

|120598e120591|

1

05

0

2

15

|120598e120591|

1

05

0

03

025

|120598e120591|

02

015

01

005

0

06

05

04

|120598e120591|

03

02

01

0


120598ee


120598ee


120598ee







0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

e120583

120583e + e120583 + 120583

e

(a) Rate NH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

e120583

120583e + e120583 + 120583

e

(b) Rate IH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

Le

L120583H120583

L120583H120583

Le HeHe

(c) 2bin NH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

Le

L120583H120583

L120583H120583

Le HeHe

(d) 2bin IH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

He + e

Le + e L120583 + 120583H120583 + 120583


0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

He + e

Le + e L120583 + 120583H120583 + 120583





119890+ ]119890and ]




1

2En

ergy

bin

s


100

50

0

minus50

minus100

(a) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ119873

120583


1

2

Ener

gy b

ins

100

50

0

minus50

minus100

(b) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ119873

120583


1

2

Ener

gy b

ins

100

50

0

minus50

minus100

(c) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ(119873

120583+ 119873120583)




120583-like and

]120583-like events



























119890119890+ 1 lt 0



2

15

|120598e120591|

1

05


120598ee

(a) NH

2

15

|120598e120591|

1

05


120598ee

(b) IH










119890120591| = 27


119890120591| = 67 green for |120598

119890120591| = 87 orange for |120598

119890120591| = 107 and grey for |120598

119890120591| = 127





119890120591| = 08 times |1 + 120598

119890119890| in


119890119890and |120598

119890120591| are small for |120598

119890119890| ≲ 2 in the case of





4 Conclusions


119890120591||1 + 120598

119890119890| ≲ 08 at 25120590CL while we



119890120591||1 +



to minus01 ≲

120598119890119890≲ 02 and |120598



119890120591| lt 034 at 25120590




119890119890and |120598







119890120572(120572 =

119890 120583 120591) 120598119891120583120572



119890119890and |120598









Acknowledgment


References
















+









119890119890 or V

119890119890 scatter-






















119890120591119881119890from










13rdquo














120583rarr ]120591and ]
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




05120590

1120590

15120590

2120590

25120590

3120590


2

15

|120598e120591|

1

05

0

(a) SK 4438 days NH

05120590

1120590

15120590

2120590

25120590

3120590


120598ee

0 1 2 3 4

2

15

|120598e120591|

1

05

0

(b) SK 4438 days IH






119890120591||1 + 120598



1003816100381610038161003816tan120573100381610038161003816

1003816equiv

1003816100381610038161003816120598119890120591

1003816100381610038161003816

10038161003816100381610038161 + 120598119890119890

1003816100381610038161003816

≲ 08 at 25120590CL (13)


and |120598119890120591|




119890119890and 120598












Δ1198982

31= 25 times 10

minus3 eV2

sin212057923= 05

120575 = 0

sin2212057912= 086

sin2212057913= 01

Δ1198982

21= 76 times 10

minus5 eV2

(14)


23 |Δ119898232| 120575 and arg(120598



13=

01 and Δ119898221= 76 times 10






1205731198982=




1205942

sub-GeV

= min12057211990412057310158401199041205741015840119904

[

[

1205732

1199041

1205902

1205731199041

+

1205732

1199042

1205902

1205731199042

+

1205742

1198711

1205902

1205741198711

+

1205742

1198712

1205902

1205741198712

+

1205742

1198671

1205902

1205741198671

+

1205742

1198672

1205902

1205741198672

+ sum

119860=119871119867

10

sum

119895=1

1

119899119904

119860119895(119890)

sdot [120572119904(1 minus

1205731199041

2

+

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]119890997888rarr ]119890)

+ 120572119904(1 +

1205731199041

2

+

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]120583997888rarr ]119890)

+ 120572119904(1 minus

1205731199041

2

minus

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]119890997888rarr ]119890)

+ 120572119904(1 +

1205731199041

2

minus

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]120583997888rarr ]119890)

minus 119899119904

119860119895(119890)]

2

+

1

119899119904

119860119895(120583)

sdot [120572119904(1 minus

1205731199041

2

+

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731199041

2

+

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]120583997888rarr ]120583)

+ 120572119904(1 minus

1205731199041

2

minus

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731199041

2

minus

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]120583997888rarr ]120583)

minus 119899119904

119860119895(120583)]

2

]

]

(15)

1205942

multi-GeV

= min12057211989812057310158401199041205741015840119904

[

[

1205732

1198981

1205902

1205731198981

+

1205732

1198982

1205902

1205731198982

+

1205742

1

1205902

1205741

+

1205742

2

1205902

1205742

+ sum

119860=119871119867

10

sum

119895=1

1

119899119898

119860119895(119890)

sdot [120572119904(1 minus

1205731198981

2

+

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]119890997888rarr ]119890)

+ 120572119904(1 +

1205731198981

2

+

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]120583997888rarr ]119890)

+ 120572119904(1 minus

1205731198981

2

minus

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]119890997888rarr ]119890)


+ 120572119904(1 +

1205731198981

2

minus

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]120583997888rarr ]119890)

minus 119899119898

119860119895(119890)]

2

+

1

119899119898

119860119895(120583)

sdot [120572119904(1 minus

1205731198981

2

+

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731198981

2

+

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]120583997888rarr ]120583)

+ 120572119904(1 minus

1205731198981

2

minus

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731198981

2

minus

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]120583997888rarr ]120583)

minus 119899119898

119860119895(120583)]

2

]

]

(16)


120574119895

11986012=

12057411986012

(119895 le 119895th 119860 = 119871119867)

minus12057411986012

(119895 gt 119895th 119860 = 119871119867)

120574119895

12=

12057412

(119895 le 119895th)

minus12057412

(119895 gt 119895th)

(17)


1205901205731199041

= 1205901205731198981

= 003

1205901205731199042

= 005

1205901205731198982

= 016

120590120572= 02

(18)

1205901205741198711

= 0005

1205901205741198712

= 0008

1205901205741198671

= 0021

1205901205741198672

= 0018

1205901205741= 0015

1205901205742= 0025

(19)


and 1205901205742





119890120591(1 + 120598

119890119890)| ≲ 03 at 25120590CL On the




119890120591| lt 034 at 25120590




119890119890in the case of 120598

119890120591= 0 In plotting



05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

2

15

|120598e120591|

1

05

0

2

15

|120598e120591|

1

05

0

03

025

|120598e120591|

02

015

01

005

0

06

05

04

|120598e120591|

03

02

01

0


120598ee


120598ee


120598ee







0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

e120583

120583e + e120583 + 120583

e

(a) Rate NH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

e120583

120583e + e120583 + 120583

e

(b) Rate IH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

Le

L120583H120583

L120583H120583

Le HeHe

(c) 2bin NH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

Le

L120583H120583

L120583H120583

Le HeHe

(d) 2bin IH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

He + e

Le + e L120583 + 120583H120583 + 120583


0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

He + e

Le + e L120583 + 120583H120583 + 120583





119890+ ]119890and ]




1

2En

ergy

bin

s


100

50

0

minus50

minus100

(a) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ119873

120583


1

2

Ener

gy b

ins

100

50

0

minus50

minus100

(b) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ119873

120583


1

2

Ener

gy b

ins

100

50

0

minus50

minus100

(c) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ(119873

120583+ 119873120583)




120583-like and

]120583-like events



























119890119890+ 1 lt 0



2

15

|120598e120591|

1

05


120598ee

(a) NH

2

15

|120598e120591|

1

05


120598ee

(b) IH










119890120591| = 27


119890120591| = 67 green for |120598

119890120591| = 87 orange for |120598

119890120591| = 107 and grey for |120598

119890120591| = 127





119890120591| = 08 times |1 + 120598

119890119890| in


119890119890and |120598

119890120591| are small for |120598

119890119890| ≲ 2 in the case of





4 Conclusions


119890120591||1 + 120598

119890119890| ≲ 08 at 25120590CL while we



119890120591||1 +



to minus01 ≲

120598119890119890≲ 02 and |120598



119890120591| lt 034 at 25120590




119890119890and |120598







119890120572(120572 =

119890 120583 120591) 120598119891120583120572



119890119890and |120598









Acknowledgment


References
















+









119890119890 or V

119890119890 scatter-






















119890120591119881119890from










13rdquo














120583rarr ]120591and ]
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics








Δ1198982

31= 25 times 10

minus3 eV2

sin212057923= 05

120575 = 0

sin2212057912= 086

sin2212057913= 01

Δ1198982

21= 76 times 10

minus5 eV2

(14)


23 |Δ119898232| 120575 and arg(120598



13=

01 and Δ119898221= 76 times 10






1205731198982=




1205942

sub-GeV

= min12057211990412057310158401199041205741015840119904

[

[

1205732

1199041

1205902

1205731199041

+

1205732

1199042

1205902

1205731199042

+

1205742

1198711

1205902

1205741198711

+

1205742

1198712

1205902

1205741198712

+

1205742

1198671

1205902

1205741198671

+

1205742

1198672

1205902

1205741198672

+ sum

119860=119871119867

10

sum

119895=1

1

119899119904

119860119895(119890)

sdot [120572119904(1 minus

1205731199041

2

+

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]119890997888rarr ]119890)

+ 120572119904(1 +

1205731199041

2

+

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]120583997888rarr ]119890)

+ 120572119904(1 minus

1205731199041

2

minus

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]119890997888rarr ]119890)

+ 120572119904(1 +

1205731199041

2

minus

1205731199042

2

+

120574119895

1198601

2

)119873119904

119860119895(]120583997888rarr ]119890)

minus 119899119904

119860119895(119890)]

2

+

1

119899119904

119860119895(120583)

sdot [120572119904(1 minus

1205731199041

2

+

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731199041

2

+

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]120583997888rarr ]120583)

+ 120572119904(1 minus

1205731199041

2

minus

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731199041

2

minus

1205731199042

2

+

120574119895

1198602

2

)119873119904

119860119895(]120583997888rarr ]120583)

minus 119899119904

119860119895(120583)]

2

]

]

(15)

1205942

multi-GeV

= min12057211989812057310158401199041205741015840119904

[

[

1205732

1198981

1205902

1205731198981

+

1205732

1198982

1205902

1205731198982

+

1205742

1

1205902

1205741

+

1205742

2

1205902

1205742

+ sum

119860=119871119867

10

sum

119895=1

1

119899119898

119860119895(119890)

sdot [120572119904(1 minus

1205731198981

2

+

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]119890997888rarr ]119890)

+ 120572119904(1 +

1205731198981

2

+

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]120583997888rarr ]119890)

+ 120572119904(1 minus

1205731198981

2

minus

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]119890997888rarr ]119890)


+ 120572119904(1 +

1205731198981

2

minus

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]120583997888rarr ]119890)

minus 119899119898

119860119895(119890)]

2

+

1

119899119898

119860119895(120583)

sdot [120572119904(1 minus

1205731198981

2

+

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731198981

2

+

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]120583997888rarr ]120583)

+ 120572119904(1 minus

1205731198981

2

minus

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731198981

2

minus

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]120583997888rarr ]120583)

minus 119899119898

119860119895(120583)]

2

]

]

(16)


120574119895

11986012=

12057411986012

(119895 le 119895th 119860 = 119871119867)

minus12057411986012

(119895 gt 119895th 119860 = 119871119867)

120574119895

12=

12057412

(119895 le 119895th)

minus12057412

(119895 gt 119895th)

(17)


1205901205731199041

= 1205901205731198981

= 003

1205901205731199042

= 005

1205901205731198982

= 016

120590120572= 02

(18)

1205901205741198711

= 0005

1205901205741198712

= 0008

1205901205741198671

= 0021

1205901205741198672

= 0018

1205901205741= 0015

1205901205742= 0025

(19)


and 1205901205742





119890120591(1 + 120598

119890119890)| ≲ 03 at 25120590CL On the




119890120591| lt 034 at 25120590




119890119890in the case of 120598

119890120591= 0 In plotting



05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

2

15

|120598e120591|

1

05

0

2

15

|120598e120591|

1

05

0

03

025

|120598e120591|

02

015

01

005

0

06

05

04

|120598e120591|

03

02

01

0


120598ee


120598ee


120598ee







0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

e120583

120583e + e120583 + 120583

e

(a) Rate NH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

e120583

120583e + e120583 + 120583

e

(b) Rate IH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

Le

L120583H120583

L120583H120583

Le HeHe

(c) 2bin NH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

Le

L120583H120583

L120583H120583

Le HeHe

(d) 2bin IH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

He + e

Le + e L120583 + 120583H120583 + 120583


0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

He + e

Le + e L120583 + 120583H120583 + 120583





119890+ ]119890and ]




1

2En

ergy

bin

s


100

50

0

minus50

minus100

(a) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ119873

120583


1

2

Ener

gy b

ins

100

50

0

minus50

minus100

(b) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ119873

120583


1

2

Ener

gy b

ins

100

50

0

minus50

minus100

(c) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ(119873

120583+ 119873120583)




120583-like and

]120583-like events



























119890119890+ 1 lt 0



2

15

|120598e120591|

1

05


120598ee

(a) NH

2

15

|120598e120591|

1

05


120598ee

(b) IH










119890120591| = 27


119890120591| = 67 green for |120598

119890120591| = 87 orange for |120598

119890120591| = 107 and grey for |120598

119890120591| = 127





119890120591| = 08 times |1 + 120598

119890119890| in


119890119890and |120598

119890120591| are small for |120598

119890119890| ≲ 2 in the case of





4 Conclusions


119890120591||1 + 120598

119890119890| ≲ 08 at 25120590CL while we



119890120591||1 +



to minus01 ≲

120598119890119890≲ 02 and |120598



119890120591| lt 034 at 25120590




119890119890and |120598







119890120572(120572 =

119890 120583 120591) 120598119891120583120572



119890119890and |120598









Acknowledgment


References
















+









119890119890 or V

119890119890 scatter-






















119890120591119881119890from










13rdquo














120583rarr ]120591and ]
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




+ 120572119904(1 +

1205731198981

2

minus

1205731198982

2

+

120574119895

1

2

)119873119898

119860119895(]120583997888rarr ]119890)

minus 119899119898

119860119895(119890)]

2

+

1

119899119898

119860119895(120583)

sdot [120572119904(1 minus

1205731198981

2

+

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731198981

2

+

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]120583997888rarr ]120583)

+ 120572119904(1 minus

1205731198981

2

minus

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]119890997888rarr ]120583)

+ 120572119904(1 +

1205731198981

2

minus

1205731198982

2

+

120574119895

2

2

)119873119898

119860119895(]120583997888rarr ]120583)

minus 119899119898

119860119895(120583)]

2

]

]

(16)


120574119895

11986012=

12057411986012

(119895 le 119895th 119860 = 119871119867)

minus12057411986012

(119895 gt 119895th 119860 = 119871119867)

120574119895

12=

12057412

(119895 le 119895th)

minus12057412

(119895 gt 119895th)

(17)


1205901205731199041

= 1205901205731198981

= 003

1205901205731199042

= 005

1205901205731198982

= 016

120590120572= 02

(18)

1205901205741198711

= 0005

1205901205741198712

= 0008

1205901205741198671

= 0021

1205901205741198672

= 0018

1205901205741= 0015

1205901205742= 0025

(19)


and 1205901205742





119890120591(1 + 120598

119890119890)| ≲ 03 at 25120590CL On the




119890120591| lt 034 at 25120590




119890119890in the case of 120598

119890120591= 0 In plotting



05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

2

15

|120598e120591|

1

05

0

2

15

|120598e120591|

1

05

0

03

025

|120598e120591|

02

015

01

005

0

06

05

04

|120598e120591|

03

02

01

0


120598ee


120598ee


120598ee







0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

e120583

120583e + e120583 + 120583

e

(a) Rate NH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

e120583

120583e + e120583 + 120583

e

(b) Rate IH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

Le

L120583H120583

L120583H120583

Le HeHe

(c) 2bin NH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

Le

L120583H120583

L120583H120583

Le HeHe

(d) 2bin IH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

He + e

Le + e L120583 + 120583H120583 + 120583


0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

He + e

Le + e L120583 + 120583H120583 + 120583





119890+ ]119890and ]




1

2En

ergy

bin

s


100

50

0

minus50

minus100

(a) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ119873

120583


1

2

Ener

gy b

ins

100

50

0

minus50

minus100

(b) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ119873

120583


1

2

Ener

gy b

ins

100

50

0

minus50

minus100

(c) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ(119873

120583+ 119873120583)




120583-like and

]120583-like events



























119890119890+ 1 lt 0



2

15

|120598e120591|

1

05


120598ee

(a) NH

2

15

|120598e120591|

1

05


120598ee

(b) IH










119890120591| = 27


119890120591| = 67 green for |120598

119890120591| = 87 orange for |120598

119890120591| = 107 and grey for |120598

119890120591| = 127





119890120591| = 08 times |1 + 120598

119890119890| in


119890119890and |120598

119890120591| are small for |120598

119890119890| ≲ 2 in the case of





4 Conclusions


119890120591||1 + 120598

119890119890| ≲ 08 at 25120590CL while we



119890120591||1 +



to minus01 ≲

120598119890119890≲ 02 and |120598



119890120591| lt 034 at 25120590




119890119890and |120598







119890120572(120572 =

119890 120583 120591) 120598119891120583120572



119890119890and |120598









Acknowledgment


References
















+









119890119890 or V

119890119890 scatter-






















119890120591119881119890from










13rdquo














120583rarr ]120591and ]
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

05120590

1120590

15120590

2120590

25120590

3120590

2

15

|120598e120591|

1

05

0

2

15

|120598e120591|

1

05

0

03

025

|120598e120591|

02

015

01

005

0

06

05

04

|120598e120591|

03

02

01

0


120598ee


120598ee


120598ee







0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

e120583

120583e + e120583 + 120583

e

(a) Rate NH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

e120583

120583e + e120583 + 120583

e

(b) Rate IH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

Le

L120583H120583

L120583H120583

Le HeHe

(c) 2bin NH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

Le

L120583H120583

L120583H120583

Le HeHe

(d) 2bin IH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

He + e

Le + e L120583 + 120583H120583 + 120583


0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

He + e

Le + e L120583 + 120583H120583 + 120583





119890+ ]119890and ]




1

2En

ergy

bin

s


100

50

0

minus50

minus100

(a) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ119873

120583


1

2

Ener

gy b

ins

100

50

0

minus50

minus100

(b) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ119873

120583


1

2

Ener

gy b

ins

100

50

0

minus50

minus100

(c) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ(119873

120583+ 119873120583)




120583-like and

]120583-like events



























119890119890+ 1 lt 0



2

15

|120598e120591|

1

05


120598ee

(a) NH

2

15

|120598e120591|

1

05


120598ee

(b) IH










119890120591| = 27


119890120591| = 67 green for |120598

119890120591| = 87 orange for |120598

119890120591| = 107 and grey for |120598

119890120591| = 127





119890120591| = 08 times |1 + 120598

119890119890| in


119890119890and |120598

119890120591| are small for |120598

119890119890| ≲ 2 in the case of





4 Conclusions


119890120591||1 + 120598

119890119890| ≲ 08 at 25120590CL while we



119890120591||1 +



to minus01 ≲

120598119890119890≲ 02 and |120598



119890120591| lt 034 at 25120590




119890119890and |120598







119890120572(120572 =

119890 120583 120591) 120598119891120583120572



119890119890and |120598









Acknowledgment


References
















+









119890119890 or V

119890119890 scatter-






















119890120591119881119890from










13rdquo














120583rarr ]120591and ]
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

e120583

120583e + e120583 + 120583

e

(a) Rate NH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

e120583

120583e + e120583 + 120583

e

(b) Rate IH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

Le

L120583H120583

L120583H120583

Le HeHe

(c) 2bin NH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

Le

L120583H120583

L120583H120583

Le HeHe

(d) 2bin IH

0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

He + e

Le + e L120583 + 120583H120583 + 120583


0

20

40

60

80

100

120

140


120598ee

1205942 m

ulti-

GeV

He + e

Le + e L120583 + 120583H120583 + 120583





119890+ ]119890and ]




1

2En

ergy

bin

s


100

50

0

minus50

minus100

(a) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ119873

120583


1

2

Ener

gy b

ins

100

50

0

minus50

minus100

(b) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ119873

120583


1

2

Ener

gy b

ins

100

50

0

minus50

minus100

(c) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ(119873

120583+ 119873120583)




120583-like and

]120583-like events



























119890119890+ 1 lt 0



2

15

|120598e120591|

1

05


120598ee

(a) NH

2

15

|120598e120591|

1

05


120598ee

(b) IH










119890120591| = 27


119890120591| = 67 green for |120598

119890120591| = 87 orange for |120598

119890120591| = 107 and grey for |120598

119890120591| = 127





119890120591| = 08 times |1 + 120598

119890119890| in


119890119890and |120598

119890120591| are small for |120598

119890119890| ≲ 2 in the case of





4 Conclusions


119890120591||1 + 120598

119890119890| ≲ 08 at 25120590CL while we



119890120591||1 +



to minus01 ≲

120598119890119890≲ 02 and |120598



119890120591| lt 034 at 25120590




119890119890and |120598







119890120572(120572 =

119890 120583 120591) 120598119891120583120572



119890119890and |120598









Acknowledgment


References
















+









119890119890 or V

119890119890 scatter-






















119890120591119881119890from










13rdquo














120583rarr ]120591and ]
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




1

2En

ergy

bin

s


100

50

0

minus50

minus100

(a) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ119873

120583


1

2

Ener

gy b

ins

100

50

0

minus50

minus100

(b) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ119873

120583


1

2

Ener

gy b

ins

100

50

0

minus50

minus100

(c) (120598119890119890 |120598119890120591|) = (2 0)multi-GeV IH Δ(119873

120583+ 119873120583)




120583-like and

]120583-like events



























119890119890+ 1 lt 0



2

15

|120598e120591|

1

05


120598ee

(a) NH

2

15

|120598e120591|

1

05


120598ee

(b) IH










119890120591| = 27


119890120591| = 67 green for |120598

119890120591| = 87 orange for |120598

119890120591| = 107 and grey for |120598

119890120591| = 127





119890120591| = 08 times |1 + 120598

119890119890| in


119890119890and |120598

119890120591| are small for |120598

119890119890| ≲ 2 in the case of





4 Conclusions


119890120591||1 + 120598

119890119890| ≲ 08 at 25120590CL while we



119890120591||1 +



to minus01 ≲

120598119890119890≲ 02 and |120598



119890120591| lt 034 at 25120590




119890119890and |120598







119890120572(120572 =

119890 120583 120591) 120598119891120583120572



119890119890and |120598









Acknowledgment


References
















+









119890119890 or V

119890119890 scatter-






















119890120591119881119890from










13rdquo














120583rarr ]120591and ]
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




2

15

|120598e120591|

1

05


120598ee

(a) NH

2

15

|120598e120591|

1

05


120598ee

(b) IH










119890120591| = 27


119890120591| = 67 green for |120598

119890120591| = 87 orange for |120598

119890120591| = 107 and grey for |120598

119890120591| = 127





119890120591| = 08 times |1 + 120598

119890119890| in


119890119890and |120598

119890120591| are small for |120598

119890119890| ≲ 2 in the case of





4 Conclusions


119890120591||1 + 120598

119890119890| ≲ 08 at 25120590CL while we



119890120591||1 +



to minus01 ≲

120598119890119890≲ 02 and |120598



119890120591| lt 034 at 25120590




119890119890and |120598







119890120572(120572 =

119890 120583 120591) 120598119891120583120572



119890119890and |120598









Acknowledgment


References
















+









119890119890 or V

119890119890 scatter-






















119890120591119881119890from










13rdquo














120583rarr ]120591and ]
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics





119890119890and |120598







119890120572(120572 =

119890 120583 120591) 120598119891120583120572



119890119890and |120598









Acknowledgment


References
















+









119890119890 or V

119890119890 scatter-






















119890120591119881119890from










13rdquo














120583rarr ]120591and ]
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics






















119890120591119881119890from










13rdquo














120583rarr ]120591and ]
















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



Research Article Constraints on the Nonstandard...

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Transcript of Research Article Constraints on the Nonstandard...