Background Study for Very Long Baseline Neutrino Oscillation Experiments with a Large Water...

8/7/2019 Background Study for Very Long Baseline Neutrino Oscillation Experiments with a Large Water Cherenkov Detector

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arXiv:1008

.1019v5[hep-ex]

23Feb2011

Background Study on e Appearance from a Beam in Very Long Baseline Neutrino

Oscillation Experiments with a Large Water Cherenkov Detector

C. Yanagisawa, C. K. Jung, P. T. Le

Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, U.S.A.

B. VirenDepartment of Physics, Brookhaven National Laboratory, Upton, NY 11973, U.S.A.

(Dated: February 24, 2011)

There is a growing interest in very long baseline neutrino oscillation experimentation using ac-celerator produced neutrino beam as a machinery to probe the last three unmeasured neutrinooscillation parameters: the mixing angle 13, the possible CP violating phase CP and the masshierarchy, namely, the sign of m232. Water Cherenkov detectors such as IMB, Kamiokande andSuper-Kamiokande have shown to be very successful at detecting neutrino interactions. Scaling upthis technology may continue to provide the required performance for the next generation of exper-iments. This report presents the latest effort to demonstrate that a next generation (> 100 kton)water Cherenkov detector can be used effectively for the rather difficult task of detecting es fromthe neutrino oscillation e despite the large expected potential background resulting from

0sproduced via neutral current interactions.

PACS numbers: 13.15.+g, 14.60.Lm,14.60.Pq

Keywords: neutrino oscillation, water Cherenkov

I. INTRODUCTION

It has been shown that there are certain advantages ina wideband neutrino beam over a now traditional narrow-band neutrino beam for neutrino oscillation experiments,especially for the observation of e oscillation, pro-vided that the baseline is reasonably long (over 1,000km) [1].

By broadening the range of energies with which multi-ple oscillations can be resolved, a richer parameter space

can become accessible than is available to an experimentfocused on only the first oscillation maximum.

In the original paper proposing the use of a wide-bandneutrino beam for a very long baseline neutrino oscil-lation (VLBNO) experiment [1] by the Brookhaven Na-tional Laboratory (BNL) neutrino working group (NWG)some simplifying assumptions were used. The sensitivi-ties presented in the paper relied on calculations basedon 4-vector level Monte Carlo (MC) simulations, a sim-ple model for energy resolution and certain assumptionsabout reconstruction capabilities. Namely, a detaileddetector simulation for the proposed water Cherenkovdetector was not included. In addition it was assumedthat the signal events were only from quasi-elastic (QE)charged current (CC) scattering (e + n e + p) andthe background events were only from single 0 neutral

email: [email protected]; Also at Science De-

partment, BMCC, City University of New York,199 Chambers

Street, New York, NY 10007, U.S.A.Currently, Department of Physics and Astronomy,Rutgers, the

State University of New Jersey,136 Frelinghuysen Rd, Piscataway,

NJ 08854

current (NC) interactions +N +0 +N where Nand N are nucleons.

In order to gain a better insight on this idea of theVLBNO experiment with a wide-band neutrino beam for e oscillation, we performed a more sophisticatedand elaborate multivariate likelihood based analysis us-ing a full MC simulation that included inelastic neu-trino interactions, water Cherenkov detector response,and well-tuned event reconstruction algorithms. ThisMC simulation and reconstruction programs were devel-oped and fine-tuned for the Super-Kamiokande-I experi-

ment (SK-I) [2].

II. ENERGY RECONSTRUCTION AND EVENTDESCRIPTION

For the discussions in this paper, we calculate a recon-structed neutrino energy using the formula

Erec =mNEe

mN (1 cose)Ee,

where mN

, Ee

and e

are the nucleon mass, the recoilelectron energy and the scattering angle of the recoil elec-tron with respect to the incident neutrino beam, respec-tively. In a strict sense, this quantity represents the in-cident neutrino energy only when the event is producedby CC QE scattering and the Fermi motion of targetnucleons is ignored. Nonetheless, we show in Figure 1the neutrino energy and Erec for CC QE (top) and allCC (bottom) events to compare the two energy distribu-tions for the two classes of CC events. Although Erec forthe CC events does not reproduce the incident neutrino
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FIG. 1: The distributions of neutrino energy (solid lines) andreconstructed neutrino energy (dotted lines) of single ring e-like events originating from CC QE interactions (top figure)and from all CC interactions (bottom figure). Note that adip at about 2 GeV is due to e neutrino oscillation.The open square boxes with error bars indicate statisticaluncertainties.

spectrum as well as it does for CC QE events, it stillreproduces it quite well.

The initial event selection is made to maximize thenumber of interactions that are consistent with comingfrom e appearing at the far end of the baseline in thebeam while minimizing events such as CC or anyevents from NC interactions. Needless to say, the clear-est event signature comes from e CC QE interactions.Inelastic e CC events also carry information about os-

cillations but are more difficult to cleanly select and havesomewhat worse energy resolution as shown in Figure 1.Regardless of the interaction, a recoil proton will rarelybe above its Cherenkov threshold of about 1.25 GeV/cand will not contribute notably to the event signature.For these reasons, a e appearance candidate event willbe initially selected if its signature is consistent with be-ing a Cherenkov radiation pattern from a single electron

(termed single ring, e-like).A CC QE event will usually be distinguishable from

one arising from a e CC QE interaction as the result-ing Cherenkov ring produced by will have a sharperrise and fall in the amount of Cherenkov light at theedges of the ring than one due to an electron. This isbecause a muon presents a relatively straight line sourceof Cherenkov light while an electron initiates an elec-tromagnetic shower. This shower consists of a distribu-tion of track directions due to the number of particles inthe shower and that they experience larger multiple scat-tering. As the muon energy approaches the Cherenkovthreshold there is an increasing chance that multiple

scattering and the collapsing Cherenkov light cone willsmooth the rise of the edge of the ring and potentiallymimic an electron.

Likewise, inelastic and NC interactions with a non-zeropion multiplicity can have additional light that is not con-sistent with the pattern of a single e-like ring. Dependingon the exact event topology these events are either easilyruled out or present challenging backgrounds. Chargedpions above their Cherenkov threshold of 160 MeV/c pro-duce a -like ring and are rejected. Events with visiblelight from both pions and the primary charged lepton arestrongly rejected based on ring counting.

Events with a final state consisting of only a single neu-tral pion present a particular challenge. The 0 decays toa pair of gamma rays, each of which initiate an electro-magnetic shower and produce an e-like ring of varying in-tensity and direction. These 0 events can become back-ground depending on how the 0 decays to two gammarays. At one extreme, the decay is symmetric such thatthe gamma rays have similar energies. If the original 0 isboosted enough, the two gamma rays are nearly collinearand produce mostly overlapping rings. They can then beimpossible to be distinguished single electron events withan energy equal to the sum of the two gammas. At theother extreme, a highly asymmetric 0 decay results inone strongly boosted and one strongly retarded gammaray. In the lab frame, the higher energy gamma will pro-

duce a single e-like ring while the other may produce nodiscernible light.

The events with a 0 in the final state can come fromtwo sources: (1) NC interactions and (2) charge ex-changes of charged pions inside the target nucleus or withan oxygen or a hydrogen nucleus while traveling in water.

Finally, there are events from electron neutrino inter-actions that are not from e that appeared in the beamfrom neutrino oscillation e. Rather, there is anintrinsic e component in the unoscillated neutrino beam


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originating from muon or kaon decays. The beam used inthis study has an intrinsic e component which is 0.7% ofthe flux. The background events from these neutrinosare irreducible.

In this analysis, to classify the events for the initial se-lection, the reconstruction algorithms used for the SK-Iatmospheric neutrino analysis are employed. In addition,a special algorithm called POLfit [8] is used. This algo-

rithm has been found to be extremely useful for removingsingle 0 background events in samples containing eventsthat are classified as single-ring and e-like [9] by the stan-dard SK-1 reconstruction. This paper describes how in-formation provided by POLfit, together with other usefulvariables, can be effectively used to significantly reducethe 0 background while retaining a sufficient efficiencyfor the signal.

III. MONTE CARLO EVENT SAMPLE

The Monte Carlo event sample used in this study was

originally produced by the SK-I collaboration to simulateatmospheric neutrino events detected by the SK-I detec-tor and corresponds to about 100 years of the exposure.The detailed description of the Monte Carlo generation aswell as the event reconstruction is described elsewhere [3].

The energy spectra for and e produced in theEarths atmosphere are different from those in the neu-trino beam proposed by the BNL NWG. To account forthis, each event is given a weight based on the neu-trino energy such that the shape of the resulting spec-trum matches that expected from the beam. An addi-tional normalization is applied so that the total numberof CC QE events is as expected.

Assuming no oscillations, it is expected that there willbe 12,000 such events for a detector with SK-I efficien-cies and fiducial volume of 500 kton (22.2 SK-I) whichis placed 2,540 km from the neutrino production targetand for five years of running as described in the paper byBNL NWG [1]. When oscillations are applied, this sam-ple is weighted by the oscillation probability taking intoaccount full three-neutrino mixing and matter effects.

The oscillated e sample is prepared by similarlyweighting and normalizing the e atmospheric MC eventsto what is expected from the component of the beam,that is, under the assumption of 100% e oscilla-tion. Actual oscillation parameters are then applied tothis sample by weighting to the appropriate oscillationprobability. The intrinsic e component in the beam istaken to be the shape predicted by the beam MC simu-lation and is normalized to be 0.7% that of the com-ponent. To include the effect of neutrino oscillation, thecontribution of the e component is calculated only whene survives as e at the water Cherenkov detector placedat a given baseline.

The expected numbers of the events to be observedfrom the intrinsic anti- component of the beam are es-timated to be 2.2% and 2.5% of the expected numbers

of the background events from the (background-1) forthe baselines of 2,540 km and of 1,480 km, respectively(see the next section for the description about the base-line). The expected numbers of the events to be observedfrom anti-e component of the beam are estimated to beless than 4.5% and 4.3% of the expected numbers of thebackground events from the intrinsic e component ofthe beam (background-2) for the baselines of 2,540 km

and of 1,480 km, respectively. Since these contributionsare much smaller than the events from the background-1and the background-2, although not negligible, we willnot take into account them further in this report.

To select MC e appearance candidate events an initialset of cuts based on the standard SK-I codes is used: (a)there is one and only one e-like ring, (b) the reconstructedevent vertex is at least 2 m from any inner photomulti-plier (PMT) surface and (c) there is no activity in theouter (veto) detector.

In addition to these standard cuts, events produced byneutrinos with energies greater than 10 GeV are ignoreddue to lack of statistics in the atmospheric MC sample.The beam has a tail that extends up to 15 GeV but itscontribution to the background is negligible as will beshown below.

IV. NEUTRINO OSCILLATIONPROBABILITIES

The oscillation probabilities applied to the componentsof the beam neutrino flux use the following parameters:

m221

= 7.3 105eV2,m231 = 2.5 10

3eV2,sin2 212 = 0.86,

sin2

223 = 1.0,sin2 213 = 0.04, and

CP = 0,45,135.

Note that the sign convention of CP follows that ofthe paper by BNL NWG [1]. Unless otherwise stated, inthis paper the value of CP is +45 and the baseline is2,540 km which corresponds to the distance from BNLto Homestake Mine in South Dakota. Later we will de-scribe the results with different values for CP as wellas with the baseline of 1,480 km which corresponds tothe distance from Fermilab to Henderson Mine in Col-orado. The result with the baseline of 1,480 km was forthe UNO detector proposed first in 1999 and later to bebuilt in Henderson Mine. See the references [4] for thedetail of the UNO detector. These results are similar towhat is expected for the Fermilab to Homestake baselineof 1,300km. This shorter baseline is considered by apply-ing inverse-square scaling of the flux and recalculation ofoscillation probabilities.

The neutrino oscillation probabilities were calculatedby the nuosc [5] package. The calculator assumes 3-os-cillation with possible CP symmetry violation and mat-ter effects. The matter densities can be vacuum, non-zero


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constant or stepwise-constant matter densities. The non-constant PREM [6] and arbitrary user provided densityprofiles are also supported. It calculates the probabili-ties either analytically for constant matter densities orfor any density profile it can use a 5th order adaptiveRunge-Kutta stepper. The package has been validatedagainst published calculations [7].

V. POLFIT

In this section we briefly describe the 0 fitter calledPattern Of Light fit (POLfit) [8]. POLfit is applied toevents which are initially classified as single-ring and e-like by the standard SK-I analysis codes in order to iden-tify 0 background events in this event sample. It as-sumes the event is a 0 event and that the ring foundby the standard codes is one of the gammas from the0 decay. It will then determine the direction and en-ergy of a secondary gamma that, along with the primaryone, is most consistent with the pattern of light collected

by the PMTs. POLfit produces two possible secondarygammas by employing two algorithms. One is optimizedassuming the secondary ring is overlapping with the pri-mary ring (forward-algorithm). The other is optimizedto find a second ring in the wider angular region (wide-algorithm).

In each algorithm, the pattern of light expected fromthe full 0 decay is calculated from a set of templates andcompared to the collected light and a likelihood is formed.These templates are pre-determined using the detectorsimulation. The energy and direction phase-space of thesecondary gamma is searched to find the point that leadsto the maximum likelihood. Each algorithm supplies the

direction of two photons, their energies, the two photoninvariant mass, and the maximum likelihood value ob-tained. It was found that the wide-algorithm methodmore reliably finds a real second ring more often thanthe forward-algorithm. Therefore, in this report we usemostly the information provided by the wide-algorithmunless otherwise stated.

To demonstrate the power of POLfit, Figure 2 showsthe relative 0 reconstruction efficiencies with (solid cir-cles) and without (open circles) POLfit employed as afunction of the opening angle between the two recon-structed gammas from the 0 decay in the lab frame andfor single 0 events produced by the NC interactions. Tobe accepted in this sample, the event must have a two-photon invariant mass (m ) within 2 of the expectedvalue given the event came from a 0. Here, the neutrinoenergy spectrum is that of the original SK-I atmosphericmuon neutrinos. In the case without POLfit, only eventsidentified as having two e-like rings by the standard SK-Isoftware can be candidates to be a 0. With POLfit in-formation, 0 events that are classified as single-ring bythe standard selection may now be selected.

Depletion of0 detection efficiencies at a small open-ing angle is due to overlap of the two e-like rings. At

FIG. 2: 0 reconstruction efficiency with the standard SK-I codes (open circles) and after accepting additional eventswith missing gamma found by POLfit (solid circles).

large opening angle it is due to the second ring being toofaint. As clearly seen in Figure 2, POLfit improves the0 reconstruction efficiency significantly.

VI. USEFUL VARIABLES TO DISTINGUISHTHE SIGNAL FROM THE BACKGROUND

A cut on m reduces background from single 0 NC

events but it also reduces signal efficiency somewhat.Alone, it is not enough to reduce the background to a

level comparable to the oscillation signal. It is, there-fore, desirable to find additional distinguishing features.

In this section, nine such features (variables) includingm are described. Distributions of these variables areshown for events that are oscillated e CC (labeled sig-nal and with solid lines) and NC, CC and beam-eCC events (background, dotted lines). The distribu-tions are plotted for different Erec regions in steps of 0.5GeV from 0 to 2 GeV, 2 GeV Erec < 3 GeV and Erec 3 GeV.

In general, at lower energies (sub-GeV range), thebackground is largely from the misidentified single-0

events discussed above. At higher energies, non-QE in-

teractions become dominant leading to additional waysfor background to mimic e CC QE events.

A. Reconstructed 0 mass (m)

As shown above, this variable is useful to remove back-ground events that come from single 0 NC production.In Figure 3 the distributions ofm are shown. In thelower reconstructed neutrino energy region (Erec 2


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like ring events for signal (solid line) and background (dottedline).

GeV), the distributions show a prominent 0 peak. Athigher energies, the contribution from multi-pion produc-tion increases and POLfit begins to reconstruct the cor-rect second gamma poorly or returns an arbitrary resultthat is not associated with any physical particle. Becauseof this, the 0 peak disappears in the higher energy re-gion.

B. Fraction of energy in the second ring (Efrac)

In general, the second e-like ring found by POLfit hasless energy than the one found by the standard SK-I re-construction software. Furthermore, POLfit must find asecond ring and if the event does not in fact have one,this wrongly reconstructed ring tends to have much lessenergy than the primary one. This effect is shown in Fig-ure 4 where the ratios of the energy of the second ring tothe sum of two ring energies are plotted.

C. Difference in log 0 likelihood ratio (log 0-lh)

As mentioned above, POLfit employs two algorithms,the wide- and forward-algorithm. Each provides a log-likelihood that the event is a 0. Signal events actuallycontain only a single ring. Nevertheless, with such events,POLfit will return a second, fake ring. In such cases, bothalgorithms tend to place this fake ring in the vicinity ofthe single primary ring. Therefore, the two algorithmstend to find similar fake rings. This makes the two like-lihoods similar to each other and the log-likelihood ratio

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ring found by POLfit in 1-ring events for the signal (solid line)and background (dotted line).

(difference between two log-likelihoods) tends to be sym-metric around zero. On the other hand, in the case of a 0

background event the secondary photon from a 0 decayis not necessarily confined in the direction of the primaryphoton. This makes the log-likelihood ratio asymmetricwith a long left tail, especially at lower energies. The dif-ference is significant in the lower energy region as shownin Figure 5. However, this trend changes above Erec =

1.0 GeV where the contribution from multi-pion produc-tion starts to increase and dilutes this effect.

D. Direction cosine of the e-like ring (cos)

The direction cosine of the primary e-like ring with re-spect to the neutrino beam is a good discriminator to sep-arate the signal from the background. Its distributions

are shown in Figure 6. This variable does not depend onthe information from POLfit.

As the energy of the neutrino decreases, the outgoingelectron direction is distributed over a wider angle withrespect to the neutrino direction. As the energy becomescomparable to that of Fermi motion, the distribution isfurther widened because the momentum of the target nu-cleon becomes significant and will tend to randomize theelectrons direction. This latter effect is less for the moremassive 0.


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FIG. 5: The distributions of the difference in log 0 likelihood

between the two algorithms. The larger this variable, themore likely an event is the 0 background. The distributionsin solid lines are for the signal and those in dotted lines arefor the background.

E. Total charge to ring energy ratio (Q/E)

Light collected in an event that is not consistent withthe single ring found by the standard SK-I codes is an in-dication of unreconstructed or missed particles and thusa non-QE interaction. A measure of this light is the ra-tio of the total charge, in unit of PE (photoelectron),

collected by all PMTs to the energy associated with theprimary reconstructed ring in MeV. Some backgroundevents where only one ring is found are expected to pro-duce some light which is not identified as a ring. Thedistributions of this variable are shown in Figure 7. Theseparation is most pronounced at lower reconstructed en-ergy where any 0s are likely to be less boosted and notput all their light in the forward direction. Thus in anasymmetric 0 decay the second ring tends to be weakerthan the standard SK codes can detect.

F. log particle-identity-likelihood (log pid-lh)

The standard SK-I reconstruction software provideslikelihoods of a Cherenkov ring to be e-like (Le) and -like (L). From these two likelihoods, the logarithm ofthe ratio of likelihoods, log(L/Le) (log pid-lh) is used asa good measure to separate electrons from muons. Themore negative log pid-lh is, the more e-like a Cherenkovring is. When two e-like rings, such as the photons froma 0 decay, overlap and reconstruct as a single ring theycan produce a log pid-lh that is more e-like than a single

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FIG. 6: The distributions of the directional cosine of the pri-

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FIG. 7: The distributions of the ratio, the total charge in PEto the ring energy in MeV are shown. The distributions insolid line are for the signal and those in dotted line are forthe background.

electron at a comparable energy would have. Figure 8shows this small but noticeable effect.


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FIG. 8: The distributions of the log-likelihood ratio between

e-like and -like of the primary e-like ring. The distributionsin solid line are for the signal and those in dotted line are forthe background.

G. log 0-likelihood (log 0-lh)

POLfit provides the logarithm of a likelihood that theevent consists of a single 0. For events that actuallydo consist of a single 0 this variable is expected to besmaller (more negative), namely more 0-like, than thatfor a signal event. This trend shows up in lower energyregion (Erec 1 GeV) as shown in Figure 9. In the higher

energy region, the distribution tends to be narrower forthe signal events.

H. Cherenkov angle (Cangle)

The distribution of reconstructed Cherenkov angle isexpected to be different between the signal and back-ground events and it depends on whether there is overlapbetween two Cherenkov rings and on the energy of theprimary ring. In Figure 10 the Cherenkov angle distri-butions for different Erec regions are shown. The shapeof the distribution for the signal events differs from that

for the background events in most of the energy regions,although degrees of differences vary from energy regionto region.

I. Log ring-count likelihood ratio (log ring-lh)

To decide how many Cherenkov rings there are in anevent, two hypotheses are compared: the first hypothesisis that there is only one Cherenkov ring and the second is

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FIG. 9: The distributions of the log 0-likelihood of single e-

like ring events. The distribution in solid line is for the signaland that in dotted line is for the background.

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FIG. 10: The distributions of the measured Cherenkov angleof the primary e-like ring. The distribution in solid line is for

the signal and that in dotted line is for the background.

that there is an additional ring in the event. The compar-ison is made using log-likelihood ratio, calculated by thestandard SK-I codes, of the two hypotheses. In Figure 11this log-likelihood ratio is plotted for different Erec re-gions. The shape of the distribution for the signal eventsdiffers from that for the background events in most ofthe energy regions, although degrees of differences again


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FIG. 11: The distributions of log-likelihood ratio of two hy-

potheses on the number of Cherenkov ring in an event: thereis only one Cherenkov ring or there are more. If the log-likelihood ratio is negative, the event is less likely to havean additional ring. The distributions in solid line are for thesignal and that in dotted line are for the background.

vary over the different energy regions.

VII. DISCRIMINATOR: LIKELIHOODFUNCTION AND LIKELIHOOD RATIO

A series of cuts on the variables described in the pre-vious section can reduce the background well. However,too many cuts in series reduce the signal selection effi-ciency. The problem for this analysis is that none of thevariables alone can separate the signal from the back-ground powerfully. Thus, this situation is well suitedfor a multivariate analysis where a likelihood functionis defined and utilizes all variables that have noticeabledistinguishing power. We have shown that the nine vari-ables described above are distributed differently depend-ing on the source of the events (signal or background),although the differences may not be large. As we willsee, an accumulation of relatively small differences, whenthe correlations among the variables are small, can makea bigger difference.

From each distribution shown in Figures 3-11, aprobability is calculated for an event to have a valueof the corresponding variable i as signal psi and asbackground pbi . Then the log-likelihood is defined bylog(Ls) = i=1,..,9 log(psi ) as signal and by log(Lb) =i=1,..,9 log(pbi) as background. These probabilities arecalculated in the same bins ofErec as used in Figures 3-11.

Then the difference between two log-likelihoods,

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FIG. 12: The distributions of log-likelihood ratio of two hy-

potheses on the origin of events: signal vs. background. Thedistributions in solid line are for the signal and those in dottedline are for the background.

log(L) = log(Lb) log(Ls), is calculated to decidewhether to accept or reject the event. Figure 12 showslog(L) distributions for the different Erec regions forthe signal events (solid line) and the background events(dotted line). The smaller log(L) is, the more likely anevent is a signal event. It is clearly seen that the log(L)distribution of the signal events differ significantly fromthat of background events over wide range ofErec.

VIII. RECONSTRUCTED NEUTRINO ENERGYDISTRIBUTIONS WITH A CUT ON log(L)

The final acceptance of an event is determined by itsvalue of log(L). As the distributions of the nine vari-ables used to define the likelihood depend on Erec, sodoes the distribution of log(L). Therefore, in order notto change the energy spectrum unnecessarily, we adopt astrategy to keep the signal detection efficiency constantover a wide range of Erec by changing the log(L) cutaccording to Erec. The cut is selected to retain 40% ofthe signal that passes the standard SK-I cuts for all Erec.

In presenting the results, first we illustrate the per-formance of the traditional analysis represented by thestandard SK-I codes for comparison. Figure 13 (top)shows the Erec distributions of the signal (dashed line),of the background (background-1) mostly from NC inter-actions (dotted line), and of the irreducible background(background-2) from the e contamination in the neu-trino beam (dash-dotted line). The signal is overwhelmedby the background, especially in the low energy region.In this case, we find 700 signal events, 1,877 background


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0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Erec

(MeV)


FIG. 14: The distributions of the reconstructed neutrino en-

ergy is shown for events that pass the standard SK-I cuts andthe cut on log(L) such that 40% of the signal events are re-tained. The distributions in dashed line are for the signal andthose in dotted (dash-dotted) line are for the background-1(background-2). CP = +45

and the baseline is 1,480 km.

TABLE III: Summary of the numbers of signal and back-ground events for different values for CP using events frombackground-1 (Bkg-1) and background-2 (Bkg-2) with the cuton log(L) to retain 40% of the signal events and using abaseline of 1,480 km. The errors are statistical due to thelimited size of the Monte Carlo event sample.

CP Sig Bkg-1 Bkg-2

+135 6469 23823 1332+45 69811 23523 1332

0 4988 23023 1322-45 3566 25024 1342

-135 6099 23723 1342

X. Erec DISTRIBUTIONS AND BASELINE

It is interesting to see how the baseline will changethe results of similar analyses presented in the pre-ceding section. For this study, the cut on log(L)is used again to retain 40% of signal and the base-line is assumed to be 1,480 km (Fermilab to Hender-son Mine). Figure 14 shows the Erec distribution ofthe signal (dashed line), background-1 (dotted line) andbackground-2 (dash-dotted) for = +45. Table III liststhe numbers of events from the signal, background-1 andbackground-2 for different values of CP.

XI. SOURCES OF BACKGROUND EVENTS

It is important to know where the background eventscome from. Information such as the true energy of neutri-nos and nature of interaction of neutrinos that producethe background events is very useful for design of theneutrino beam for a VLBNO experiment.

Figures 15-16 show the neutrino energy distributions ofthe signal, background-1 and background-2 events for thebaseline of 2,540 km and 1,480 km, respectively. Theseevents are chosen with the log(L) cut that retains 40%of the signal events after the first set of the cuts (thestandard SK-I cuts).

As mentioned earlier, for the most of the results pre-sented in this report, we apply the cut on the neutrinoenergy at 10 GeV. To justify this cut, we checked to seehow much more the background contribution would in-crease if we allowed events produced by neutrinos whoseenergies were greater than 10 GeV and less than 15 GeV.For these additional events we fixed the weight value tothat used at 10 GeV. The atmospheric e flux times thee cross section decreased by about 60% while that forthe wideband beam by about 50% in this energy re-gion. Therefore the atmospheric e and spectrum areonly slightly softer than the wideband spectrum from10 GeV to 15 GeV. This argument, therefore, gives areasonable estimate of the extra contribution from highenergy neutrinos. All the neutrino oscillation parametersare the same as in the case with CP = +45

, the base-line of 2,450 km, and the 40% log(L) cut. The numbersof the signal, background-1, and background-2 events ac-cepted are 281, 91 and 45, respectively, which should becompared with 280 for the signal, 87 for the background-

1 and 45 for the background-2 with the neutrino energycut at 10 GeV. Thus the percent increases in the numberof the signal, background-1 and background-2 events are1%, 4%, and 0%, respectively.

Tables IV and V summarize all neutrino interactionsthat produce candidate events passing all cuts with 40%efficiency for the baseline of 2,540 km and 1,480 km, re-spectively. In these tables, 0,, and n stand for sin-gle 0, single and multiple production, respectively.The co label stands for production via coherent inter-action with the oxygen nucleus. The others includeseta and kaon production as well as deep inelastic scatter-ing (DIS). However, for the background, the label nincludes DIS. Note that in the tables there is no contribu-tion From NC interaction for signal events by definition.CC QE contributions to background-1 are due to in-teractions. Since the cross section of the coherent pionproduction is known only to an accuracy of 30% (seereference [3]), we estimate the effect of this error on ourbackground-1 contribution by varying the cross sectionby 30%. For CP = +45 with the baseline of 2,450 km30% changes in this cross section result in changes inthe numbers of background-1 events by 3%.


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tector by imposing a cut on the distance to the PMTsurface from the 0 production point in the direction ofthe 0 (Dwall). For this study we use single

0 eventsproduced by NC interactions. When the 0 energy isabout 1 GeV, the minimum opening angle of two pho-tons is about 20 and less at higher energies. As Dwallgets larger, the number of PMTs that detect Cherenkovphotons increases (improved granularity) which can help

to resolve light patterns. Two negative impacts competewith this effect. The Cherenkov cone is more spread outso less light is seen by any one PMT. The light musttravel further and is thus more subject to absorptionand scattering (attenuation) in the water. These bothlead to a decrease in the number of detected photons perPMT which may degrade the pattern of light that theCherenkov cone produces. In the first case, since infor-mation is not lost and is just spread out to more PMTsthe problem can likely be handled in improvements to re-construction codes. In the second case, some informationabout the original Cherenkov light emitting particles isunrecoverable.

Figure 17 shows the

0

detection efficiency as a func-tion of the opening angle for Dwall ranges: 5 m - 10 m,15 m - 20 m, and 25 m - 30 m and includes POLfit infor-mation. It is clearly seen that when the opening angle issmaller (less than 60), the efficiency is improved as thedistance to the PMT surface in the 0 direction increases.Note that above the opening angle of 60, the 0 detec-tion efficiency seems more or less independent of Dwall.Because of the finite size of the detector and at such largeopening angles selecting events based on Dwall becomesa less capable means of emulating a larger detector.

Nevertheless, this indicates that the granularity of thedetector in terms of the PMT density is an importantfactor to improve the 0 detection efficiency. It also ap-pears that the effect of light attenuation is not a majorissue at least for Cherenkov light traveling up to 30-40 min SK-I water which has an attenuation length of 80-100m (depending on wavelength).

Therefore for the same PMT coverage using the samePMTs, a larger detector than SK-I will perform better,on average, to reconstruct 0. Limitations may be ex-pected once the typical path length for Cherenkov lightapproaches attenuation length.

A similar study can be done by looking at how theS/B ratio varies as a function of Dwall for other eventtypes. In this case we look at the S/B ratio for valuesof Dwall for the primary e-like ring. For Dwall > 20 m

the S/B ratio changes from the average of 1.4 to 3.8 forevents with Erec 1.2 GeV, and for events with 2 GeV Erec < 4 GeV the S/B ratio essentially stays the same.

The large improvement in the S/B ratio for events withErec 1.2 GeV results from an increase in the number ofPMTs (pixels) in a Cherenkov ring. This improvementis significant as in the energy region Erec 1.2 GeV thecontribution from the NC events is reduced to a levelas low as that from the irreducible background. This im-provement, however, is not realized for events with 2 GeV

0

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G 5 m - 10 m

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L 25 m - 30 m

FIG. 17: The 0 detection efficiency as a function of the two

photon opening angle for three ranges of the distance fromthe 0 production vertex to the closest PMT surface in thedirection of0.

Erec < 4 GeV presumably because in this energy re-gion multi-pion events are the major background.

This observation is also true if the minimum distanceDwall is set at 10 or 15 m, although the improvement inthe S/B ratio is less than the case of the 20-m cut. Fora SK-I sized detector, this 20-m cut reduces the numberof the signal events by 41%. However, if the detector islarger, this loss of efficiency can be greatly reduced. In

other words, for a given detector size, the finer granu-larity, not necessarily the number of Cherenkov photonscollected by individual PMT, improves the S/B ratio.

XIII. CONCLUSION

For the baseline of 2,540 (1,480) km the detection ef-ficiency of the signal events using the SK-I cuts only isfound to be 0.3610.003 (0.373 0.003) and the final ef-ficiency with the further 40% cut on the log-likelihoodratio is found to be 0.1450.002 (0.1490.002). The de-tection efficiency of the background-1 events using theSK-I cuts only is found to be 0.0540.001 (0.0590.001)and the final efficiency with the further 40% cut onthe log-likelihood ratio is found to be 0.00250.0002(0.00260.0003). The 40% cut on the log-likelihoodshould be considered as a guidance and the actual cutshould be optimized after a detailed study of figure ofmerit that depends on the experimental design includingthe neutrino beam properties of a given experiment.

We have demonstrated that a large water Cherenkovdetector can be used to detect efficiently the signal eventsby es from the neutrino oscillation e while keep-


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ing the background at a reasonably low level in a VLBNOexperiment for the baseline of over 1,400 km with a wide-band beam.

Acknowledgments

The authors gratefully acknowledge the work of the

Super-Kamiokande collaboration in developing the mostof tools used for this analysis. However, the result and

its interpretation are responsibility of the authors ofthis paper. The work is partially supported by fund-ing from Stony Brook University Office of the Vice Pres-ident for Research, DOE grant DEFG0292ER40697 atStony Brook University and DOE contract DE-AC02-98CH10886 at Brookhaven National Laboratory, andthe City University of New York PSC-CUNY ResearchAward Program at Borough of Manhattan Community

College/the City University of New York.

[1] D. Beavis et al., Report of the BNL neutrino workinggroup, BNL-69395, hep-ph/0211001; M. V. Diwan et al.,Phys. Rev. D68 (2003) 012002, also hep-ex/0303081.

[2] M. Shiozawa, Nucl. Instr. Meth. A433 (1999) 240.[3] Y. Ashie et al., Phys. Rev. D71 (2005) 112005.[4] C. K. Jung, Feasibility of a Next Generation Under-

ground Water Cherenkov Detector: UNO, Talk atNNN99, Stony Brook, New York, 1999, available at

arXiv:hep-ex/0005046. Also see the expression of inter-est and the proposal by the UNO collaboration available athttp://nngroup.physics.sunysb.edu/uno/publications.shtml

[5] B. Viren. http://www.phy.bnl.gov/trac/nuosc/.[6] Dziewonski and Anderson, Preliminary Reference Earth

Model, Phys. Earth. Planet. Int., 25, 297-356 (1981).[7] I. Mocioiu, R. Shrock, Matter Effects on Neutrino Oscilla-

tions in Long Baseline Experiments, Phys.Rev. D62 (2000)053017 and I. Mocioiu, R. Shrock, Neutrino Oscillationswith Two m2 Scales, JHEP 0111, (2001) 050.

[8] T. Barszczek, Ph.D Thesis, University of Cal-ifornia, Irvine, unpublished (2005). Avail-able at the Super-Kamiokande website athttp://www-sk.icrr.u-tokyo.ac.jp/sk/pub/index.html.

[9] Y. Itow et al., The JHF-Kamioka neutrino project, KEK

report 2001-4, ICRR-report-477-2001-7, TRI-PP-01-05,hep-ex/0106019 (2001); C. Yanagisawa, Background Un-derstanding and Supression in Very Long Baseline Neu-trino Oscillation Experiments with Water Cherenkov De-tectors Talk at NNN05, Aussois, France, 2005, availableat http://nnn05.in2p3.fr/schedule.html/.
http://arxiv.org/abs/hep-ph/0211001http://arxiv.org/abs/hep-ex/0303081http://arxiv.org/abs/hep-ex/0005046http://nngroup.physics.sunysb.edu/uno/publications.shtmlhttp://www.phy.bnl.gov/trac/nuosc/http://www-sk.icrr.u-tokyo.ac.jp/sk/pub/index.htmlhttp://arxiv.org/abs/hep-ex/0106019http://nnn05.in2p3.fr/schedule.html/http://nnn05.in2p3.fr/schedule.html/http://arxiv.org/abs/hep-ex/0106019http://www-sk.icrr.u-tokyo.ac.jp/sk/pub/index.htmlhttp://www.phy.bnl.gov/trac/nuosc/http://nngroup.physics.sunysb.edu/uno/publications.shtmlhttp://arxiv.org/abs/hep-ex/0005046http://arxiv.org/abs/hep-ex/0303081http://arxiv.org/abs/hep-ph/0211001

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