Shoei NAKAYAMA (ICRR)for Super-Kamiokande Collaboration

December 9, 2004@ RCCN International Workshop

Effect of solar terms to23 determination in Super-Kamiokande

andimportant systematic errors

for future improvements

• There is no evidence for atmospheric e oscillation. sin2

13 is consistent with 0 in the present 3 flavor analysis.(m223,

sin2 23, sin2 13)

• After solar and KamLAND results, we can say that oscillation of low energy e should appear at some level even if sin2 13 = 0. (sub-leading oscillations driven by m2

12)

• We perform an oscillation analysis taking into account solar parameters (m2

12, sin2 212) and study their effects.

especially in determination of sin2 23

1. Motivation

The analyses in my talk choose

sin2 13 = 0

m212 = 8.3 x 10 -5 eV2

sin2 212 = 0.83 ( tan2 12 = 0.41 )

from KamLAND (@ NEUTRINO2004)

Oscillation effects in e-like events

Fosce = F0

e P(e e) + F0 P( e)F0

e ,F0flux w/o osc.

= F0e [ P(e e) + r P( e) ] r = F0

/ F0e : /e flux ratio

= F0e [ 1 – P2 + r cos2 23 P2 ] P2 = |Ae|2 : 2 transition

probability e in matter

driven by m212

(Fosce / F0

e) – 1 = P2 (r cos2 23 – 1)

screening factor for low energy (r ~ 2)

~ 0 if cos2 23 = 0.5 (sin2 23 = 0.5)

< 0 if cos2 23 < 0.5 (sin2 23 > 0.5)

> 0 if cos2 23 > 0.5 (sin2 23 < 0.5)

m212 = 8.3 x 10-5 eV2

sin2 212 = 0.82 , sin2 13 = 0 , sin2 23 = 0.5

E = 500 MeVcos = - 0.6

P(

e

e)

P(

e)

w/o matter effect

P( e)

solar : onsin2 13 = 0sin2 23 = 0.5

sub-GeV e-like zenith angle

sub-GeV e-like

m212 = 8.3 x 10-5 eV2

m223 = 2.5 x 10-3 eV2

sin2 212 = 0.82

sin2 23 = 0.4sin2 23 = 0.5sin2 23 = 0.6

X : zenith angleY : N_e (3 flavor) / N_e (2 flavor full-mixing)

(Pe :100 ~ 1330 MeV) (Pe :100 ~ 400 MeV) (Pe :400 ~ 1330 MeV)

Lepton scattering angle as a function of momentum

Low energy leptons haveweak angular correlationto the parent direction.

sub-GeV e-like momentum

sub-GeV e-like

m212 = 8.3 x 10-5 eV2

m223 = 2.5 x 10-3 eV2

sin2 212 = 0.82

sin2 23 = 0.4sin2 23 = 0.5sin2 23 = 0.6

X : electron momentum (MeV/c)Y : N_e (3 flavor) / N_e (2 flavor full-mixing)

sub-GeV -like zenith angle

sub-GeV -like

(P : 200 ~ 1330 MeV)

m212 = 8.3 x 10-5 eV2

m223 = 2.5 x 10-3 eV2

sin2 212 = 0.82

sin2 23 = 0.4sin2 23 = 0.5sin2 23 = 0.62 flavor (sin2 223 = 0.96)

X : zenith angleY : N_ (3 flavor) / N_ (2 flavor full-mixing)

(P : 200 ~ 400 MeV) (P : 400 ~ 1330 MeV)

sub-GeV /e ratio (zenith angle dependence)

sub-GeV P , e < 400 MeV P , e > 400 MeV

m212 = 8.3 x 10-5 eV2

m223 = 2.5 x 10-3 eV2

sin2 212 = 0.82

X : zenith angleY : Re (3 flavor) / Re (2 flavor full-mixing)

sin2 23 = 0.4sin2 23 = 0.5sin2 23 = 0.62 flavor (sin2 223 = 0.96)

Oscillation analysis with SK-I data

• Data set and analysis tools : same as the current standard 3 flavor analysis.

• Oscillation maps : m212 = 8.3 x 10-5 eV2

sin2 212 = 0.82

sin2 13 = 0

m223 = 10-3.2 ~ 10-2 eV2

sin2 23 = 0 ~ 1

2 dimensional analysis

• Find a 2min point : projection to the sin2 23 axis

deviation from the 2-3 full mixing ?

fixed valuesfrom KamLAND

same as thestandard analysis

fixed value

Result

2 distributionas a function of sin2 23

where m223 is chosen

to minimize 2

sub-GeV zenith angle distribution

sub-GeV /e ratio (zenith angle dependence)

What kind of systematic errors are importantfor future sin2 23 determination ?

• 44 systematic error parameters in the current standard 3 flavor analysis tools.

• Test with 20yr oscillated MC instead of observed data.

(sin2 23 = 0.4, 0.45, 0.55, 0.6 and m223 = 2.5 x 10-3 eV2)

• Reduce each systematic error one by one

down to ¼ of original

2 distribution with reduced systematic errors

true : sin2 23 = 0.4

Reducing interaction relatedsystematic errors is most importantto distinguish sin2 23 = 0.4 fromsin2 23 = 0.6.

Flux errors also give big effects.

2 contribution from sub-samplesno change in systematic errorsall systematic errors 1/4

Sub-GeV samples play an important role in determination ofthe sign of the sin2 23 deviation. (in case of sin2 13 = 0)

2 distribution for various true sin2 23

true : sin2 23 = 0.55 true : sin2 23 = 0.6true : sin2 23 = 0.45

Which systematic error should be reduced ? (1)

Flux sys. errors Flux sys. errors

Which systematic error should be reduced ? (2)

Flux, interaction sys. errors interaction sys. errors

Which systematic error should be reduced ? (3)

interaction sys. errors SK related sys. errors

Which systematic error should be reduced ? (4)

SK related sys. errors

Systematic uncertainties in flux ratios

3 % error for E < 5 GeV

flavor ratio anti- / ratios

5 % error for E < 10 GeV

Systematic uncertainties in flux up/down ratio

P<400MeV/c e-like 0.5%

P<400MeV/c -like 0.8%

P>400MeV/c e-like 2.1%

P>400MeV/c -like 1.8%

Systematic uncertainties in MA

for QE and single- production models

lepton scattering angle lepton scattering angle

R(M

A=

1.01

/MA=

1.11

)

R(M

A=

1.01

/MA=

1.11

)

MA = 1.11 MA = 1.01

Sub-GeV single-ring e-like(Pe<400MeV/c)

Sub-GeV single-ring e-like(Pe>400MeV/c)

MA = 1.11 MA = 1.01

Systematic uncertainties in nuclear effectsin QE cross section calculation

e e

Neut relativistic Fermi gas model with flat momentum dist.

Singh and Oset’s model

QE cross section

Other important systematic errors

• primary cosmic ray energy spectral index

0.05 uncertainty ( >100GeV )

• NC/CC cross section ratio

+- 20 %

• Nuclear effect in 16O (absorption, charge exchange, inelastic scattering)

+- 30 %

• Hadron simulation

difference between CALOR and FLUKA

• Energy calibration for FC events

+- 2 %

100GeV

Reduce 7 dominant systematic errors at once

/ e

anti-e / e , anti- /

flux up / down

MA in QE, single-QE cross section modelNC / CC

½¼

½¼

true : sin2 23 = 0.4 true : sin2 23 = 0.45

Summary

• Effects of solar oscillation parameters on atmospheric oscillations have been studied.

• Future atmospheric oscillation analysis with 1-2 parameters might provide unique information on the sign of the sin2 23 deviation (if exists).

• It’s important to reduce systematic uncertainties on interaction models and flux calculations for low energy (Sub-GeV) neutrinos.

Supplement

Paolo Lipari @NOON2004

Paolo Lipari @NOON2004

Smirnov

m212 = 7.3 x 10-5 eV2

sin2 212 = 0.82

P2

sub-GeV /e ratio (zenith angle dependence) contd.

Sub-GeV (P,e < 400 MeV/c) Sub-GeV (P,e > 400 MeV/c)

Systematic errors in flux calculations (Up/down asymmetry)

Honda Fluka Bartol difference

P<400MeV/c e-like 1.018 1.027 1.024 -0.5% (fluka)

P<400MeV/c -like 1.030 1.047 1.038 -0.8% (fluka)

P>400MeV/c e-like 1.051 1.096 1.059 -2.1% (fluka)

P>400MeV/c -like 1.040 1.079 1.051 -1.8% (fluka)

Multi-GeV e-like 0.997 1.028 0.990 -1.5% (fluka)

Multi-GeV -like 1.003 1.019 1.019 -0.8% (bartol,fluka)

PC 0.995 1.005 0.990 -0.5% (fluka)

Sub-GeV multi-ring -like 1.005 1.022 1.008 -0.8% (fluka)

Multi-GeV multi-ring -like 0.994 1.008 0.990 -0.7% (fluka)

Compare Honda2003 flux to Fluka2003 and Bartol2003 flux calculations. Take the difference to be the systematic errors.

Predictions of up/down ratio

Up-stop

Up-stop

Up-through

Up-throughProduced from K

Produced from Fraction of neutrinos produced from K

Change the fraction of K by 20%

Systematic error

Systematic uncertainties inK/ ratio in flux calculation

Systematic uncertainty in primary cosmic ray energy spectrum index

e

e

Neutrino flux produced by primary cosmic ray with

> 1, 10, 100 1000 GeV

Estimate the difference of neutrino flux caused by the E (>100GeV) in primary spectrum

Systematic uncertainty

Note: for <100GeV energy spectrum of primary cosmic ray has been measured accurately by BESS and AMS

Systematic uncertainty 100GeV

Systematic uncertainties in MA for QE and single- production(angular difference between neutrino and outgoing lepton)

MA=1.01 / MA=1.11 (q2 correction)

Reconstructed (e)

-like -

251MeV

-like 251 -

400MeV

-like 400 -

630MeV

-like 630 -

1000MeV

-like

1000MeV -

e-like -

251MeV

e-like 251 -

400MeV

e-like 400 -

630MeV

e-like 630 -

1000MeV

e-like 1000MeV -

Systematic uncertainties in nuclear effectsin QE cross section calculation

e e

Neut relativistic Fermi gas model with flat momentum dist.

independent

Singh and Oset’s model

(QE)Singh / (QE)Neut

A different point fromthe current standard 3 flavor analysis

• Our standard 3 flavor analysis uses an averaging method for the last propagation in mantle.

• At the present moment, this analysis does not use this averaging method. The 20-neutrino-energies method are used for all MC events.

Averaged probability in 3-flavor oscillation

Simple in 2-flavor case, but not in 3-flavor case 2-flavor vacuum oscillation : 1-sin22qsin2(Dm2E/L)

→ 1-1/2·sin22q due to matter effect and multi-layer density in the

earth, oscillation probability is very difficult to be solved analytically

We derived averaged transition matrix by following relation:

We applied average method for last propagation in the mantle. In the core layers, there is known enhancement by combination of multiple core layers and we don’t take average in the core region.

)2(

,2

)2/,(),(

mantle

mantlemantle

L

LETLETT

Lmantle

Lmantle

Probability calculation

• recycle MC events to effectively increase MC statistics• for each MC event, select 20 MC events with same event type which observed energy is closest to that of original MC event.• use 1(original)+20(closest) neutrino energy in calculations of oscillation probability for the original MC event.

• neutrino production height in the atmosphere

• updated production height distribution based on HONDA3D calculation• 20 probability calculations using 20 neutrino production height, and then take average of the probabilities.