1. L/E analysis of the atmospheric neutrino data from Super-Kamiokande
Itaru Higuchi
ICRR
for Super-Kamiokande collaboration
ICRC Aug.5, 2005

2. Motivation
Other models can explain zenith angle dependent muon deficit. How can we distinguish oscillation from other hypotheses ?
Muon neutrino disappearance probability as a function of neutrino flight length L over neutrino energy E was studied to distinguish neutrino oscillation from other hypotheses.
A dip in the L/E distribution was observed in the data from Super-Kamiokande-I during 1489 live-days exposure.
We report preliminary result from SK-II during 627 days live-days exposure.

3. Use events with high resolution in L/E
Survive probability
Dm2L
Neutrino oscillation :
Pmm = 1 – sin22qsin2( ) E m L
Neutrino decay :
Pmm = (cos2q + sin2q x exp(– ))2 2t E 1 L
Neutrino decoherence :
Pmm = 1 – sin22q x (1 – exp(–g )) 2 E
Use events with high resolution in L/E
The first dip can be observed
Direct evidence for oscillations
Strong constraint to oscillation
parameters, especially Dm2 value

4. Event samples in L/E analysis
FC (tracks are contained inside the ID)
Single-ring , μ-like
Multi-ring , μ-like
observed charge / expectation from through-going
PC (deposits visible energy in the OD)
OD stopping
OD through-going
Classify PC events using OD charge
OD through-going MC
OD stopping
OD through going
OD stopping MC

5. Reconstruction of E and L
Neutrino energy
Neutrino direction En
Eobserved
Eobserved  En
Zenith angle  Flight length
Neutrino energy is reconstructed from observed energy using relations based on MC simulation
Neutrino flight length is estimated from zenith angle of particle direction

6. L/E resolution cut Select events with high resolution in L/E
Full oscillation
1/2 oscillation
Bad L/E resolution for
horizontally going events  due to large dL/dcosq
low energy events  due to large scattering angle
D(L/E)=70%

7. Event summary of L/E analysis
SK-I 1489 days
SK-II 627 days FC
Data MC CC nm
Data MC CC nm
single-ring
multi-ring
stopping
through-going
(98.3%)
(94.2%)
(95.4%)
(99.2%)
(98.6%)
(93.6%)
(94.4%)
(99.2%) PC
Total

8. L/E in atmospheric neutrino data
Mostly upward
Mostly upward
SK-I FC+PC
SK-II FC+PC
Preliminary
Null oscillation MC
Null oscillation MC
Mostly downward
Mostly downward
Best-fit expectation
Best-fit expectation

9. L/E in atmospheric neutrino data
SK-I FC+PC
SK-II FC+PC
Best fit expectation w/ systematic errors
Best fit expectation w/ systematic errors
Preliminary
First dip is observed as expected from neutrino oscillation

10. Constraint to neutrino oscillation parameters
SK-I
SK-II
Preliminary
Best fit result
Dm2=2.4x10-3,sin22q=1.00
c2min=37.8/40 d.o.f
(sin22q=1.02, c2min=37.7/40 d.o.f)
Dm2=2.6x10-3,sin22q=1.00
c2min=54.8/40 d.o.f
(sin22q=1.02, c2min=54.7/40 d.o.f)
1.9x10-3 < Dm2 < 3.0x10-3 eV2
0.90 < sin22q at 90% C.L.
1.8x10-3 < Dm2 < 4.0x10-3 eV2
0.83 < sin22q at 90% C.L.

11. Tests for neutrino decay & decoherence
SK-I
SK-II
Oscillation
Decay
Decoherence
Dc2 = c2decay - c2osc
　　 =11.4(3.4σ)
Dc2 = c2decoherence - c2osc
=14.6(3.8 σ)
Dc2 = c2decay - c2osc
　　 =7.9(2.8σ)
Dc2 = c2decoherence - c2osc
=8.7(2.9 σ)
Preliminary
cannot be explained by alternative hypotheses

12. Next step : combine SK-I and SK-II
Conclusions
Measurement of L/E dependence of flavor transition probability
First dip was observed as expected from neutrino oscillation
 cannot be explained by alternative hypotheses
 gives strong constraint to neutrino oscillation parameters
The results from SK-I and SK-II agree well.
Next step : combine SK-I and SK-II

14. Zenith angle distributions
Motivation
Zenith angle distributions
SK-I
m-like sub-GeV < 400 MeV
m-like sub-GeV > 400 MeV
m-like multi-GeV PC
m-like sub-GeV multi-ring
m-like multi-GeV multi-ring
Oscillation
Decay
Decoherence
Other models can explain zenith angle dependent muon deficit.
How can we distinguish oscillation from other hypotheses ?

15. Angular resolutions

16. Lepton scattering angle as a function of momentum
ne CC elastic
Low energy leptons have
weak angular correlation
to the parent n direction. 0o
180o
nm CC elastic 0o
3000 (MeV/c)

17. Energy and path length reconstruction
Momentum weighted vector sum  Reconstructed neutrino direction
Momentum sum  Eobserved
Resolution of neutrino direction
FC single-ring En
Eobserved  En
Eobserved
Resolution of neutrino energy
 flight length
Due to large dL/dcosq near horizon, events near horizon have bad L/E resolution

18. Definition of c2 Poisson with systematic errors
Nobs : observed number of events
Nexp : expectation from MC
ei : systematic error term
si: sigma of systematic error
Various systematic effects in detector, flux calculation and neutrino interaction are taken into account

19. Constraint to neutrino oscillation parameters
Preliminary
1.9x10-3 < Dm2 < 3.0x10-3 eV2
0.90 < sin22q at 90% C.L.
Dm2=2.4x10-3,sin22q=1.00
c2min=37.8/40 d.o.f
(sin22q=1.02, c2min=37.7/40 d.o.f)
Consistent with standard zenith angle analysis
L/E analysis
Zenith angle analysis
90% allowed regions

20. Tests for neutrino decay & decoherence for SK-I
Oscillation
Decay
Decoherence
c2min=37.8/40 d.o.f
c2min=49.2/40 d.o.f  Dc2 =11.4
c2min=52.4/40 d.o.f  Dc2 =14.6
3.4 s to n decay
3.8 s to n decoherence
First dip observed in data cannot be explained by alternative hypotheses

21. Tests for neutrino decay & decoherence for SK-II
Preliminary
Oscillation
Decay
Decoherence
c2min=54.8/40 d.o.f
c2min=62.8/40 d.o.f  Dc2 =7.9
c2min=63.5/40 d.o.f  Dc2 =8.7
2.8 s to n decay
2.9 s to n decoherence
First dip observed in data cannot be explained by alternative hypotheses

22. Sensitivities to alternative models
n decoherence
obtained Dc2
Consistent with the expectation
n decay
Assumption
nm nt
2 flavor oscillation
(Dm2=2.0x10-3eV2,sin22q=1.0)
L/E resolution cut at 70%

23. SK-I chi2 dist

24. SK-II chi2 dist

25. SK-I SK-II Neutrino decay χ2min,Δχ2 χ2min = 49.1/40 d.o.f
Neutrino decoherenceχ2min,Δχ2
SK-I
χ2min = 49.1/40 d.o.f
Δχ2 = 11.3/40 d.o.f
(3.4 standard deviations)
χ2min = 52.4/40 d.o.f
Δχ2 = 14.5/40 d.o.f
(3.8 standard deviations)
SK-II
χ2min = 62.8/40 d.o.f
Δχ2 = 7.9/40 d.o.f
(2.8 standard deviations)
χ2min = 63.5/40 d.o.f
Δχ2 = 8.7/40 d.o.f
(2.9 standard deviations)

26. Results from the oscillation analysis on the SK-I and SK-II
χ2 at (sin22θ,Δm2)
include unphysical region
90% C.L. allowed region
SK-I
37.9/40 d.o.f
(1.00,2.4×10-3eV2)
(1.00,2.4×10-3eV)
sin22θ> 0.9
1.9<Δm2<3.0×10-3eV2
SK-II
54.8/40 d.o.f
(1.00,2.6×10-3eV)
sin22θ> 0.83
1.8<Δm2<4.0×10-3eV2