1. L/E analysis of the atmospheric neutrino data from Super-Kamiokande
Itaru Higuchi
ICRR
for Super-Kamiokande collaboration
ICRC Aug, 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 flight length 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 results
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. Constraint to neutrino oscillation parameters
SK-I
SK-II
Preliminary
Best fit results
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.

12. Constraint to neutrino oscillation parameters
SK-I
SK-II
Preliminary
Best fit results
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.

13. 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

14. 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