K2K oscillation analysis using the spectrum information.

The oscillation analysis using the spectrum information of SK, ND and PIMON was performed on the K2K experiment. The basic strategy of the analysis is that we compare total number of events and spectrum shape that were observed at SK and their expectation based on near detector system. Several new progress have been made. The change from the last collaboration meeting are listed below.

1. The flux at near detector site
a) KT spectrum fit method has not been changed from last collaboration meeting.
b) SciFi spectrum fit has changed by handling the threshold and the energy scale uncertainties.
c) KT and SciFi data are merged to be fitted simultaneously to measure the  spectrum and the nonQE/QE ratio.
d) observed harder Q^2 distribution in both KT and SciFi data can be explained by changing neutrino interaction model. The phenomenologically tuned MC is characterized by
   QE  : MA=1.01 -> 1.11
   1pi : MA=1.01 -> 1.21
   coherent pi model by Marteau
   multi-pi : (pre-)scaling variable hep-ex/0203009
   NOTE THE EFFECT TO THE OSCILLATION ANALYSIS IS VERY SMALL BY CHANGE OF MODEL.
The best fit result with merged fit with 'tuned' NEUT is
f=ratio of fitted flux/MC
chi2=227 for 197 dof
f(Enu<500) = 1.3+-0.5
f(500<Enu<750) = 1.02+-0.12
f(750<Enu<1000) = 1.01+-0.09
f(1000<Enu<1500) = 1 (fixed)
f(1500<Enu<2000) = 0.95+-0.07
f(2000<Enu<2500) = 0.96+-0.08
f(2500<Enu<3000) = 1.18+-0.19
f(3000<Enu) = 1.07+-0.20
nonQE/QE= 0.93+-0.20            This error of 0.20 is assigned based on the disagreement of SciFi and KT results.
Comment: This tuning is still preliminary and need more work of study interaction model. BUT again oscillation analysis with various parameters (MA(QE)=1.01-1.11, MA(1PI)=1.01-1.5, structure  function GRV94-modified GRV94) showed very small difference.

2.SK oscillation analysis
We performed the oscillation analysis by dlogL method, using SK data and the error matrix estimated by ND, PIMON and MC. The likelihood has been calculated  by two methods. One is that log likelihood with additional systematic terms. Systematic error parametes are adjusted to mixmize entire log likelihood at each (dm^2, sin^22th) to find the best fit. This method was used in CDF (Phys. Rev. D61, 072005 (2000) 11) etc. The oscillation analysis on SK atm/pd is not maximum likelihood mathod but bined-chi^2 method with similar treatment of systematic term. The other method is based on MC generation of L; the systematic parameters are generated numerically around the mean values according to the error matrix. The mean was assign as L at that (dm^2, sin^22th) (Nucl. Instrum. Meth. A411:153-158, 1998) This method was used in L3 etc. Since there is no a priori reason which is right, we chose to present both methods to outside.  On both analysis, the data disagree with the MC expectation w/o the neutrino oscillation. The oscillated reproduce data well.
Goodness of fit for best  (obtained by KS-test for 1-ring mu-like reconstructed Enu) are as follows,
               analysis 1           analysis 2
# of event                             82%
shape              79%                93%
# + shape                              50%
The null oscillation probability for each analysis are as follows,
                  analysis 1                analysis 2
# of events      1.3%                        0.7%
shape            15.7% (1.0 ,3.0E-3)   14.3% (1.0 ,3.16E-3)  (physical)
                           (1.09,3.0E-3)           (1.05,3.16E-3)  (unphysical)
# + shape         0.7% (1.0 ,2.8E-3)    0.4% (1.0 ,2.66E-3)
                            (1.03,2.8E-3)          (1.05,2.66E-3)
where, null oscillation probability is calclated from the difference of log likelihood from the best fit point. The main improvement of the sensitivity for # of events analysis comes from the improvement of Far/Near ratio and the spectrum by the study on the correlation and so on. From this table, The null oscillation probability is less than 1%.
The allowed region are obtained by both analysis. Both # of events analysis and shape analysis are consistent with SK atmospheric neutrino oscillation results. Again, results of both analysis (1 and 2) agree well.

Quick summary of official statement
(1) null oscillation probability
    "less than 1%"
(2) Best fit point
    "(sin^22th, Dm^2)=(1.0,2.7E-3)

Link for each analysis
KT spectrum study
SciFi spectrum study
merged study
oscillation analysis by T.Kobayashi
oscillation analysis by C.Walter