Have Superkamiokande Really Measured the Direction of the Atmospheric Neutrinos which Produce Fully Contained Events and Partially Contained Events ?

Quasi Elastic Scattering (QEL) is the dominant source for producing both Fully Contained Events and Partially Contained Events in the Superkamiokande(SK) detector for the atmospheric neutrinos, in the range 0.1 GeV to 10 GeV. In the analysis of SK events, it is assumed that the direction of the incident neutrino is the same as that of the detected charged lepton. In the present letter, we derive the distribution function for the scattering angle of the charged leptons, their averaged scattering angle and their standard deviation due to QEL. Then, it is shown that the SK assumption for the scattering angle of the charged leptons in the QEL is not valid. Further, we examine the influence of the azimuthal angle of the charged leptons over their zenith angle. As the result, we conclude that the zenith angle distribution of the neutrino under the SK assumption does not reflect the real zenith angle distribution of the atmospheric neutrino which produces Fully Contained Events and Partially Contained Events. This result has clear implication for attempts to detect neutrino oscillations from the analyses of Fully Contained Events and Partially Contained Events in Superkamiokande.