Deflected angles of muons induced by cosmic ray neutrino-nucleon reactions

Cosmic ray neutrinos coming from astrophysical objects such as CygX-3 come to the earth, penetrate into the great depth and induce muons which are detected as up going muons. High energy muons retain the same direction of incident neutrinos, so that the source is seen within the resolution angle of the detector. However low energy limit of the search for the neutrino source is determined by the deflected angle θ between the incident neutrino and the muon induced by inclusive charged current neutrino-nucleon reaction. Therefore it is necessary to evaluate in advance this angle as precisely as possible before the detector is designed. <θ> and <θ2>1/2 are calculated as a function of neutrino energy on the basis of quark-parton model. A brief discussion is given. (author)