Upper bound on neutrino cross sections

Asymptotic bounds on the total cross sections of neutrino (weak) scattering processes are obtained. It is shown that the elastic neutrino-neutrino cross section obeys the following bound in the high energy region: sigma sub T (S) equals ImF(S,0)/S is less than or equal to const. (LogS) squared. Assumptions of analyticity, crossing, unitarity, polynomial boundaries, and a zero-condition on the absorptive part of the scattering amplitude, are used to obtain this bound.