Self-consistent high-energy scattering of zero-mass leptons: the coupled-channel case

Abstract

The method devised in a preceding article for calculating a consistent high-energy behavior of neutrino scattering due to neutrino exchange is extended to the case of two coupled massless fermions. It is argued that the two fermions either could be the two types of neutrinos, V_e and V_μ or could even be massive leptons like the electron, as long as the mass is small compared to 1/√G. If we call the two particles a and b, it is shown that the a-a, a-a̅ , b-b, and b-b̅ total cross sections, due to the exchange of aa̅ and bb̅ pairs, approach constant values as the energy tends to infinity. It is further shown that the a-a and a-a̅ cross sections approach one another, as do the b-b and b-b̅ cross sections. On the other hand, the a-b and a-b̅ cross sections vanish at high energies.