Effect of Intermediate Vector Mesons on Neutrino Production of Lepton Pairs

Abstract

The total cross section for the production of lepton pairs by the scattering of high-energy muon neutrinos and protons is calculated with an assumed weakly interacting vector meson $W$ which has an anomalous magnetic moment $\kappa$. We use a modified Weizsäcker-Williams approximation, with added correction terms which change the result about 50%. In addition to these correction terms, we keep $t^3$, the square of the four-momentum of the exchanged photon, in the denominator of the lepton propagators. This results in an additional deviation of 30% from the standard Weizsäcker-Williams approximation. The cross sections are calculated as a function of $\kappa$ for meson masses of 2.0, 2.5, and 3.0 BeV, and for neutrino energies above the threshold for $W$ production. Numerical results are presented for $\kappa =1\mathrm{}$, 0, -1. The cross sections for muon-pair and muon-electron production are equal, and larger by a factor of approximately ${10}^4$ than the equivalent cross sections in the four-fermion theory.