Baryon- and lepton-number violation by electroweak instantons

Abstract

We make a quantitative study of instanton-induced baryon- and lepton-number-violating processes in an SU(2) x U(1) electroweak gauge theory at zero and finite temperatures (in the ''dilute-instanton-gas'' approximation). As an example we consider a simplified model involving only the proton, neutron, electron, and electron neutrino. At zero temperature the total cross sections for p+n..-->.. e-bar+nu-bar and eleven other similar reactions are of order s x 10/sup -195/ cm/sup 2/, where s is the total center-of-momentum energy squared in GeV/sup 2/. The neutron decays via n..-->..p-bar+e-bar+nu-bar with a lifetime of the order 10/sup 146/ years. The cross sections and neutron decay width decrease with temperature because color-electric-charge screening reduces the self-dual-instanton density at finite temperature. At high temperature the cross sections (for a given s) and neutron decay width fall off as T/sup -47/3/ in this simplified model. It is suggested that correctly treating the instanton gas as very dense (as discussed by Berg, Luscher, and Stehr) and including finite-energy tunneling solutions could increase the predicted reaction rates.