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)×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 $p+n\to \overline{e}+\overline{\nu }$ and eleven other similar reactions are of order $s\times {10}^{-195\mathrm{}}$ ${\mathrm{cm}}^2$, where $s$ is the total center-of-momentum energy squared in Ge${\mathrm{V}}^2$. The neutron decays via $n\to \overline{p}+\overline{e}+\overline{\nu }$ with a lifetime of the order ${10}^{146}$ 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 $T^{-\frac{47}{3}}$ 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.