Cross section of monopole-induced Skyrmion decay.

Abstract

The inclusive process of monopole catalysis of proton decay (M+p\ensuremath{\rightarrow}M+${e}^{+}$+pions) is analyzed within the chiral-soliton (Skyrmion) approach proposed by Callan and Witten. Monopole-induced baryon decay is described in terms of an effective radial (1+1)-dimensional bosonic action for a coupled scalar chiral kink field (baryon) and scalar sine-Gordon field (lepton). We construct the initial data appropriate to a Skyrmion impinging on the monopole with fixed impact parameter and velocity \ensuremath{\beta} and integrate numerically the classical field equations in terms of a spatially discretized version of the action. The results show that baryon-number violation at the monopole suffers practically no suppression at the classical level. In particular, there is no sign of a crossover, in terms of some critical impact parameter, from a positron to a proton in the final state. The numerical calculations predict a time scale for baryon-number violation which supports a catalysis cross section of standard size \ensuremath{\sigma}\ensuremath{\simeq}1 mb/\ensuremath{\beta}.