Bloch-Nordsieck Violation in Spontaneously Broken Abelian Theories

TL;DR

The charge mixing allowed by symmetry breaking and the ensuing Bloch-Nordsieck violation are here analyzed in a few relevant cases and in particular for processes initiated by longitudinal gauge bosons.

Abstract

We point out that, in a spontaneously broken U(1) gauge theory, inclusive processes, whose primary particles are mass eigenstates that do not coincide with the gauge eigenstates, are not free of infrared logarithms. The charge mixing allowed by symmetry breaking and the ensuing Bloch-Nordsieck violation are here analyzed in a few relevant cases and in particular for processes initiated by longitudinal gauge bosons. Of particular interest is the example of weak hypercharge in the Standard Model where, in addition, left-right mixing effects arise in transversely polarized fermion beams.

Figures (1)

• Figure 1: Picture of radiative corrections to the overlap matrix in (a) the mass eigenstates basis and (b) the charge eigenstates basis, where off-diagonal matrix elements occur.