New types of instability and CP violation in electroweak theory

TL;DR

This paper investigates new types of instabilities and CP violation in electroweak theory caused by small neutrino masses, revealing potential sources of lepton asymmetry independent of the standard quark mixing CP phase.

Contribution

It extends singularity analysis to electroweak theory, identifying novel CP violating terms and instabilities related to neutrino masses and background gauge fields.

Findings

Effective Lagrangian exhibits a logarithmic singularity proportional to neutrino mass.

New CP violating terms proportional to background gauge fields are identified.

At finite temperature, a more singular behavior with CP violation is found.

Abstract

It is known that the Schwinger mechanism of vector-like QED theory is afflicted by a logarithmic singularity under background electromagnetic field due to a hypothetical massless charged fermion. We extend singularity analysis to a more realistic case of the chiral electroweak theory, to show that the effective lagrangian under background gauge field at zero temperature exhibits a similar instability proportional to $\ln (1/m_{\nu}^2)$ with $m_{\nu}$ a small neutrino mass. Moreover, the effective lagrangian of chiral fermion loop contains CP violating pieces proportional to background gauge fields in odd powers of $\vec{E}_Z\cdot\vec{B}_Z$ or $(\vec{E}_{W^+}\cdot\vec{B}_{W^-}+ \vec{E}_{W^-}\cdot\vec{B}_{W^+})/2 $. This brings in a new source of CP violation and time-reversal symmetry violation in the standard particle theory independent of the Kobayashi-Maskawa phase of quark mass mixing matrix. The effective action in thermal equilibrium at finite temperature $T$ is then calculated under background SU(2)$\times $U(1) gauge fields in the spontaneously broken phase. An even more singular power-law behavior $\propto (m_{\nu} T)^{-5/2}$ is found and it contains CP violating term as well. The case of Majorana neutrino satisfies almost all necessary conditions to generate a large lepton number asymmetry, though not necessarily convertible to a baryon asymmetry due to lower cosmic temperatures at which this may occur.