http://arxiv.org/abs/2209.00166
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.
M. Yoshimura
Fri, 2 Sep 22
48/62
Comments: 11 pages, 1 figure