CP violation in neutral lepton transition dipole moment

TL;DR

This paper investigates $CP$ violation effects in neutrino transition dipole moments within the Standard Model extended by right-handed neutrinos, revealing suppressed asymmetries in some decays but potentially large effects in heavy neutrino transitions.

Contribution

It provides a full one-loop calculation of neutrino electromagnetic form factors and introduces a formalism for $CP$ violation in neutrino oscillations applied to a minimal seesaw model.

Findings

$CP$ asymmetry in light neutrino decays is extremely suppressed (~10^{-17})

$CP$ asymmetry in heavy neutrino transition $N_2 o N_1 o u ext{ or } ext{photon}$ can reach order unity

Large $CP$ asymmetries (~10^{-5} to 10^{-3}) are achievable even with a single Dirac phase.

Abstract

The $CP$ violation in the neutrino transition electromagnetic dipole moment is discussed in the context of the Standard Model with an arbitrary number of right-handed singlet neutrinos. A full one-loop calculation of the neutrino electromagnetic form factors is performed in the Feynman gauge. A non-zero $CP$ asymmetry is generated by a required threshold condition for the neutrino masses along with non-vanishing $CP$ violating phases in the lepton flavour mixing matrix. We follow the paradiagm of $CP$ violation in neutrino oscillations to parametrise the flavour mixing contribution into a series of Jarlskog-like parameters. This formalism is then applied to a minimal seesaw model with two heavy right-handed neutrinos denoted $N_1$ and $N_2$. We observe that the $CP$ asymmetries for decays into light neutrinos $N\to \nu\gamma$ are extremely suppressed, maximally around $10^{-17}$. However the $CP$ asymmetry for $N_2 \to N_1 \gamma$ can reach of order unity. Even if the Dirac $CP$ phase $\delta$ is the only source of $CP$ violation, a large $CP$ asymmetry around $10^{-5}$-$10^{-3}$ is comfortably achieved.