An effective field theory for non-relativistic Majorana neutrinos

TL;DR

This paper develops an effective field theory for non-relativistic Majorana neutrinos, enabling simplified calculations of thermal corrections relevant for models beyond the Standard Model, such as leptogenesis.

Contribution

It introduces a novel effective field theory framework for non-relativistic Majorana neutrinos, analogous to heavy-quark effective theory, facilitating thermal correction computations.

Findings

Thermal corrections are restricted by symmetry and power counting.

The final thermal correction results agree with recent independent calculations.

The framework applies broadly to models with non-relativistic Majorana fermions.

Abstract

Heavy Majorana neutrinos enter in many scenarios of physics beyond the Standard Model: in the original seesaw mechanism they provide a natural explanation for the small masses of the Standard Model neutrinos and in the simplest leptogenesis framework they are at the origin of the baryonic matter of the universe. In this paper, we develop an effective field theory for non-relativistic Majorana particles, which is analogous to the heavy-quark effective theory. Then, we apply it to the case of a heavy Majorana neutrino decaying in a hot and dense plasma of Standard Model particles, whose temperature is much smaller than the mass of the Majorana neutrino but still much larger than the electroweak scale. The neutrino width gets zero-temperature contributions that can be computed from in-vacuum matrix elements, and thermal corrections. Only the latter will be addressed. Symmetry and power counting arguments made manifest by the effective field theory restrict the form of the thermal corrections and simplify their calculation. The final result agrees with recent determinations obtained with different methods. The effective field theory presented here is suitable to be used for a variety of different models involving non-relativistic Majorana fermions.