# Neutrinoless double beta decay in effective field theory

## TL;DR

This paper develops an effective field theory framework to connect high-scale lepton-number-violating operators with neutrinoless double beta decay observables, incorporating operator evolution, chiral perturbation theory, and many-body methods.

## Contribution

It provides a systematic approach to relate effective operators at high scales to the neutrinoless double beta decay half-life, highlighting the importance of a new contact interaction for consistent renormalization.

## Key findings

- Derived the lepton-number violating potential using chiral perturbation theory.
- Showed the necessity of including a new contact interaction at leading order.
- Connected high-scale operators to observable decay half-life.

## Abstract

We discuss the contributions of lepton-number-violating sources to neutrinoless double beta decay ($0\nu\beta\beta$). Assuming that these sources arise at scales well above the electroweak scale, they can be described within an effective field theory. Here, we outline the steps required to express the $0\nu\beta\beta$ half-life in terms of the effective interactions, focusing on the dimension-five operator that induces a Majorana mass for the neutrinos. This process involves the evolution of the operators down to scales of a few GeV where they can be matched onto Chiral Perturbation Theory. The resulting Chiral Lagrangian can then used be to derive the lepton-number violating potential, which, in combination with many-body methods, gives the $0\nu\beta\beta$ half-life. We will show that consistent renormalization requires the inclusion of a new contact interaction at leading order in this potential. We also briefly comment on the constraints that can be set on the operators appearing beyond dimension five.