A neutrinoless double beta decay master formula from effective field theory

TL;DR

This paper develops a comprehensive effective field theory framework to connect high-energy lepton-number-violating operators to neutrinoless double beta decay rates, incorporating nuclear physics and QCD effects.

Contribution

It provides the first complete master formula for $0 uetaeta$ decay rates from dimension-nine LNV operators, including all interference effects and matching to specific models.

Findings

Derived a master formula linking high-energy LNV operators to decay rates.

Showed the importance of short-range operator enhancements in certain cases.

Demonstrated the applicability of the formula to the minimal left-right-symmetric model.

Abstract

We present a master formula describing the neutrinoless-double-beta decay ($0\nu\beta\beta$) rate induced by lepton-number-violating (LNV) operators up to dimension nine in the Standard Model Effective Field Theory. We provide an end-to-end framework connecting the possibly very high LNV scale to the nuclear scale, through a chain of effective field theories. Starting at the electroweak scale, we integrate out the heavy Standard Model degrees of freedom and we match to an $SU(3)_c\otimes U(1)_{\mathrm{em}}$ effective theory. After evolving the resulting effective Lagrangian to the QCD scale, we use chiral perturbation theory to derive the lepton-number-violating chiral Lagrangian. The chiral Lagrangian is used to derive the two-nucleon $0\nu\beta\beta$ transition operators to leading order in the chiral power counting. Based on renormalization arguments we show that in various cases short-range two-nucleon operators need to be enhanced to leading order. We show that all required nuclear matrix elements can be taken from existing calculations. Our final result is a master formula that describes the $0\nu\beta\beta$ rate in terms of phase-space factors, nuclear matrix elements, hadronic low-energy constants, QCD evolution factors, and high-energy LNV Wilson coefficients, including all the interference terms. Our master formula can be easily matched to any model where LNV originates at energy scales above the electroweak scale. As an explicit example, we match our formula to the minimal left-right-symmetric model in which contributions of operators of different dimension compete, and we discuss the resulting phenomenology.