QCD running in neutrinoless double beta decay: Short-range mechanisms

TL;DR

This paper calculates QCD corrections to short-range operators in neutrinoless double beta decay, refining limits on heavy particle exchange contributions by including operator running effects.

Contribution

It provides the first comprehensive calculation of leading order QCD corrections and RGE running for all relevant dimension-9 operators in $0 uetaeta$ decay.

Findings

QCD running significantly alters limits on operator coefficients.

Operator mixing can change limits by up to two orders of magnitude.

Results enable more accurate constraints when combined with experimental data.

Abstract

The decay rate of neutrinoless double beta ($0\nu\beta\beta$) decay contains terms from heavy particle exchange, which lead to dimension-9 (d=9) six fermion operators at low energies. Limits on the coefficients of these operators have been derived previously neglecting the running of the operators between the high-scale, where they are generated, and the energy scale of double beta decay, where they are measured. Here we calculate the leading order QCD corrections to all possible d=9 operators contributing to the $0\nu\beta\beta$ amplitude and use RGE running to calculate 1-loop improved limits. Numerically, QCD running changes limits by factors of the order of or larger than typical uncertainties in nuclear matrix element calculations. For some specific cases, operator mixing in the running changes limits even by up to two orders of magnitude. Our results can be straightforwardly combined with new experimental limits or improved nuclear matrix element calculations to re-derive updated limits on all short-range contributions to $0\nu\beta\beta$ decay.