QCD Corrections and Long-Range Mechanisms of neutrinoless double beta decay

TL;DR

This paper investigates QCD corrections to long-range mechanisms of neutrinoless double beta decay, finding that these corrections are less significant than for short-range mechanisms but still improve the robustness of theoretical predictions.

Contribution

It provides the first detailed analysis of QCD corrections for long-range mechanisms, highlighting the absence of operator mixing due to nuclear correlations and color invariance.

Findings

QCD corrections to LRM are at most 60% depending on the operator.

No operator mixing occurs in LRM due to nuclear correlations and color invariance.

QCD running enhances the robustness of $0 uetaeta$ decay predictions.

Abstract

Recently it has been demonstrated that QCD corrections are numerically important for short-range mechanisms (SRM) of neutrinoless double beta decay ($0\nu\beta\beta$) mediated by heavy particle exchange. This is due to the effect of color mismatch for certain effective operators, which leads to mixing between different operators with vastly different nuclear matrix elements (NMEs). In this note we analyze the QCD corrections for long-range mechanisms (LRM), due to diagrams with light-neutrino exchange between a Standard Model (V-A)$\times$(V-A) and a beyond the SM lepton number violating vertex. We argue that in contrast to the SRM in the LRM case, there is no operator mixing from color-mismatched operators. This is due to a combined effect of the nuclear short-range correlations and color invariance. As a result, the QCD corrections to the LRM amount to an effect no more than 60%, depending on the operator in question. Although less crucial, taken into account QCD running makes theoretical predictions for $0\nu\beta\beta$-decay more robust also for LRM diagrams. We derive the current experimental constraints on the Wilson coefficients for all LRM effective operators.