Neutrinoless double beta decay and QCD running at low energy scales

TL;DR

This paper investigates the impact of non-perturbative QCD effects on neutrinoless double beta decay analysis, especially at low energy scales around 100 MeV, revealing moderate modifications to existing perturbative results.

Contribution

It explores the extrapolation of perturbative QCD corrections to non-perturbative scales using Background Perturbation Theory, highlighting the stability of scalar and tensor operator combinations at low energies.

Findings

Infrared extrapolation moderately modifies decay mechanism results.

Tensor operator alone cannot appear in low-energy limits of renormalizable models.

Scalar and tensor operator combinations are infrared stable.

Abstract

There is a common belief that the main uncertainties in the theoretical analysis of neutrinoless double beta ($0\nu\beta\beta$) decay originate from the nuclear matrix elements. Here, we uncover another previously overlooked source of potentially large uncertainties stemming from non-perturbative QCD effects. Recently perturbative QCD corrections have been calculated for all dimension 6 and 9 effective operators describing $0\nu\beta\beta$-decay and their importance for a reliable treatment of $0\nu\beta\beta$-decay has been demonstrated. However, these perturbative results are valid at energy scales above $\sim 1$ GeV, while the typical $0\nu\beta\beta$-scale is about $\sim 100$ MeV. In view of this fact we examine the possibility of extrapolating the perturbative results towards sub-GeV non-perturbative scales on the basis of the QCD coupling constant "freezing" behavior using Background Perturbation Theory. Our analysis suggests that such an infrared extrapolation does modify the perturbative results for both short-range and long-range mechanisms of $0\nu\beta\beta$-decay in general only moderately. We also discuss that the tensor$\otimes$tensor effective operator can not appear alone in the low-energy limit of any renormalizable high-scale model and then demonstrate that all five linearly independent combinations of the scalar and tensor operators, that can appear in renormalizable models, are infrared stable.