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.
Highlights
From neutrino oscillation experiments it is nowadays well known that at least two neutrinos have nonzero masses
We discuss that the tensor ⊗ tensor effective operator cannot appear alone in the low energy limit of any renormalizable high-scale model and demonstrate that all five linearly independent combinations of the scalar and tensor operators, which can appear in renormalizable models, are infrared stable
Neutrinoless double beta decay (0νββ), for recent reviews see for instance [4,5,6], is by far the most powerful available probe of lepton number violation, and its nonobservation allows us to constrain Lepton number violating (LNV) beyond standard model (BSM) physics
Summary
From neutrino oscillation experiments it is nowadays well known that at least two neutrinos have nonzero masses. It has been recently demonstrated that QCD corrections to 0νββ are important, especially in the SRM case [13] due to the presence of the color-mismatch effect and the corresponding mixing of different operators, with numerically very different nuclear matrix elements (NME). The conventional approach relies on the operator product expansion for observables, such as 0νββ half-life, and on a proper matching of the quark- and nucleon-level theories at a certain scale μ0. This is a low energy scale, down to which perturbative QCD for the quark-level theory is valid. In a sense it can be thought of as a rough modeling of the matching scale dependence of the nucleon matrix elements alleviating the dependence of the 0νββ half-life on this scale
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