QCD corrections and long-range mechanisms of neutrinoless double beta decay

Abstract

Recently it has been demonstrated that QCD corrections are numerically important for shortrange mechanisms (SRM) of neutrinoless double beta decay (0νββ) 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 lightneutrino exchange between a Standard Model (V-A)×(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 shortrange 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 0νββ-decay more robust also for LRM diagrams. We derive the current experimental constraints on the Wilson coefficients for all LRM effective operators.

Neutrinoless double beta decay in chiral effective field theory: lepton number violation at dimension seven

“…The above RGEs correct the anomalous dimensions derived in ref. [43]. The RGEs of the dimension-nine operators are given by [44,45] …”

Neutrinoless double beta decay and QCD running at low energy scales

“…On the other hand, the LRM operate between two different and distant nucleons, so that no color-mismatch appears and only QCD vertex corrections have to be taken into account. Their effect on the extracted limits does not exceed 60% [14], less than the typical estimate of the uncertainties of the nuclear matrix elements (NMEs).…”

“…We mention also [33], quoting M B = 0.95 GeV, and [28], which give M B = 2.15 GeV. Below we revisit the QCD corrections to the SRM and LRM of 0νββ-decay [13,14] applying Eq. (2) in order to extrapolate the pQCD results towards µ ∼ 100 MeV, the characteristic scale of 0νββ-decay.…”

“…Here we apply the IR extrapolation based on "freezing", discussed above, to the pQCD results for 0νββdecay derived in refs [13,14,35].…”

“…As was shown in [39] there are 5 possible linear combinations of these two operators, which can originate from renormalizable high-scale models (for details see Ref. [14]) that appear in the tree-level decomposition of the 0νββ decay operator, see [39]. For a discussion see text.…”