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

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 0 nu beta 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 renormalization group running to calculate 1-loop improved limits. Numerically, QCD running dramatically changes some 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 3 orders of magnitude. Our results can be straightforwardly combined with new experimental limits or improved nuclear matrix element calculations to rederive updated limits on all short-range contributions to 0 nu beta beta decay.