Erratum: QCD running in neutrinoless double beta decay: Short-range mechanisms (Physical Review D (2016) 93 (013017) DOI: 10.1103/PhysRevD.93.013017)

The decay rate of neutrinoless double beta (0νββ) decay contains terms from heavy particle exchange,
which lead to dimension-9 (d ¼ 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 0νββ decay, where they are measured. Here we calculate the
leading-order QCD corrections to all possible d ¼ 9 operators contributing to the 0νββ 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 0νββ decay.