Evaluation of neutrinoless double beta decay: QCD running to sub-GeV scales

We evaluate QCD effects in the neutrinoless double beta (0 nu beta beta) decay, originating from a new physics short-range mechanism in the form of five dimension-9 operators. For this, we employ the one-loop and two-loop renormalization group equations for the corresponding Wilson coefficients, performing the RGE evolution from the new physics scales (estimated as Lambda similar to 10(2) GeV) to the typical spacelike 0 nu beta beta scale Q similar to 0.1 GeV. Since the latter scale is clearly nonperturbative, we apply various IR-safe variants of QCD in which the running coupling has no Landau singularities at low spacelike Q. We point out that the correct treatment of the IR-safe analogs of the (noninteger) powers of the couplings is important. It turns out that in most cases of the considered operators the resulting QCD effects can be significant in this process, i.e., can be stronger than the effects of the present uncertainties in the nuclear matrix elements.