  We evaluate QCD effects in the neutrinoless double beta ($0\nu\beta\beta$)
decay, originating from 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 (RGEs) for the corresponding Wilson
coefficients, performing the RGE-evolution from the new physics scales
(estimated as $\Lambda ~ \sim 10^2$ GeV) to the typical spacelike
$0\nu\beta\beta$-scale $Q \sim 0.1$ GeV. Since the latter scale is clearly
nonperturbative, we apply various infrared-safe (IR-safe) variants of QCD where
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.
