Erratum: QCD corrections and long-range mechanisms of neutrinoless double beta decay (Physical Review D (2016) 94 (096014)

Recently it has been demonstrated that QCD corrections are numerically important for short-range
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 light-neutrino 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 short-range 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.