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Neutrinoless double beta decay and QCD corrections

We consider one loop QCD corrections and renormalization group running of the neutrinoless double beta decay amplitude focusing on the short-range part of the amplitude (without the light neutrino exchange) and find that these corrections can be sizeable. Depending on the operator under consideration, there can be moderate to large cancellations or significant enhancements. We discuss several specific examples in this context. Such large corrections will lead to significant shifts in the half-life estimates which currently are known to be plagued with the uncertainties due to nuclear physics inputs to the physical matrix elements.