QCD Corrections and Long-Range Mechanisms of neutrinoless double beta decay

Understand

Recently it has been demonstrated that QCD corrections are numerically important for short-range mechanisms (SRM) of neutrinoless double beta decay ($0\nu\beta\beta$) 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)$\times$(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.