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Below the electroweak scale, new physics that violates lepton number in twounits ($\Delta L = 2$) and is mediated by heavy particle exchange can beparameterized by a dimension-9 low-energy effective Lagrangian. Operators inthis Lagrangian involving first-generation quarks and leptons contribute to theshort-range mechanism of neutrinoless double beta decay ($0\nu\beta\beta$) andtherefore they are strongly constrained. On the other hand, operators withother quark and lepton families are bounded by the non-observation of differentlepton number violating (LNV) meson and tau decays, such as $M_1^- \toM_2^+\ell_1^-\ell_2^-$ and $\tau^- \to \ell^+ M_1^- M_2^-$. In this work, wecalculate RGE-improved bounds on the Wilson coefficients involved in thesedecays. We calculate QCD corrections to the dimension-9 operator basis and findRG evolution matrices that describe the evolution of the Wilson coefficientsacross different energy scales. Unlike the running of operators involved in$0\nu\beta\beta$-decay, the general flavor structure leads to the mixing of notonly different Lorentz structures but also of different quark-flavorconfigurations. Additionally, operators that vanish for the identical leptoncase need to be added to the operator basis. We find new constraints onpreviously unbounded operators and the enhancement of bounds for specificWilson coefficients. We also find new bounds coming from the mixing betweenoperators with different quark-flavor configurations.

QCD Running in Lepton Number Violating Meson and Tau Decays