Renormalization-group evolution of new physics contributions to (semi)leptonic meson decays

We study the renormalization group evolution (RGE) of new physics contributions to (semi)leptonic charged-current meson decays, focusing on operators involving a chirality flip at the quark level. We calculate their evolution under electroweak and electromagnetic interactions, including also the three-loop QCD running and provide numerical formulas that allow us to connect the values of the corresponding Wilson coefficients from scales at the TeV to the low-energy scales. The large mixing of the tensor operator into the (pseudo)scalar ones has important phenomenological implications, such as the RGE of new physics bounds obtained from light quark decays or in $b\to c\ell\nu$ transitions. For instance, we study scenarios involving tensor effective operators, which have been proposed in the literature to address the $B$-decay anomalies, most notably those concerning the $R_{D^{(*)}}$ ratios. We conclude that the loop effects are important and should be taken into account in the analysis of these processes, especially if the operators are generated at an energy scale of $\sim 1$ TeV or higher.