Two-loop anomalous dimensions for baryon-number-violating operators in SMEFT

Abstract: We compute the two-loop renormalization-group equations for the baryon-number-violating dimension-six operators in the SMEFT. This includes all three gauge interactions, the Yukawa, and Higgs self-interaction contributions. In addition, we present the one-loop matching of the $S_1$ scalar leptoquark on the SMEFT, which can generate the Wilson coefficients of all four gauge-invariant baryon-number-violating SMEFT operators. Using this example, we demonstrate the cancellation of scheme and matching-scale dependences. Together with the known two-loop renormalization-group evolution below the electroweak scale in the LEFT, as well as the one-loop matching of SMEFT onto LEFT, our results enable consistent next-to-leading-log analyses of nucleon decays, provided that the relevant matrix elements are known at next-to-leading-order accuracy.