Leptonic Operators for Cabbibo Angle Anomaly with SMEFT RG Evolution

Abstract

The measurements of the Cabibbo--Kobayashi--Maskawa (CKM) elements can be contaminated by new-physics effects. We point out that purely leptonic operators at the high scale can influence semileptonic $K$ decays and nuclear beta decay through renormalization group (RG) running, and hence can influence the measurements of $V_{us}$. Interestingly, through this mechanism, a single six-dimensional effective operator $O_{\ell \ell }$ at the high scale can alleviate the tension due to the Cabibbo angle anomaly, by generating the desired operators at the low scale through RG running. When generated as a result of a $Z^{\prime }$ model, the non-universal leptonic couplings of this operator can also contribute to the lepton flavor universality violating ratios such as $R_{K^{(\ast )}}$, which would act as stringent constraints on such scenarios. By performing a global fit of the $Z^{\prime }$ model, we find that it is essential to have non-universal couplings of such a $Z^{\prime }$ boson to all three generations of leptons.

Comments: 5 Pages, 2 Figures, Major changes. Theoretical expressions and corresponding figure revised. The conditions at high scale, required to account for the anomalies, have been modified, v3: matches with the accepted version