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.

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

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• Scrutinizing CKM unitarity with a new measurement of the $K_{\mu 3}/K_{\mu 2}$ branching fraction
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Cited by in corpus (2)

• Impact of $b\to s\ell \ell$ anomalies on rare charm decays in non-universal $Z^{\prime }$ models
• Discriminating 1D new physics solutions in $b\to s\ell \ell$ decays