Constraining $|V_{cs}|$ and physics beyond the Standard Model from exclusive (semi)leptonic charm decays

We study the available data on exclusive leptonic and semileptonic $c\to s\ell^+\nu$ decays within the Standard Model and beyond. Our analysis accounts for theory correlations between the relevant hadronic matrix elements through application of dispersive bounds. We find that, within a global analysis, the dispersive bounds are generally well respected and only mildly affect the extraction of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{cs}|$. Assuming Standard Model dynamics, we obtain $$ |V_{cs}| = 0.957 \pm 0.003\,, $$ which is compatible with the HFLAV/PDG reference value $|V_{cs}| = 0.975 \pm 0.006$ at the $2.7\,\sigma$ level. Our findings lead to significant deficits in the second-row and second-column unitarity relations of the CKM matrix. Allowing for beyond the SM contributions in the Weak Effective Theory, we find very strong constraints on potential (pseudo)scalar and tensor effects. However, the data still permits sizeable CP-violating right-handed currents.