Global Effective-Field-Theory analysis of New-Physics effects in (semi)leptonic kaon decays

Abstract

We analyze the decays $K\to\pi\ell\nu$ and $P\to\ell\nu$ ($P=K,\pi$, $\ell=e,\,\mu$) using a low-energy Effective-Field-Theory approach to parametrize New Physics and study the complementarity with baryon $\beta$ decays. We then provide a road map for a global analysis of the experimental data, with all the Wilson coefficients simultaneously, and perform a fit leading to numerical bounds for them and for $V_{us}$. A prominent result of our analysis is a reinterpretation of the well-known $V_{ud}-V_{us}$ diagram as a strong constraint on new physics. Finally, we reinterpret our bounds in terms of the $SU(2)_L\times~U(1)_Y$-invariant operators, provide bounds to the corresponding Wilson coefficients at the TeV scale and compare our results with collider searches at the LHC.