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.
Highlights
Uncertainty) [5, 6]
We focus on CP -even observables, and only the real parts of the Wilson coefficients (WC) will interfere with the SM
This can not be improved by adding other low-energy charged-current processes and the only way to access the orthogonal directions to these WC combinations is through the use of high-energy data, or neutral-current low-energy processes connected to those studied in this work due to the SU(2)L × U(1)Y symmetry in the Effective Field Theory (EFT)
Summary
If the NP is coming from dynamics at Λ v and electro-weak symmetry breaking is linearly realized, one can use an SU(2)L × U(1)Y invariant effective theory [38, 42, 44, 45]. In this case [32, 38, 46]: De R. so that, up to a subleading corrections in the EFT expansion, a NP effect involving a righthanded current necessarily involves a Higgs-current fermion-current operator [42] and its contribution must be lepton universal. The form of the Lagrangian is convenient as it allows to separate the effects of a combination of currentcurrent operators affecting the normalization of the rates and which can be only accessed through CKM-unitarity and lepton-universality tests
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