Kaon radiative leptonic decay rates from lattice QCD simulations at the physical point

Abstract

We present a lattice QCD calculation of the radiative leptonic decay rates of the kaon, improving upon our previous work in Ref. [1]. Our analysis uses gauge ensembles generated by the Extended Twisted Mass Collaboration (ETMC) with Nf = 2 + 1 + 1 flavors of Wilson-clover twisted mass fermions. For the first time, we go beyond the electro quenched approximation by including quark-disconnected contributions. Several key improvements have been implemented: (i) the simulations are now performed directly at physical light- and strange-quark masses, (ii) finite-size effects are carefully investigated using lattices with spatial extents ranging from L ≃ 3.8 fm to L ≃ 7.7 fm, and(iii) the continuum extrapolation is based on three lattice spacings in the range a ∈ [0.08, 0.058] fm. As a result of the high-precision determination of the relevant correlation functions, we reduce the uncertainties on both the axial and vector form factors by nearly a factor of two compared to our previous analysis. When compared to experimental measurements in the electron channel(K− → e−ν¯eγ), our results show a tension—at the level of 2.6 standard deviations—with respect to KLOE data. On the other hand, they are compatible with measurements from the E36 Collaboration at J-PARC. In the muonic decay channel (K− → µ−ν¯µγ), we confirm the tensions, already observed in our previous study, between lattice QCD predictions and ISTRA+ and OKA data, which are both primarily sensitive to the value of the negative-helicity form factor F−.

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