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, arXiv:2006.05358. Our analysis uses gauge ensembles generated by the Extended Twisted Mass Collaboration (ETMC) with $N_f=2+1+1$ flavors of Wilson-clover twisted mass fermions. For the first time, we go beyond the electroquenched 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 $L\simeq 3.8\mathrm{fm}$ to $L\simeq 7.7\mathrm{fm}$, and (iii) the continuum extrapolation is based on three lattice spacings in the range $a\in [0.08,0.058]\mathrm{fm}$. 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 ($K^{-}\to e^{-}{\bar{\nu }}_e\gamma$), 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 ($K^{-}\to {\mu }^{-}{\bar{\nu }}_{\mu }\gamma$), 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 $F^{-}$.

Comments: 32 pages, 20 figures, 6 tables. Published version