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arXiv · 2504.08680

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

R. Di Palma·R. Frezzotti·G. Gagliardi·V. Lubicz·G. Martinelli·C. T. Sachrajda·F. Sanfilippo·S. Simula·N. Tantalo
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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 $F^{-}$.

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R. Di Palma, R. Frezzotti, G. Gagliardi, V. Lubicz, G. Martinelli, C. T. Sachrajda, F. Sanfilippo, S. Simula, N. Tantalo. 2025-04-11. Kaon radiative leptonic decay rates from lattice QCD simulations at the physical point. https://doi.org/10.1103/r55k-cnqg

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