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First lattice calculation of radiative leptonic decay rates of pseudoscalar mesons

2021; American Physical Society; Volume: 103; Issue: 1 Linguagem: Inglês

10.1103/physrevd.103.014502

2470-0037

Antonio Desiderio, R. Frezzotti, Marco Garofalo, D. Giusti, Martin Hansen, V. Lubicz, G. Martinelli, Christopher Sachrajda, Francesco Sanfilippo, Silvano Simula, Nazario Tantalo,

Nuclear physics research studies

We present a non-perturbative lattice calculation of the form factors which contribute to the amplitudes for the radiative decays $P\to \ell \bar \nu_\ell \gamma$, where $P$ is a pseudoscalar meson and $\ell$ is a charged lepton. Together with the non-perturbative determination of the corrections to the processes $P\to \ell \bar \nu_\ell$ due to the exchange of a virtual photon, this allows accurate predictions at $O(\alpha_{em})$ to be made for leptonic decay rates for pseudoscalar mesons ranging from the pion to the $D_s$ meson. We are able to separate unambiguously and non-pertubatively the point-like contribution, from the structure-dependent, infrared-safe, terms in the amplitude. The fully non-perturbative $O(a)$ improved calculation of the inclusive leptonic decay rates will lead to the determination of the corresponding Cabibbo-Kobayashi-Maskawa (CKM) matrix elements also at $O(\alpha_{em})$. Prospects for a precise evaluation of leptonic decay rates with emission of a hard photon are also very interesting, especially for the decays of heavy $D$ and $B$ mesons for which currently only model-dependent predictions are available to compare with existing experimental data.