PoS - Proceedings of Science
Volume 363 - 37th International Symposium on Lattice Field Theory (LATTICE2019) - Main session
Real photon emissions leptonic decays
G. Martinelli,* M.D. Carlo, F. Mazzetti, G.M. "de Divitiis", A. Desiderio, R. Frezzotti, M. Garofalo, M. Hansen, N. Tantalo, D. Giusti, V. Lubicz, C.T. Sachrajda, F. Sanfilippo, S. Simula
*corresponding author
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Pre-published on: December 05, 2019
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We present a non-perturbative 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 virtual photon corrections to the processes $P\to \ell \bar \nu_\ell$, this will allow accurate predictions to be made at $O(\alpha_{em})$ for leptonic decay rates for pseudoscalar mesons ranging from the pion to the $B$ meson. We are able to separate unambiguously the point-like contribution, the square of which leads to the infrared divergence in the decay rate, 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 significantly improved precision in the determination of the corresponding Cabibbo-Kobayashi-Maskawa (CKM) matrix elements. Precise predictions for the 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.
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