Real photon emissions in leptonic decays

• Main Authors: de Divitiis, G. M, Desiderio, A, Di Carlo, M, Frezzotti, R, Garofalo, M, Giusti, D, Hansen, M, Lubicz, V, Mazzetti, F, Martinelli, G, Sachrajda, C. T, Sanfilippo, F, Simula, S, Tantalo, N
• Format: Journal Article
• Language: English
• Published: 27-08-2019
• Subjects: Physics - High Energy Physics - Lattice; Physics - High Energy Physics - Phenomenology
• DOI: 10.48550/arxiv.1908.10160

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.