First lattice calculation of radiative leptonic decay rates of pseudoscalar mesons
Antonio Desiderio, R. Frezzotti, Marco Garofalo, D. Giusti, Martin Hansen, V. Lubicz, G. Martinelli, Christopher Sachrajda, Francesco Sanfilippo, Silvano Simula, Nazario Tantalo
Abstract
We present a nonperturbative lattice calculation of the form factors which contribute to the amplitudes for the radiative decays $P\ensuremath{\rightarrow}\ensuremath{\ell}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}\ensuremath{\gamma}$, where $P$ is a pseudoscalar meson and $\ensuremath{\ell}$ is a charged lepton. Together with the nonperturbative determination of the corrections to the processes $P\ensuremath{\rightarrow}\ensuremath{\ell}{\overline{\ensuremath{\nu}}}_{\ensuremath{\ell}}$ due to the exchange of a virtual photon, this allows accurate predictions at $O({\ensuremath{\alpha}}_{\mathrm{em}})$ 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 nonpertubatively the pointlike contribution, from the structure-dependent, infrared-safe, terms in the amplitude. The fully nonperturbative $O(a)$ improved calculation of the inclusive leptonic decay rates will lead to the determination of the corresponding Cabibbo-Kobayashi-Maskawa matrix elements also at $O({\ensuremath{\alpha}}_{\mathrm{em}})$. 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.