Radiative corrections of $O(\alpha)$ to $B^- \rightarrow V^0 \ell^- \bar{\nu}_{\ell}$ decays

TL;DR

This paper calculates electromagnetic radiative corrections at order alpha for B meson semileptonic decays, improving precision in determining quark mixing angles by addressing virtual and real photon effects with a cutoff method.

Contribution

It introduces a method combining cutoff regularization and resonance states to evaluate radiative corrections, extending the validity of soft-photon approximation in B decay analyses.

Findings

Corrections are mildly dependent on the cutoff scale Λ.

Photon-inclusive rates are dominated by short-distance effects.

Numerical radiative correction values are provided for Dalitz plot regions.

Abstract

The $O(\alpha)$ electromagnetic radiative corrections to the $B^- \rightarrow V^0 \ell^- \bar{\nu}_{\ell}$ ($V$ is a vector meson and $\ell$ a charged lepton) decay rates are evaluated using the cutoff method to regularize virtual corrections and incorporating intermediate resonance states in the real-photon amplitude to extend the region of validity of the soft-photon approximation. The electromagnetic and weak form factors of hadrons are assumed to vary smoothly over the energies of virtual and real photons under consideration. The cutoff dependence of radiative corrections upon the scale $\Lambda$ that separates the long- and short-distance regimes is found to be mild and is considered as an uncertainty of the calculation. Owing to partial cancellations of electromagnetic corrections evaluated over the three- and four-body regions of phase space, the photon-inclusive corrected rates are found to be dominated by the short-distance contribution. These corrections will be relevant for a precise determination of the $b$ quark mixing angles by testing isospin symmetry when measurements of semileptonic rates of charged and neutral $B$ mesons at the few percent level become available. For completeness, we also provide numerical values of radiative corrections in the three-body region of the Dalitz plot distributions of these decays.