Form factors and branching ratio for the B -> l nu gamma decay

Abstract

Form factors parameterizing radiative leptonic decays of heavy mesons $% (B^{+}\to \gamma l^{+}\nu_{l}) $ for photon energy are computed in the language of dispersion relation. The contributing states to the absorptive part in the dispersion relation are the multiparticle continum, estimated by quark triangle graph and resonances with quantum numbers $1^{-}$ and $1^{+}$ which includes $B^{*}$ and $B_{A}^{*}$ and thier radial excitations, which model the higher state contributions. Constraints provided by the asymptotic behavior of the structure dependent amplitude, Ward Identities and gauge invariance are used to provide useful information for parameters needed. The couplings $g_{BB^{*}\gamma}$ and $% f_{BB_{A}^{*}\gamma}$ are predicted if we restrict to first radial excitation; otherwise using these as an input the radiative decay coupling constants for radial excitations are predicted. The value of the branching ratio for the process $B^{+}\to \gamma \mu ^{+}\nu_{\mu}$ is found to be in the range $0.5\times 10^{-6}$. A detailed comparison is given with other approaches.