Form factors parametrizing radiative leptonic decays of heavy mesons(B~(+) ->(gamma)l~(+)(upsilon)_(l)) for photon energy are computed in the language of dispersion relations. The contributing states to the absorptive part in the dispersion relation are the multiparticle continuum, estimated by the quark triangle graph, and resonances with quantum numbers 1~(-) and 1~(+) which include B~(*) and B_(A)~(*) and their 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 the 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~(+) ->(gamma)(mu)~(+)(upsilon)_(mu) is found to be in the range 0.5 X 10~(-6). A detailed comparison is given with other approaches.
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