Two photon decays of heavy vector mesons, B^(*)to Bγ γ,D^(*)to Dγ γ, and the possible determination of the g_(B^(*)(D^(*))B(D)π) and g_{{B^(*)}⁰B⁰γ} couplings

We study the novel decays $B^{*}\to B\gamma\gamma $ and $D^{*}\to D\gamma \gamma $ using the framework of the Heavy Meson Chiral Lagrangian (HM$\chi$L) to leading order in chiral perturbation theory. The branching ratios of these decays are expressed in terms of the strong $g_{B^{*}(D^{*})B(D)\pi}$ and the electromagnetic $g_{B^{*}(D^*)B(D)\gamma}$ couplings, thus providing a possible tool for their determination. In the charm case, using the experimentally determined ratios $({D^*}^{0,+}\to D\pi)/({D^*}^{0,+}\to D\gamma),$ we are able to express the branching ratio as a function of the strong coupling only. We thus find $1.6\times 10^{-6}<{\rm Br} ({D^{*}}^{0}\to D^0\gamma\gamma)<3.3\times 10^{-5}$ for $0.25<g<1,$ where $g$ is the strong coupling of HM$\chi$L. In the beauty sector, the ${\rm Br}({B^{*}}^{0} \to B^0 \gamma\gamma)$ which we estimate to be in the $10^{-7}-10^{-5}$ range is a function of both $g_{B^{*}B\pi}$ and $g_{B^{*}B\gamma}.$ Its behaviour does not afford an unambiguous determination of these couplings except for the region of high $g$ values like $g>0.6.$ The expected two-photon differential distributions are presented for both ${B^{*}}^{0} \to B^0 \gamma\gamma$ and ${D^{*}}^{0}\to D^0\gamma\gamma,$ for different values of the couplings involved.