Two photon decays of heavy vector mesons, $B^{*}\to Bγγ$,$D^{*}\to Dγγ$, and the possible determination of the $g_{B^{*}(D^{*})B(D)π}$ and $g_{B^{*}^0B^0γ}$ couplings

Abstract

We study the novel decays $B^{*}\to Bγγ$ and $D^{*}\to Dγγ$ using the framework of the Heavy Meson Chiral Lagrangian (HM$χ$L) to leading order in chiral perturbation theory. The branching ratios of these decays are expressed in terms of the strong $g_{B^{*}(D^{*})B(D)π}$ and the electromagnetic $g_{B^{*}(D^*)B(D)γ}$ couplings, thus providing a possible tool for their determination. In the charm case, using the experimentally determined ratios $({D^*}^{0,+}\to Dπ)/({D^*}^{0,+}\to Dγ),$ we are able to express the branching ratio as a function of the strong coupling only. We thus find $1.6\times 10^{-6}<{\rm Br} ({D^{*}}^{0}\to D^0γγ)<3.3\times 10^{-5}$ for $0.25<g<1,$ where $g$ is the strong coupling of HM$χ$L. In the beauty sector, the ${\rm Br}({B^{*}}^{0} \to B^0 γγ)$ which we estimate to be in the $10^{-7}-10^{-5}$ range is a function of both $g_{B^{*}Bπ}$ and $g_{B^{*}Bγ}.$ 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 ${B^{*}}^{0} \to B^0 γγ$ and ${D^{*}}^{0}\to D^0γγ,$ for different values of the couplings involved.