Two photon decays of heavy vector mesons, $B^{\ast }\to B\gamma \gamma$,$D^{\ast }\to D\gamma \gamma$, and the possible determination of the $g_{B^{\ast }(D^{\ast })B(D)\pi }$ and $g_{{B^{\ast }}^0{B}^0\gamma }$ couplings

Abstract

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

Comments: 22 pages, LaTeX, 5 ps-figures (uses subfigure.sty). Accepted by Phys. Rev. D