Soft-QCD effects in B⇒γγ decay: quark level form factors

Soft-QCD effects of quark-level form factors in γγ decay of Bs-mesons via DD̄ intermediate states, suggested by Ellis et al., are examined in the “Salpeter” model [reinterpreted in terms of the Markov-Yukawa Transversality Principle (MYTP)] when formulated on a covariant light front (null-plane). The gluonic kernel in the infrared regime which generates the constituent mass via standard DBχS, is calibrated to both qq̄ and qqq spectra, meson mass splittings, pion form factor, and other parameters. With this check, an exact evaluation of the DD̄γ vertex form factor F(α) (normalized to F(0)=1), gives a multiplicative effect of F2(α) on the Bs⇒γγ amplitude via D-meson triangle loop, where α = (p2+M2)/M2 is the off-shellness parameter of the exchanged D-meson of mass M and 4-momentum pμ, and is a variables of the (internal) loop integration. Unfortunately, the F2(α) effect decreases the loop amplitude by a factor of 30 w.r.t. the point hadron value, resulting in a reduction of 3 orders of magnitude in long distance (hadronic) contributions to the Bs⇒γγ decay rate, thus greatly impairing the visibility of such modes.