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

Abstract

Soft-QCD effects of quark-level form factors in γγ decay of B_s-mesons via DD̅ 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 qq̅ and qqq spectra, meson mass splittings, pion form factor, and other parameters. With this check, an exact evaluation of the DD̅γ vertex form factor F(α) (normalized to F(0)=1), gives a multiplicative effect of F²(α) on the B_s⇒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 p_μ, 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 B_s⇒γγ decay rate, thus greatly impairing the visibility of such modes.