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 D D ̄ 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 q q ̄ and qqq spectra, meson mass splittings, pion form factor, and other parameters. With this check, an exact evaluation of the D D ̄ γ vertex form factor F( α) (normalized to F(0)=1), gives a multiplicative effect of F 2( α) on the B s ⇒ γγ amplitude via D-meson triangle loop, where α = ( p 2+ M 2)/ M 2 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 F 2( 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.