Soft-QCD Effects In B to gamma gamma Decay: Quark Level Form Factors

Abstract

Soft-QCD effects of quark-level form factors in $γγ$ decay of $B_s$-mesons via $D{\bar D}$ 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 $q{\bar q}$ and qqq spectra, meson mass splittings, pion form factor,and other parameters. With this check, an exact evaluation of the $D{\bar D}γ$ vertex form factor $F(α)$ (normalized to F(0)=1), gives a multiplicative effect of $F^2(α)$ on the $B_s \Rightarrow γγ$ 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 $B_s \Rightarrow γγ$ decay rate, thus greatly impairing the visibility of such modes. PACS: 11.10.St ; 12.38.Lg ; 13.20.Gd ; 13.40.Hq Keywords: $B_s$ radiative decay; Soft-QCD; Vertex-Fn; Form-factor; Markov-Yukawa-Transversality Principle; Salpeter eq; Cov. light front