Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1999-02-17
Physics
High Energy Physics
High Energy Physics - Phenomenology
11 pages, 1 figure, LaTex
Scientific paper
10.1016/S0370-2693(99)01504-X
Soft-QCD effects of quark-level form factors in $\gamma\gamma$ 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 $DB{\chi}S$, 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 $D{\bar D}\gamma$ vertex form factor $F(\alpha)$ (normalized to F(0)=1), gives a multiplicative effect of $F^2(\alpha)$ on the $B_s \Rightarrow \gamma\gamma$ amplitude via D-meson triangle loop, where $\alpha$ = $(p^2+M^2)/M^2$ is the off-shellness parameter of the exchanged D-meson of mass M and 4-momentum $p_\mu$, and is a variables of the (internal)loop integration. Unfortunately, the $F^2(\alpha)$ 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 $B_s \Rightarrow \gamma\gamma$ 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
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