Final state rescattering as a contribution to $B\to \rho \gamma$

Abstract

We provide a new estimate of the long-distance component to the radiative transition $B\to \rho \gamma$. Our mechanism involves the soft-scattering of on-shell hadronic products of nonleptonic $B$ decay, as in the chain $B\to \rho \rho \to \rho \gamma$. We employ a phenomenological fit to scattering data to estimate the effect. The specific intermediate states considered here modify the $B\to \rho \gamma$ decay rate at roughly the $5\to 8$ level, although the underlying effect has the potential to be larger. Contrary to other mechanisms of long distance physics which have been discussed in the literature, this yields a non-negligible modification of the $B^0\to {\rho }^0\gamma$ channel and hence will provide an uncertainty in the extraction of $V_{td}$. This mechanism also affects the isospin relation between the rates for $B^{-}\to {\rho }^{-}\gamma$ and $B^0\to {\rho }^0\gamma$ and may generate CP asymmetries at experimentally observable levels.

15 pages, RevTex, 3 figures

References in corpus (4)

• Systematics of soft final state interactions in $B$ decay
• Estimates of the Weak Annihilation Contributions to the Decays $B\to \rho +\gamma$ and $B\to \omega +\gamma$
• Regge asymptotics and color suppressed heavy meson decays
• Is $B\to X_s\gamma$ equal to $b\to s\gamma$ ? Spectator contributions to rare inclusive B decays

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