Supersymmetric Effects on Isospin Symmetry Breaking and Direct CP Violation in $B \to ργ$

Abstract

We argue that one can search for physics beyond the standard model through measurements of the isospin-violating quantity $Δ^{-0} \equiv Γ(B^- \to ρ^- γ)/2Γ(B^0 \to ρ^0 γ)-1$, its charge conjugate $Δ^{+0}$, and direct CP violation in the partial decay rates of $B^\pm \to ρ^\pm γ$. We illustrate this by working out theoretical profiles of the charge-conjugate averaged ratio $Δ\equiv {1 \over 2}(Δ^{+0} +Δ^{-0})$ and the CP asymmetry $A_{CP}(B^\pm \to ρ^\pm γ)$ in the standard model and in some variants of the minimal supersymmetric standard model. We find that chargino contributions in the large $\tan β$ region may modify the magnitudes and flip the signs of $Δ$ and $A_{CP}(B^\pm \to ρ^\pm γ)$ compared to their standard-model values, providing an unmistakeable signature of supersymmetry.