Extended minimal flavour violating MSSM and implications for B physics

The recently reported measurements of the CP asymmetry $a_{\psi K}$ by the BABAR and BELLE collaborations, obtained from the rate differences in the decays $B^0 \to (J/\psi K_s), (J/\psi K_L)$ etc., and their charge conjugates, are in good agreement with the standard model (SM) prediction of the same, resulting from the unitarity of the CKM matrix. The so-called minimal flavour violating (MFV) supersymmetric extensions of the standard model, in which the CKM matrix remains the only flavour changing structure, predict $a_{\psi K}$ similar to the one in the SM. With the anticipated precision in $a_{\psi K}$ and other CP asymmetries at the B factories and hadron colliders, one hopes to pin down any possible deviation from the SM. We discuss an extension of the MFV-supersymmetric models which comfortably accommodates the current measurements of the CP asymmetry $a_{\psi K}$ , but differs from the SM and the MFV-supersymmetric models due to an additional flavour changing structure beyond the CKM matrix. We suggest specific tests in forthcoming experiments in B physics. In addition to the CP-asymmetries in B-meson decays, such as $a_{\psi K}$ and $a_{\pi \pi}$ , and the mass difference $\Delta M_s$ in the $B_s^0 - \overline{B_s^0}$ system, we emphasize measurements of the radiative transition $b \to d \gamma$ as sensitive probes of the postulated flavour changing structure. This is quantified in terms of the ratio $R(\rho \gamma/K^* \gamma) = 2{\cal B}(B^0 \to \rho^0 \gamma)/{\cal B}(B^0 \to K^{* 0} \gamma)$ , the isospin violating ratio $\Delta^{\pm 0}={\cal B}(B^\pm \to \rho^\pm \gamma)/2{\cal B}(B^0 \to\rho^0 \gamma) -1$ , and the CP-asymmetry in the decay rates for $B^+ \to \rho^+ \gamma$ and its charge conjugate. Interestingly, the CKM–unitarity analysis in the Extended–MFV model also allows solutions $\bar\rho <0$ for the Wolfenstein parameter, as opposed to the SM and the MFV-supersymmetric models for which only $\bar\rho > 0$ solutions are now admissible, implying $\gamma > \pi/2$ , where $\gamma=-\arg V_{ub}$ . Such large values of $\gamma$ are hinted by the current measurements of the branching ratios for the decays $B\to \pi\pi$ and $B\to K \pi$ .