Profiles of the unitarity triangle and CP-violating phases in the standard model and supersymmetric theories

Abstract

We report on a comparative study of the profile of the CKM unitarity triangle, and the resulting CP asymmetries in B decays, in the standard model and in several variants of the minimal supersymmetric standard model (MSSM), characterized by a single phase in the quark flavour mixing matrix. The supersymmetric contributions to the mass differences $\Delta M_d$ , $\Delta M_s$ and to the CP-violating quantity $\vert\epsilon\vert$ are, to an excellent approximation, equal to each other in these theories, allowing for a particularly simple way of implementing the resulting constraints on the elements of $V_{CKM}$ from the present knowledge of these quantities. Incorporating the next-to-leading-order corrections and applying the current direct and indirect constraints on the supersymmetric parameters, we find that the predicted ranges of $\sin 2 \beta$ in the standard model and in MSSM models are very similar. However, precise measurements at B-factories and hadron machines may be able to distinguish these theories in terms of the other two CP-violating phases $\alpha$ and $\gamma$ . This is illustrated for some representative values of the supersymmetric contributions in $\Delta M_d$ , $\Delta M_s$ and $\vert \epsilon\vert$ .