U(2) and Minimal Flavour Violation in Supersymmetry

Abstract

Rather than sticking to the full $U(3)^3$ approximate symmetry normally invoked in Minimal Flavour Violation, we analyze the consequences on the current flavour data of a suitably broken $U(2)^3$ symmetry acting on the first two generations of quarks and squarks. A definite correlation emerges between the $\Delta F=2$ amplitudes $\cM(K^0 \to \bar K^0)$, $\cM(B_d \to \bar B_d)$ and $\cM(B_s \to \bar B_s)$, which can resolve the current tension between between $\cM(K^0 \to \bar K^0)$ and $\cM(B_d \to \bar B_d)$, while predicting $\cM(B_s \to \bar B_s)$. In particular, the CP violating asymmetry in $B_s \to \psi \phi$ is predicted to be positive and above its Standard Model value ($0.05 \lsim S_{\psi\phi} \lsim 0.2$). The preferred region for the gluino and the left-handed sbottom masses is below about $1\div 1.5$ TeV. An existence proof of a dynamical model realizing the $U(2)^3$ pictured is outlined.