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 $B_s\to \psi \varphi$ is predicted to be positive and above its Standard Model value ($0.05 \lsim S_{ψϕ} \lsim 0.2$). The preferred region for the gluino and the left-handed sbottom masses is below about $1÷1.5$ TeV. An existence proof of a dynamical model realizing the $U(2{)}^3$ pictured is outlined.

19 pages, 4 figures. v2: sign error in eqs. (11)-(15) and fig. 3 corrected, conclusions unchanged. Matches published version

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