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 $\text{cM}(K^0\to {\bar{K}}^0)$, $\text{cM}(B_d\to {\bar{B}}_d)$ and $\text{cM}(B_s\to {\bar{B}}_s)$, which can resolve the current tension between between $\text{cM}(K^0\to {\bar{K}}^0)$ and $\text{cM}(B_d\to {\bar{B}}_d)$, while predicting $\text{cM}(B_s\to {\bar{B}}_s)$. In particular, the CP violating asymmetry in $B_s\to \psi \varphi$ is predicted to be positive and above its Standard Model value ($0.05\text{lsim}{S}_{\psi \varphi }\text{lsim}0.2$). 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.

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