Shedding Light on the "Dark Side" of $B_d^0$--${\bar{B}}_d^0$ Mixing through $B_d\to {\pi }^{+}{\pi }^{-}$, $K\to \pi \nu \bar{\nu }$ and $B_{d,s}\to {\mu }^{+}{\mu }^{-}$

Abstract

In a wide class of NP models, which can be motivated through generic arguments and within SUSY, we obtain large contributions to $B_d^0$--${\bar{B}}_d^0$ mixing, but not to $\Delta B=1$ processes. If we assume such a scenario, the solutions ${\varphi }_d\sim 47^{\circ }\vee 133^{\circ }$ for the $B_d^0$--${\bar{B}}_d^0$ mixing phase implied by $A_{CP}^{mix}(B_d\to J/\psi K_S)$ cannot be converted directly into a constraint in the $\rho$--$\eta$ plane. However, we may complement ${\varphi }_d$ with $|V_{ub}/V_{cb}|$ and the recently measured CP asymmetries in $B_d\to {\pi }^{+}{\pi }^{-}$ to determine the unitarity triangle, with its angles $\alpha$, $\beta$ and $\gamma$. To this end, we have also to control penguin effects, which we do by means of the $B_d\to {\pi }^{\mp }{K}^{\pm }$ branching ratio. Interestingly, the present data show a perfectly consistent picture not only for the ``standard'' solution of ${\varphi }_d\sim 47^{\circ }$, but also for ${\varphi }_d\sim 133^{\circ }$. In the latter case, the preferred region for the apex of the unitarity triangle is in the second quadrant, allowing us to accommodate conveniently $\gamma >90^{\circ }$, which is also favoured by other non-leptonic B decays such as $B\to \pi K$. Moreover, also the prediction for BR(K^+\to\pi^+\nu\bar\nu}) can be brought to better agreement with experiment. Further strategies to explore this scenario with the help of $B_{d,s}\to {\mu }^{+}{\mu }^{-}$ decays are discussed as well.

Comments: 26 pages, 3 figures, minor modifications, to appear in JHEP