Shedding Light on the "Dark Side" of $B^0_d$--$\bar B^0_d$ Mixing through $B_d\toπ^+π^-$, $K\toπν\barν$ and $B_{d,s}\toμ^+μ^-$

Abstract

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