Predictions for $b \rightarrow ss\overline{d}$ and $b \rightarrow dd\overline{s}$ decays in the SM and with new physics

The b -> ssdbar and b -> ddsbar decays are highly suppressed in the SM, and are thus good probes of new physics (NP) effects. We discuss in detail the structure of the relevant SM effective Hamiltonian pointing out the presence of nonlocal contributions which can be about \lambda^{-4} (m_c^2/m_t^2) ~ 30% of the local operators (\lambda = 0.21 is the Cabibbo angle). The matrix elements of the local operators are computed with little hadronic uncertainty by relating them through flavor SU(3) to the observed \Delta S = 0 decays. We identify a general NP mechanism which can lead to the branching fractions of the b\to ss\bar d modes at or just below the present experimental bounds, while satisfying the bounds from K-Kbar and B_{(s)}-Bbar_{(s)} mixing. It involves the exchange of a NP field carrying a conserved charge, broken only by its flavor couplings. The size of branching fractions within MFV, NMFV and general flavor violating NP are also predicted. We show that in the future energy scales higher than 10^3 TeV could be probed without hadronic uncertainties even for b-> s and b-> d transitions, if enough statistics becomes available.