The anatomy of neutral scalars with FCNCs in the flavour precision era

In many extensions of the Standard Model flavour changing neutral current processes can be mediated by tree-level heavy neutral scalars and/or pseudo-scalars H^0(A^0). This generally introduces new sources of flavour violation and CP violation as well as left-handed and right-handed scalar currents. These new physics contributions imply a pattern of deviations from SM expectations for FCNC processes that depends only on the couplings of H^0(A^0) to fermions and on their masses. In situations in which a single H^0 or A^0 dominates NP contributions stringent correlations between Delta F=2 and Delta F=1 observables exist. Anticipating the Flavour Precision Era ahead of us we illustrate this by searching for allowed oases in the landscape of a given model assuming significantly smaller uncertainties in CKM and hadronic parameters than presently available. To this end we analyze Delta F=2 observables in B^0_{s,d}-bar B^0_{s,d} and K^0-bar K^0 systems and rare B and K decays with charged leptons in the final state including both left-handed and right-handed scalar couplings of H^0 and A^0 to quarks in various combinations. We identify a number of correlations between various flavour observables that could test and distinguish these different scenarios. The prominent role of the decays B_{s,d}-> mu^+ mu^- in these studies is emphasized. Imposing the existing flavour constraints, a rich pattern of deviations from the SM expectations in rare B_{s,d} decays emerges provided M_H< 1 TeV. NP effects in rare K decays are very small. Neutral SM Higgs contributions to rare B and K decays turn out to be negligible once the constraints from Delta F=2 processes are taken into account. Finally, we point out striking differences between the correlations found here and in scenarios in which tree-level FCNC are mediated by a new neutral gauge boson Z'.