If t → hq (q = c, u) or h → τ ℓ (ℓ = µ, e) decays are observed, it will be a clear signal of new physics. We investigate whether natural and viable flavor models can saturate the present direct upper bounds without violating the indirect constraints from low energy loop processes. We carry out our analysis in two theoretical frameworks: minimal flavor violation (MFV) and Froggatt-Nielsen symmetry (FN). The simplest models in either framework predict flavor changing couplings that are too small to be directly observed. Yet, in the MFV framework, it is possible to have lepton flavor changing Higgs couplings close to the bound if spurions related to heavy singlet neutrinos play a role. In the FN framework, it is possible to have large flavor changing couplings in both the up and the charged lepton sectors if supersymmetry plays a role.

We clarify several subtleties concerning the implementation of minimal flavor violation (MFV) in two Higgs doublet models. We derive all the exact and approximate predictions of MFV for the neutral scalar (h, H, A) Yukawa couplings to fermions. We point out several possible tests of this framework at the LHC.

The ATLAS and CMS experiments at the LHC have reported an excess of diphoton events with invariant mass around 750 GeV, with local significance of about 3.6 σ and 2.6 σ, respectively. We entertain the possibility that this excess is due to new physics, in which case the data suggest a new particle with 13 TeV LHC production cross section times diphoton branching ratio of about 5 fb. Interestingly, ATLAS reports a mild preference for a sizeable width for the signal of about 45 GeV; this result appears consistent with CMS, and is further supported by improving the compatibility of the 8 TeV and 13 TeV analyses. We focus on the possibility that the new state is a scalar. First, we show that, in addition to the new state that is needed directly to produce the diphoton bump, yet more new particles beyond the Standard Model are needed to induce diphoton decay rate of the right size. Second, we note that if the excess is attributed to the Breit-Wigner peak of a single new state, then the signal strength and width -taken together -suggest a total LHC production cross section of order 10 5 fb. Restricting to perturbative models without ad-hoc introduction of many new states or exotic charges, we reach the following conclusions: (i) Gluon-fusion cannot explain the required large production cross section. (ii) Tree level production from initial state quarks cannot explain the required branching ratio to two photons. (iii) Tree level production is constrained by flavor data as well as LHC Run-I and Tevatron dijet analyses. Insisting on a large width we are led to suggest that more than one scalar states, nearly degenerate in mass, could conspire to produce an observed wide bump.

The recent measurement of ∆ACP by the LHCb collaboration requires an O(10) enhancement coming from hadronic physics in order to be explained within the SM. We examine to what extent can NP models explain ∆ACP without such enhancements. We discuss the implications in terms of a low energy effective theory as well as in the context of several explicit NP models.

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