Model building for flavor changing Higgs couplings
  If $t\rightarrow hq$ ($q=c,u$) or $h\rightarrow\tau\ell$ ($\ell=\mu,e$) 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. 
Avital Dery, Aielet Efrati, Yosef Nir, Yotam Soreq, and Vasja   Susi\v{c}
hep-ph