Chiral heavy fermions in a two Higgs doublet model: 750 GeV resonance or not

We revisit models where a heavy chiral 4th generation doublet of fermions is embedded in a class of two Higgs doublets models (2HDM) with a discrete $Z_2$ symmetry, which couples the heavy scalar doublet only to the 4th generation fermions and the light one to the Standard Model (SM) fermions - the so-called 4G2HDM introduced by us several years ago. We study the constraints imposed on the 4G2HDM from direct searches of heavy fermions, from precision electroweak data (PEWD) and from the measured production and decay signals of the 125 GeV scalar, which in the 4G2HDM corresponds to the lightest CP-even scalar h. We then show that the recently reported excess in the $gammagamma$ spectrum around 750 GeV can be accommodated by the heavy CP-even scalar of the 4G2HDM, H, resulting in a unique choice of parameter space: negligible mixing (sinalpha ~ O(0.001)) between the two CP-even scalars h,H and heavy 4th generation quark and lepton masses m_t,m_b < 400 GeV and $m_{ u},m_{tau}$ > 900 GeV, respectively. Whether or not the 750 GeV gamma gamma resonance is confirmed, interesting phenomenology emerges in q - Higgs systems (q=t,b), that can be searched for at the LHC. For example, the heavy scalar states of the model, S=H,A,H^+, may have BR(S -> qq) ~ O(1), giving rise to observable qq signals on resonance, followed by the flavor changing q decays t->uh (u=u,c) and/or b->dh (d=d,s,b). This leads to distinct high jet-multiplicity signatures, with or without charged leptons, of the form qq -> (nj + mb + lW)_S (j and b being light and b-quark jets, respectively), with n+m+l =6-8 and unique kinematic features. It is also shown that the 4G2HDM can easily accommodate the interesting recent indications of a percent-level branching ratio in the lepton-flavor-violating (LFV) decay $h to tau mu$ of the 125 GeV Higgs, if confirmed.