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 $\gamma\gamma$ 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 (sin\alpha ~ 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 $m_{\nu'},m_{\tau'}$>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 ->q'q') ~ O(1), giving rise to observable q'q' 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 q'q' ->(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.


I. INTRODUCTION
The on going search for new physics (NP) is mostly inspired by the shortcomings of the SM in addressing some of the fundamental questions in modern particle physics, such as the hierarchy problem, the flavor patterns in the fermionic sector and dark matter. Some of these unresolved issues may be closely related and may have TeV-scale origins, thus inspiring the search for TeV-scale NP, both theoretically and experimentally. Indeed, two seemingly unrelated interesting measurements of both the ATLAS [1,2] and the CMS [3,4] collaborations at CERN, have been recently reported: 1. A possible (2 − 4)σ (local) excess in the diphoton invariant mass distribution around 750 GeV, corresponding to a signal cross-section roughly in the range σ(pp → γγ) ∼ 3 − 13 fb (1σ), see e.g., [5][6][7]. The interpretation of this excess signal has a slight preference to a spin 0 resonance, produced via gluon-fusion and having a total width ranging from sub-GeV to 45 GeV, with a more significant signal obtained in the ATLAS analysis for a scalar with a total width Γ ∼ 45 GeV [1].
GeV γγ excess (too many to be cited here); in most cases involving new degrees of freedom beyond just the 750 GeV resonating particle. In particular, the relevance of 2HDM frameworks to the 750 GeV γγ excess has been intensively studied in the past several months, where it was shown that the simplest 2HDM extension to the SM, in which no additional heavy degrees of freedom are added (i.e., beyond the extended scalar sector), cannot accommodate the necessary enhancement in σ(pp → H(750) → γγ), see e.g., [28]. Consequently, extended 2HDM models with TEV scale vector-like (VL) fermions have been suggested for addressing the 750 GeV resonance signal [29]. The upshot of these studies is that, the needed enhancement in the 1-loop production and decay channels gg → H(750) and H(750) → γγ, requires several copies of VL fermions and/or VL fermions with charges appreciably larger than those of the SM fermions, unless their Yukawa couplings are much larger than one. The 4G2HDM considered in this work is, therefore, conceptually simpler, relying on new heavy fermionic degrees of freedom with properties similar to the SM fermions in a model that already exists in the literature. The paper is organized as follows: in section 2 we describe the type I 4G2HDM and we layout the physical parameters that are used in the numerical analysis. In section 3 we show our results and in section 4 we discuss their phenomenological consequences. In section 5 we discuss our results and summarize.

II. THE 4G2HDM: A 2HDM WITH 4TH GENERATION FERMIONS
Motivated by the idea that TeV-scale scalar degrees of freedom may emerge as composites associated with heavy fermions, we assume that the low-energy (sub-TeV) effective framework is parameterized by a 2HDM with a chiral SM-like 4th generation of heavy fermions. Specifically, the model is constructed following [18], such that one of the Higgs fields (φ h -the "heavier" field) couples only to the new heavy 4th generation fermionic fields, while the second Higgs field (φ ℓ -the "lighter" field) is responsible for the mass generation of all other (lighter) fermions (i.e., the 1st-3rd generation SM fermions). In this model, named in [18] the 4G2HDM of type I (here we will refer to it simply as the 4G2HDM), the Yukawa interaction Lagrangian can be realized in terms of a Z 2 -symmetry under which the fields transform as follows: where F L and f R , f ′ R are the SU(2) fermion (quark or lepton) doublets and singlets, respectively, and Φ ℓ,h are the two Higgs doublets , i = ℓ, h. The Yukawa potential that respects the above Z 2 -symmetry is: where f u,R and f d,R are the up and down-type SU(2) fermion singlets (quark or lepton of all four generations), I is the identity matrix and I is the diagonal 4 × 4 matrix I ≡ diag (0, 0, 0, 1). The scalar sector contains five massive states: a charged scalar H + , a CP-odd state A and two CP-even scalars h, H, so that h is the lighter one, corresponding to the observed 125 GeV Higgs boson. These physical states are related to the components of the two SU(2) scalar doublets via: where s α (c α ) = sin α(cos α), α being the Higgs mixing angle in the CP-even sector and s β (c β ) = sin β(cos β), where tan β ≡ v h /v ℓ is the ratio between the VEV's of the heavy and light Higgs fields. The Yukawa Higgs-quark-quark interactions in the 4G2HDM are (similar terms can be written for the leptons) [18]: where V is the 4 × 4 CKM matrix, q = d or u for down or up-quarks with I d = −1 and I u = +1, respectively, and R(L) = 1 2 (1 + (−)γ 5 ). Also, Σ d and Σ u are new mixing matrices where all FCNC effects of the 4G2HDM are encoded. They are obtained after diagonalizing the quark mass matrices and, therefore, depend on the rotation (unitary) matrices of the right-handed down and up-quarks D R and U R , respectively. In particular, for I ≡ diag (0, 0, 0, 1) in Eq. 2, we have (see [18]): [2] The Yukawa structure and couplings defined by Eqs. 2-8 is assumed to be copied to the leptonic sector, see [30]. In the following sections III and IV, for illustrative purposes (and without loss of generality), we will set Σ d,u → diag (0, 0, 0, 1) in both the quark and lepton sectors, so that FCNC effects (in particular, between the 4th generation fermions and the SM fermions) are "turned off". In fact, from the phenomenological point of view, it is sufficient to assume that Σ u 34,43 → 0 (i.e., forbidding the decay t ′ → th) and V i4,4i → 0 (i = 1, 2, 3, thus forbidding the decays t ′ → d i W and b ′ → u i W with d i = d, s, b and u i = u, c, t) in order to accommodate relatively light t ′ and b ′ with masses as low as 350 GeV, since the existing stringent exclusion limits of m t ′ , m b ′ > ∼ 700 GeV, are based on searches that assume 100% branching ratios of the 4th generation quarks into one of the channels: t ′ → th, tZ, d i W and b ′ → Zb, u i W [31,32]. We will, therefore, assume that the dominant t ′ and b ′ decays are into one of the FC channels t ′ → u i h and b ′ → d i h (u i = u, c and d i = d, s, b), due to small FCNC entries in Σ u,d (which have no effect on the results presented in sections III and IV), in which case small off-diagonal CKM entries V 14,41 and/or V 24,42 are also allowed as long as [32]. Such flavor structures, may have interesting phenomenological implications, as will be discussed in section V.
The 2HDM scalar sector is parameterized by seven free parameters (after minimization of the potential), which, in the so called "physical basis", can be chosen as the four physical Higgs masses (m h , m H , m A , m H + ), the two angles β and α and one parameter from the scalar potential, which is needed in order to specify the scalar couplings, in particular, hH + H − (which enters in the 1-loop h → γγ decay), HH + H − (which enters the 1-loop H → γγ decay) and Hhh (required for the decay H → hh). In the physical basis, these scalar couplings can be written at tree-level as (see e.g., [33]): where m 2 ℓh is a mass-like term, m 2 ℓh Φ † ℓ Φ h + h.c., which softly breaks the above Z 2 -symmetry (i.e., Φ ℓ → −Φ ℓ , Φ h → +Φ h ), and which can be used to specify the above tree-level scalar couplings.
However, since the working assumption of the 4G2HDM is that the scalar sector may be strongly interacting at the near by few TeV scale, the scalar potential is expected to be subject to significant renormalization and threshold effects. Thus, the above scalar couplings are expected to deviate from their tree-level values, depending on the details of the UV completion and on the masses of the heavy degrees of freedom of this model, see e.g., [33,34]. As an example, consider the 1-loop corrections to the Hhh coupling λ Hhh , for |α| → π/2, in which case there is no mixing between the light and heavy Higgs fields (see Eq. 3), as required in order to accommodate the 750 GeV γγ excess in the 4G2HDM (see section IV). In this limit, the Yukawa couplings of the 4th generation fermions to the light Higgs state h (i.e., t ′ t ′ h) vanish (see Eq. 4 and Table IV) and we find that the dominant effect arises from the 1-loop triangle diagram with the charged Higgs exchange in the loop, giving a "renormalized" Hhh couplingλ Hhh ≡ a Hhh λ Hhh , with: [2] Note that this is in contrast to "standard" frameworks such as the SM and the 2HDM's of types I and II, where the right-handed mixing matrices U R and D R are non-physical, being "rotated away" in the diagonalization procedure of the quark masses.
where I (m h , m H , m H + ) is the charged Higgs triangle loop integral, given by: In particular, one roughly finds |a Hhh | ∈ {0, 2} when m H + ∈ {500 GeV, 1 TeV} and with m H = 750 GeV, m h = 125 GeV and m ℓh ∼ O(1 TeV). For example, a Hhh ∼ −0.15 for m H + = m H = 750 GeV and m ℓh = 1.2 TeV. In what follows we will, therefore, define the "renormalized" scalar couplings as:λ i ≡ a i λ i , where λ i (i = Hhh, hH + H − , HH + H − ) are the corresponding tree-level couplings in Eqs. 9-11, and a i will be treated as free-parameters in the fit that will be varied in the range |a i | ∈ {0, 2}.

III. THE 125 GEV HIGGS SIGNALS AND PEWD
The measured signals of the 125 GeV Higgs particle, which in the 4G2HDM is the light Higgs h, and PEWD impose stringent constraints on the free parameter space of the 4G2HDM. For the 125 GeV Higgs signals we use the measured values of the "signal strength" parameters, which are defined as the ratio between the measured rates and their SM expectation. In particular, for a specific production and decay channel i → h → f , the signal strength is defined as: with where k j is the 4G2HDM coupling involved in j → h or h → j production or decay processes, normalized by its SM value, and R T is the ratio between the total width of h in the 4G2HDM and the total width of the SM 125 GeV Higgs. In particular, so that µ f i = k 2 i k 2 f /R T . In Table I we list the latest combined ATLAS and CMS six parameter fit from RUN1 [35], of the measured values for µ γγ gg , µ W W ⋆ gg , µ ZZ ⋆ gg , µ bb gg , µ τ τ gg and µ V /µ gg , where µ V stands for Higgs production via vector-boson fusion (VBF) or in association with a vector-boson (VH). [3] . We also write in Table I [35] and model predictions in terms of normalized couplings (see text) of the various production and decay channels for the 125 GeV Higgs, using the signal strength prescription. Note that while kV , k b and kτ are ratios of treelevel couplings, kg and kγ are the normalized (with respect to the SM) 1-loop 4G2HDM couplings hgg and hγγ, respectively, calculated using the formula in [36]. Also, in our 4G2HDM kW = kZ = kV . [3] We neglect Higgs production via pp → tth which, although included in the fit, is 2-3 orders of magnitudes smaller than the gluon-fusion channel For the PEWD constraints on the 4G2HDM, we update our study in [18]. In particular, the effects of any new physics can be divided into those which do and which do not couple directly to the ordinary SM fermions. For the former, the leading effect in the 4G2HDM comes from the decay Z → bb, which is mainly sensitive to the H + t ′ b and W + t ′ b couplings through one-loop exchanges of H + and W + , as was analyzed in detail in [18]. These contributions to Z → bb are, however, absent in the currently studied versions of the 4G2HDM, since our working assumption here is that V t ′ b → 0 and Σ d,u → diag (0, 0, 0, 1), so that the H + t ′ b and W + t ′ b vertices vanish or are negligibly small (see previous section).
The effects which do not involve direct couplings to the ordinary fermions, can be analyzed in the formalism of the oblique parameters S,T and U [37]. The contribution of a 2HDM with a 4th generation of chiral fermions to the oblique parameters were studied in [18]. This includes the pure 1-loop Higgs exchanges to the gauge-bosons 2-point functions and the 1-loop exchanges of t ′ and b ′ which shift the T parameter and which involve the new SM4-like diagonal coupling W t ′ b ′ (here also the contributions involving the off-diagonal couplings W t ′ b and W tb ′ are absent since we assume V t ′ b , V tb ′ → 0, see also [38]). These are calculated with respect to the SM values and are bounded by a global fit to PEWD [39]: with a correlation coefficient of ρ = +0.91. These values are obtained for ∆U = 0 (the U parameter is often set to zero since it can be neglected in most new physics models and, in particular in our 4G2HDM) and with the SM reference values M H,ref = 125 GeV and m t,ref = 173 GeV. We, thus, consider below the constraints from the 2-dimensional ellipse in the S − T plane which, for a given confidence level (CL), is defined by: where S exp = 0.06 and T exp = 0.1 are the best fitted (central) values, σ S = 0.09, σ T = 0.07 are the corresponding standard deviations and ρ = 0.91 is the (strong) correlation factor between S and T. We thus perform a random ("blind") scan of the relevant parameter space, imposing compatibility at 95% CL of the 4G2HDM with the measured 125 GeV Higgs signals listed above and with the best fitted values of S and T using Eqs. 17 and 18. In particular, we fix m H = 750 GeV (for compatibility with the recent 750 GeV γγ signal, see next section) and scan the rest of the parameters over the following ranges: We find two types of possible 4G2HDM "solutions": case 1: tan β ≤ 0.5, sin α → −1 and m 2 ℓh > 0. case 2: tan β ≥ 2, sin α ∼ 0.1 − 0.45 and any m 2 ℓh in the entire range scanned. In both cases above, m A , m H + and the 4th generation fermion masses can have values spanning over the entire scan ranges. In Fig. 1 we plot the resulting distributions of the relevant parameter space in the S − T , tan β − sin α and ∆m ℓ ′ − ∆m q ′ planes, where ∆m ℓ ′ ≡ m ν ′ − m τ ′ and ∆m q ′ ≡ m t ′ − m b ′ . We also show in Fig. 1 the resulting predicted 125 GeV Higgs signal strengths for the two cases above, which, as can seen, have different characteristics.
We next discuss the compatibility of the above two 4G2HDM solutions with the recently observed 750 GeV γγ excess.

IV. THE 4G2HDM AND THE 750 GEV γγ RESONANCE
We search here for the portion of parameter space of the two 4G2HDM cases found in the previous section, that survive once the 4G2HDM is also required to accommodate the 750 GeV γγ excess, which is being interpreted here as the decay of one or both of the heavy neutral Higgs (i.e., assumed to have masses ∼ 750 GeV) H → γγ and/or A → γγ.
Given the exploratory nature of our study, we will simplify our analysis at this point, assuming that the scalar spectrum have the characteristics of the so-called decoupling limit (see e.g., [40]). In particular, we assume that it is split into 2 typical scales: m light ∼ 125 GeV, corresponding to the observed light Higgs and m heavy ∼ 750 GeV around which the three heavy Higgs masses lie, i.e., m H , m A , m H + ∼ 750 GeV. Even though we find a wider range of allowed masses for the non-resonant heavy scalar states (i.e., for m A and m H + , see below) that can accommodate the 750 GeV signal, the choice m H , m A , m H + ∼ 750 GeV will suffice for conveying our point: that the 750 GeV resonance in the γγ channel can be accommodated by one of the heavy scalars of the 4G2HDM without any conflict with other existing relevant data. Indeed, if this measurement will be eventually confirmed, then it will be instructive to study the 4G2HDM within a wider range of the relevant parameter space.
We, thus, re-scan the 4G2HDM parameter space corresponding to two 4G2HDM cases found in the previous section, where now m H , m A and m H + are varied within a 30 GeV mass range around 750 GeV, i.e., m H,A,H + ∈ 750 ± 30 GeV. The scan is performed with the following additional "filters"/requirements (i.e., in addition to the requirement of compatibility with PEWD and with the measured 125 GeV Higgs signals, as outlined in the previous section): • Reproducing the 750 GeV γγ excess within the range 3 fb < σ(pp → H/A → γγ) < 13 fb. We find that the (by far) dominant H and/or A production mechanism is the gluon-fusion one gg → H/A, so that all the relevant cross-sections σ(pp → H/A → f ) are calculated in the narrow width approximation via: where √ s = 8 or 13 TeV and C gg is the gluon luminosity: giving C gg ∼ 2140(175) at √ s = 13(8) TeV, see [41].
• The resonating scalar which produces the 750 GeV γγ excess is required to have a width smaller than 45 GeV, i.e., Γ H/A < 45 GeV.
• We impose the existing experimental bounds on the production and decays of the heavy neutral scalars H and A, as obtained at the 8 and 13 TeV LHC runs (in particular when applied to m H , m A ∼ 750 GeV) in all other channels which are relevant to our study: pp → W + W − , ZZ, tt, τ τ, bb, hh, hZ. In particular, we use the 95% CL bounds in Table II quoted in [7].    Table II. The scatter plots are given for the mass splitting spectrum of the heavy fermions (left), the correlation between the soft breaking mass parameter m ℓh and the renormalization factor of the scalar couplings ai =λi/λi, i = Hhh, hH + H − , HH + H − (middle), and the resulting allowed ranges of the 125 GeV light Higgs signal strengths in all the measured channels (right).
Applying the above filters, we find that: 1. Only the CP-even scalar state H (with m H = 750 GeV), can accommodate the 750 GeV γγ resonance, since σ(pp → A → γγ) < ∼ O(0.01) fb, which is 2-3 orders of magnitudes smaller than the measured γγ excess, see also Table IV. 2. Only a "shrinked" version of the 4G2HDM case 1 survives out of the two cases that were found to be compatible with PEWD and the 125 GeV light Higgs signals. In particular, the surviving 4G2HDM models have (see Fig. 2): tan β ≤ 0.5, α → −π/2 and m ℓh > 600 GeV, having some correlation with the renormalization factors of the scalar couplings a i =λ i /λ i , i = Hhh, hH + H − , HH + H − .
3. The resulting heavy fermions mass ranges are narrowed to: 350 GeV < ∼ m t ′ , m b ′ < ∼ 390 GeV, where the lower limit is from direct searches (see section II), and 900 GeV < ∼ m ν ′ , m τ ′ < ∼ 1200 GeV, where the upper limit is a rough estimate of the perturbativity bound on heavy chiral leptons.
In Fig. 2 we show three scatter plots of the resulting 4G2HDM parameter space, corresponding to the mass spectrum of the heavy fermions, the correlation between the soft breaking mass parameter m ℓh and the renormalization factor of the scalar couplings a i =λ i /λ i , i = Hhh, hH + H − , HH + H − , and the resulting allowed ranges of the 125 GeV light Higgs signal strengths in all the measured channels. We see that, while |m t ′ − m b ′ | < ∼ 30 GeV, the mass splitting of the heavy leptons is typically |m ν ′ − m τ ′ | > ∼ m W . We also see that smaller values of m ℓh typically require larger values of the renormalization factors of the scalar vertices a i , e.g., a Hhh ∼ 1 for m ℓh ∼ 700 GeV.
It is interesting to note that the resulting mass spectrum of the heavy chiral quarks, which is required to accommodate the 750 GeV γγ resonance, is rather narrow and roughly centered around m H /2, i.e., m t ′ , m b ′ ∼ 350 − 390 GeV. This may hint back to the possibility that the the heavy scalars are composites primarily of the heavy chiral quarks, in which case the 4G2HDM might indeed be interpreted as a low energy effective framework for some TeV-scale strongly interacting theory. Such an effective low energy 2HDM, with features similar to the 4G2HDM discussed here, was introduced in [22], where it was shown that, using the Nambu-Jona-Lasinio (NJL) mechanism [42], it is possible to construct an effective sub-TeV 2HDM hybrid framework, in which the 125 GeV light Higgs is mostly a fundamental scalar, while the heavy Higgs states are components of a composite field of the form Φ h ∼ g ⋆ t ′ <Q ′c L (iτ 2 )t ′c R > +g b ′ <Q ′ L b ′ R >, which is responsible for EW symmetry breaking and for the dynamical mass generation of the heavy quarks. [4] V. PHENOMENOLOGY OF THE 4G2HDM Inspired by the indications of the 750 GeV γγ resonance and following the analysis of the previous section, we briefly consider here some of the distinct phenomenological consequences of the 4G2HDM with characteristics similar to those required to accommodate such a heavy scalar resonance.
In particular, we will assume below that tan β ∼ 0.5 and sin α ∼ −1, in which case the light 125 GeV Higgs of the 4G2HDM, h, does not couple to f ′ f ′ , while the heavy CP-even Higgs, H, does not couple to a pair of SM fermions (see Eqs. 4-7 and Table III). Also, the 4th generation heavy fermions are assumed to have masses in the ranges 350 GeV < ∼ m t ′ , m b ′ < ∼ 400 GeV and 900 GeV < ∼ m ν ′ , m τ ′ < ∼ 1200 GeV, and the dominant decay channels of the heavy quarks are t ′ → uh (u = u, c) and b ′ → dh (d = d, s, b), with corresponding branching ratios > ∼ 0.5, due to small off diagonal-entries Σ u 4i (i = 1, 2) and/or Σ d 4i (i = 1, 2, 3) (see Table III and discussion in section II). In the first column f is a SM fermion of the 1st-3rd generations, while in the second column f ′ stands for a 4th generation fermion. In the 3rd column fi correspond to any fermion of the ith generation. Also, I f = 1(−1) for up(down) type fermions.

Yukawa couplings in the 4G2HDM with sin
In Table IV we list three benchmark points (BMP1,BMP2,BMP3) which have some distinct characteristics and which are compatible with PEWD, with the 125 GeV Higgs signals, with the 750 GeV γγ signal and with the LHC bounds on all relevant 750 GeV Higgs resonance channels pp → H/A → f given in Table II. For definiteness, we have generated the benchmark points for the case of m H = 750 GeV and m A , m H + ∼ m H ± 50 GeV, but the discussion below has a more general scope, i.e., with regard to some of the possible phenomenological signatures of the 4G2HDM associated with the TeV-scale heavy scalars of the model and independent of whether the 750 GeV γγ resonance is confirmed or not. The three benchmark points include cases where the 750 GeV Higgs total width ranges from a few GeV to ∼ 45 GeV, having a resonance cross-section to γγ between 4-12 fb. They also correspond to cases where BR(H/A →q ′ q ′ ) ∼ 1 and BR(H + →q ′ q ′ ) ∼ 1.
In particular, if m H , m A > m q ′ /2, then H/A →q ′ q ′ is open and typically dominates, having a branching ratio of O(1) (see Table IV). In that case, we find that within the 4G2HDM parameter space discussed here, the corresponding resonance cross-sections forq ′ q ′ production at the 13 TeV LHC are typically σ(pp → H → q ′ q ′ ) ∼ O (10) [pb] and σ(pp → A → q ′ q ′ ) ∼ O(0.1) [pb], (both H and A produced through gluon-fusion gg → H/A), so that in the case of H → q ′ q ′ (see Table IV), this is about an order of magnitude larger than the QCD (continuum)q ′ q ′ production rate. Therefore, if the 750 GeV γγ resonance persists, one should also expect an observable resonance signal at least in the H →q ′ q ′ channel.
Let us, therefore, briefly investigate the signal H →q ′ q ′ under more general grounds, i.e., when m H > m q ′ /2 but not necessarily m H ∼ 750 GeV. For example, in the case of H →t ′ t ′ , the t ′ will further decay either via [4] Another interesting framework which entertains the idea that heavy chiral quarks may form the 750 GeV composite was recently suggested in [43].
15000, 0, 0.015, 5 0, 4000, 0.65, 109 7500, 6000, 0.02, 9 σ  the FC channels t ′ → uh (u = u or c) or via the 3-body decay Fig. 1). If the former case (i.e., t ′ → uh) dominates, then the resulting resonance signal should be searched for in pp In either case, the SM-like light Higgs (h) further decays into bb or W W with SM rates, giving rise to resonance signatures of the form pp → (nj + mb + ℓW ) H , with (n, m, ℓ) = (2,4,0), (2,0,4), (2,2,2), (2,4,2), (2,2,4), (2,0,6), (0, 2, 6), (0, 4, 4), (0, 6, 2) and with unique kinematic features that distinguishes them from more conventional signatures. Similar signals are also expected for H →b ′ b ′ . We recognize that these type of signals are very challenging and may require new strategies, in particular, for reconstructing the parent q ′ 's in such a high jet-multiplicity environment. The decay pattern of the charged Higgs may also change in the 4G2HDM, in particular for the case when m H + > m t ′ + m b ′ , for which the decay of H + into a pair of heavy 4th generation fermions can dominate (see BMP1 in Table  IV). In particular, taking m t ′ ∼ m b ′ ≡ m q ′ and assuming that H + is sufficiently heavier than 2m q ′ , so that we can ignore corrections of O(4m 2 q ′ /m 2 H + ) in the phase-space factors, we have in the 4G2HDM: Thus, for α ∼ −π/2, tan β ∼ 0.5 (i.e., cos(β − α) ∼ −0.45), m q ′ ∼ 350 GeV (i.e., values of the 4G2HDM parameter space that can accommodate the 750 GeV γγ signal) and taking m H + ∼ O(1) TeV, we obtain: (10), in which case BR(H + → t ′ b ′ ) ∼ 1 (e.g., as in the case of BMP2), leading to some interesting signatures of the heavy charged Higgs at the LHC. In particular, the dominant production channels of H + at the LHC are gg/gb → H + bt, H + W − /H +t , with a typical cross-section of ∼ 100 fb when tan β ∼ 1 [44]. The subsequent H + decay to a pair of 4th generation heavy fermions with BR(H + → t ′b′ ) ∼ 1 will, thus, lead to new H + signals, e.g., again with the typical 4G2HDM heavy fermion high jet-multiplicity signatures of the form pp → nj + mb + ℓW . This is in contrast to "standard" 2HDM frameworks where the heavy charged Higgs will dominantly decay to W h and/or tb (see BMP1 and BMP3), leading to a lower multiplicity of jets in the final state.
As noted earlier, a wider range of solutions exist (which are not being discussed here) to all data and filters mentioned above (i.e., including the 750 GeV γγ resonance), in which lighter pseudoscalar A and charged Higgs H + are allowed, with masses as low as 300 GeV. In such 4G2HDM scenarios, the heavy 4th generation quarks (and leptons) can have substantial decay rates in channels involving also the heavy Higgs species, i.e., t ′ → H + d, Au (d = d, s, b and u = u, c) and b ′ → H + u, Ad (d = d, s, b and u = u, c), followed by H + → W + h, tb and A → hZ, tt. Indeed, such decay patterns can also lead to some un-explored collider signatures of the 4G2HDM. We leave the discussion of the phenomenology of such wider range of 4G2HDM scenarios to a later work.
Finally, we wish to comment on the flavor violating structure of the 4G2HDM and its compatibility with the recently reported indications of the LFV decay of the 125 GeV light Higgs h → τ µ [2,4]. Writing the LFV couplings of h in a general form: one obtains: In our 4G2HDM we have for the case of the LFV decay h → τ µ (neglecting terms of O(m µ /m τ ), see Eq. 4): where we have defined Σ ℓ 32 = Σ ℓ 23 ≡ ξ τ µ (see Eq. 8) and: f (β, α) = cos(β − α) s β c β .

VI. SUMMARY
We have revisited a class of models beyond the SM, suggested by us a few years ago in [18], which put together an additional Higgs doublet with a heavy chiral 4th generation quark and lepton doublet and which have several important and attractive theoretical features. In particular, we focused on the so-called 4G2HDM of type I (in [18]), in which a discrete Z 2 symmetry couples the "heavy" scalar doublet only to the heavy 4th generation fermions and the "light" one to the lighter SM fermions.
We have confronted this model with PEWD, with the measured 125 GeV light Higgs signals and also studied its compatibility with the recent indication of a 750 GeV γγ resonance and with the current LHC bounds on heavy scalar resonances in other relevant channels. We found that the CP-even heavy Higgs state of the 4G2HDM with a mass ∼ 750 GeV can accommodate the measured 750 GeV excess for a rather unique choice of the parameter space: tan β ∼ 0.5, α ∼ −π/2 (the Higgs mixing angle) and with heavy chiral fermion masses m t ′ ,b ′ < ∼ 400 GeV and m ν ′ ,τ ′ > ∼ 900 GeV. We have shown that the heavy chiral quarks (and leptons) of the 4G2HDM may have FCNC decays into the light 125 GeV Higgs plus a light-quark jet, q ′ → jh, with branching ratios of O(1), thus leading to some un-explored signatures of q ′q′ production at the LHC and, therefore, being consistent with the current direct bounds on the masses of new heavy fermions. Indeed, new and rich phenomenology in q ′ -heavy Higgs systems is expected, including possible resonance production of q ′ q ′ pairs via either the heavy neutral or heavy charged Higgs particles of the 4G2HDM, which leads to high jet-multiplicity signatures, with or without charged leptons, of the formq ′ q ′ → nj + mb + ℓW , with n + m + ℓ = 6 − 8 and unique kinematic features which are related to the resonating heavy scalar and the decay pattern of the heavy quarks. The reconstruction of the q ′ q ′ pairs in such high jet-multiplicity signals is very challenging and require more thought and possibly new search strategies.
We also show that the recent indication of a percent-level branching ratio in the LFV decay of the 125 GeV Higgs h → τ µ, if it persists, can be readily addressed within the distinct flavor structure of the 4G2HDM.