The 125 GeV Higgs in the context of four generations with 2 Higgs doublets
Abstract
We interpret the recent discovery of a 125 GeV Higgslike state in the context of a two Higgs doublets model with a heavy 4th sequential generation of fermions, in which one Higgs doublet couples only to the 4th generation fermions, while the second doublet couples to the lighter fermions of the 1st3rd families. This model is designed to accommodate the apparent heaviness of the 4th generation fermions and to effectively address the lowenergy phenomenology of a dynamical electroweak symmetry breaking scenario. The physical Higgs states of the model are, therefore, viewed as composites primarily of the 4th generation fermions. We find that the lightest Higgs, , is a good candidate for the recently discovered 125 GeV spinzero particle, when , for typical 4th generation fermion masses of GeV, and with a large mixing in the righthanded quarks sector. This, in turn, leads to , which drastically changes the decay pattern. We also find that, based on the current Higgs data, this two Higgs doublet model generically predicts an enhanced production rate (compared to the SM) in the channel and a reduced and ones. Finally, the heavier CPeven Higgs is excluded by the current data up to GeV, while the pseudoscalar state, , can be as light as 130 GeV. These heavier Higgs states and the expected deviations from the SM in some of the Higgs production channels can be further excluded or discovered with more data.
I Introduction
The LHC has recently observed a new scalar particle with a mass around GeV that could be consistent with the Higgs boson of the Standard Model (SM) CMSHiggs (); ATLASHiggs (). In addition, a study of the combined Tevatron data has revealed a smaller broad excess corresponding to a mass between 115 GeV and 135 GeV TevatronHiggs () which is consistent with this LHC discovery. With more data collected, the LHC is expected to be able to unveil the detailed properties of the new scalar particle and verify its nature.
From the theoretical side, there has been a collective effort in the past decades in the search for new physics beyond the SM, that can address some of the fundamental unresolved questions in particle physics. One simple candidate that was extensively studied in the past several years is the so called SM4 (also referred to as “naive” or “simple” SM4); the SM with a fourth sequential generation of fermions (for reviews see sher0 (); hou2009rev (); SM4proc (); khlopov ()). This simple extension of the SM was studied for addressing some of the challenges in particle physics, such as: the hierarchy problem DEWSB (); holdomnew (); hung1 (); ghnew (), the origin of matter  anti matter asymmetry in the universe baryoref (); fok () and the apparent anomalies in flavor physics SAGMN08 (); SAGMN10 (); ajb10B (); buras_charm (); 4Gflavor ().
Unfortunately, the recent LHC searches for the SM4 heavy 4th generation quarks have now pushed the exclusion limits to GeV for the and GeV for the LHC_4G (), which is on the border of their perturbative regime. Moreover, the SM4 Higgs was already excluded in the mass range GeV by the 2011 data SM4Higgsbound () when . Thus, the above reported discovery of a light Higgs with a mass around 125 GeV is not compatible with the SM4 that includes a heavy 4th generation neutrino with a mass GeV, i.e., with a mass larger than the current lower bound on PDG (). In fact, it was further pointed out recently in Lenz (); Lenz2 (); Nir (); Lenz3 () that the interpretation of the measured Higgs signals is not consistent with the SM4 also for the case . In particular, in the SM4, the leading gluonfusion light Higgs production mechanism is enhanced by a factor of due to the contribution of diagrams with and in the loops Kribs_EWPT (), which in general leads to larger signals (than what was observed at the LHC) in the channels. However, if the 4th generation masses are of GeV, then the decay channels are suppressed due to NLO corrections Passarino (); Passarino2 (), and the exclusion of the SM4 is based mainly on the channel. In the channel there is also a substantial suppression of due to (accidental) destructive interference in the loops Kribs_EWPT (); He3 () and another factor due to NLO corrections Passarino (); Passarino2 (). When is taken to be light enough so that becomes , then the channel becomes further suppressed to the level that the observed excess can no longer be accounted for Lenz2 (). For a recent comprehensive analysis of the SM4 status in light of the latest Higgs results and electroweak precision data (EWPD), we refer the reader to 12091101 ().
However, as was noted already 20 years ago Luty () and more recently in hashimoto1 (); 4G2HDM (), if heavy 4th generation fermions are viewed as the agents of electroweak symmetry breaking (and are, therefore, linked to strong dynamics at the nearby TeVscale), then more Higgs particles are expected at the subTeV regime. In this case, the Higgs particles may be composites of the 4th generation fermions and the lowenergy composite Higgs sector should resemble a two (or more) Higgs doublet framework. Indeed, the phenomenology of multiHiggs 4th generation models was studied recently in hashimoto1 (); 4G2HDM (); soninew (); sher2HDM (); sher1 (); Bern (); Gunion (); FermCond (); gustavo1 (); gustavo2 (); hung3 (); hung2 (); wise1 (); valencia (); He2 (); alfonso1 () and within a SUSY framework in fok (); shersusy (); dawson (); rizzo (), for a review see AHEPrev (). In Geller () it was also shown that the current exclusion limits on the SM4 and could be significantly relaxed if the four generations scenario is embedded in a 2HDM framework.
Adopting this viewpoint, i.e., that the 4th generation setup should be more adequately described within a multiHiggs framework, we will study in this paper the expected Higgs signals of a 2HDM with a 4th generation family, investigating whether the interpretation of the recently measured 125 GeV Higgs properties are consistent with one of the neutral scalars of the 4th generation 2HDM.
Ii 2HDM’s and 4th generation fermions
The 2HDM structure has an inherent freedom of choosing which doublet couples to which fermions. For the three generations 2HDM, three popular setups were suggested which are usually referred to as type I, type II and type III 2HDM. In the case where the 2HDM is assumed to underly some form of TeVscale strong dynamics mediated by the 4th generation fermions, we expect the Higgs composites to couple differently to the 4th generation fermions. This can be realized in a class of 2HDM models named the 4G2HDM, suggested in 4G2HDM (). Most of our analysis below is performed in this 4G2HDM framework and a comparison to a 2HDM of type II (which also underlies the SUSY Higgs sector) with and without 4th generations will also be discussed.
Let us recapitulate the salient features of the 2HDM frameworks with a 4th generation of fermions (we will focus below on the quarks sector, but a generalization to the leptonic sector is straight forward). Assuming a common generic 2HDM potential, the phenomenology of 2HDM’s is generically encoded in the texture of the Yukawa interaction Lagrangian. The simplest variant of a 2HDM with 4th generations of fermions, can be constructed based on the so called type II 2HDM (which we denote hereafter by 2HDMII), in which one of the Higgs doublets couples only to uptype fermions and the other to downtype ones. This setup ensures the absence of treelevel flavor changing neutral currents (FCNC) and is, therefore, widely favored when confronted with low energy flavor data. The Yukawa terms for the quarks of the 2HDMII, extended to include the extra 4th generation quark doublet is:
(1) 
where () are left(right)handed fermion fields, is the lefthanded quark doublet, are general Yukawa matrices in flavor space and are the Higgs doublets:
(2) 
As mentioned above, motivated by the idea that the low energy scalar degrees of freedom may be the composites of the heavy 4th generation fermions, 4G2HDM () have constructed a new class of 2HDM’s, named the 4G2HDM, that can effectively parameterize 4th generation condensation by giving a special status to the 4th family fermions. The possible viable variants of this approach can be parameterized as 4G2HDM ():
(3) 
where are the two Higgs doublets, is the identity matrix and () are diagonal matrices defined by .
In particular, in the type I 4G2HDM of 4G2HDM () (which we will focus on below and which will be denoted hereafter simply as the 4G2HDM), one sets , so that the “heavier” Higgs field () is assumed to couple only to the 4th generation quarks, while the “lighter” Higgs field () is responsible for the mass generation of all other (lighter 1st3rd generations) fermions.
The Yukawa interactions for these 4G2HDM models in terms of the physical states were given in 4G2HDM (). For the lighter CPeven Higgs it reads:
(4) 
where is mixing angle in the CPeven neutral Higgs sector, is the ratio between the VEVs of and and , are new mixing matrices in the down(up)quark sectors, which are obtained after diagonalizing the quarks mass matrices. These matrices are key parameters of the model, which depend on the rotation (unitary) matrices of the righthanded down and upquarks, and , and on whether and/or are “turned on”:
(6) 
Thus, as opposed to “standard” 2HDM’s, in the 4G2HDM some elements of and are physical and can, in principle, be measured in Higgsfermion systems. In particular, inspired by the working assumption of the 4G2HDM and by the observed flavor pattern in the up and downquark sectors, it was shown in 4G2HDM () that, for , the new mixing matrices and are expected to have the following form:
(7) 
and similarly for by replacing . The new parameters and are free parameters of the model that effectively control the mixing between the 4th generation and the 3rd generation quarks. We therefore expect , so that a natural choice for these parameter would be and (see also 4G2HDM ()). In what follows we will thus set and vary the mixing parameter in the range .
Iii 2HDM’s and the 125 GeV Higgs Signals
Clearly, once a new Higgs doublet is introduced, the phenomenology of the Higgs particles production and decays becomes more complicated. In particular, the new Yukawa couplings depend on several more parameters (i.e., in the 4G2HDM on , , and ) and the CPeven Higgs couplings to the and to the bosons have extra prefactors of and (the pseudoscalar does not couple at treelevel to the and the ). As a result, the oneloop decay and the leading Higgs production mechanism can be significantly altered compared to their SM and SM4 values, depending on , , and on the 4th generation fermion masses (i.e., assuming , therefore setting throughout our analysis). This is demonstrated in Fig. 1, where we plot the widths and , as a function of these three parameters setting GeV. The dependence on is depicted in a narrow range around , for which the 4G2HDM is consistent with both EWPD 4G2HDM () and with the observed 125 GeV Higgs signals (see below).
We see that both and have a strong dependence on the Higgs mixing angle , while is also very sensitive to and to the new mixing parameter , due to their role in the interference between the fermion loops and the Wboson loop. In Fig. 2 we further plot the various relevant branching ratios of a 125 GeV in the 4G2HDM, as a function of for , and GeV.
Let us now turn to the recently reported LHC Higgs searches and the implications of the discovery of a 125 GeV Higgslike particle on the 4G2HDM setup with a 4th generation of fermions. The quantity that is usually being used for comparison between the LHC and Tevatron results and the expected signals in various models is the normalized crosssection:
(8) 
For the observed ratios of crosssections, i.e., the signal strengths , and the corresponding errors , we use the latest results as published in CMSHiggs (); ATLASHiggs (); TevatronHiggs ():

: (taken from

:

:

:

:

:
The values given above are the result of a combination of the most recent data in each channel.^{1}^{1}footnotetext: We combine the results from the CMS and ATLAS experiments (for we combine the results from CMS and Tevatron), where in cases where the measured value was not explicitly given we estimate it from the published plots. The uncertainties are calculated by treating the reported experimental uncertainties as statistical and assigning 15% theoretical uncertainty to the gluon fusion production mechanism and 5% theoretical uncertainty on electroweak production mechanisms and on the branching fractions uncertainty (). One can easily notice that the channels which have the highest sensitivity to the Higgs signals and contributed the most to the recent 125 GeV Higgs discovery are and . In all other channels the results are not conclusive and at this time they are consistent with the background only hypothesis at the level of less than .
Clearly, a SM Higgs is ideally most consistent with in every channel, while in other models we expect some deviations in the various measured channels, depending on the parameters of the model and on the mass of the scalar candidate which should be compatible with the LHC results. Thus, the comparison to any given model can be performed using a fit:
(9) 
where are the errors on the observed crosssections and is the calculated normalized crosssection in any given model. In particular, we take advantage of the fact that , and calculate using
(10) 
where is the Higgs production mechanism, i.e., either by gluon fusion , vector boson fusion or the associated HiggsW production at the Tevatron.
The Higgs signals in a 2HDM setup with a 4th generation of fermions have already been discussed to some extent in the literature Bern (); Gunion (); valencia (); He2 (); new2HDM4G (), but with no general picture of how these signals match all the observed Higgs crosssections reported above. Here, we try to quantify how well the 2HDM scenarios (where the lightest Higgs particle, , has a mass of 125 GeV) fit all the available Higgs data, by calculating the for all the relevant channels in two 2HDM realizations with four generations  the 2HDMII and the 4G2HDM (see section II).
We use the latest version of Hdecay Hdecay (), with recent NLO contributions which also include the heavy 4th generation fermions, where we have inserted all the relevant couplings of the 4G2HDM and the 2HDMII frameworks described in section II. For the 4th generation fermion masses involved in the loops of the decays (i.e., in the 1loop NLO corrections for the cases ), we have used the approximation of a degenerate 4th generation fermion sector, where we have tested below two representative cases: and GeV (the effect of mass splittings between 4th generation fermions on is negligible). It is important to note that, while the first case ( GeV) is excluded for the SM4 LHC_4G (), it is not necessarily excluded for the 4G2HDM, since in this model the decay patterns of and can have a completely different topology, e.g., having , for which the current limits (which are based on the “standard” SM4 decays and ) do not apply, see Geller ().
As mentioned earlier, we find that the simple SM4 case, with a 125 GeV Higgs is excluded to many ’s when confronted with the Higgs search results. Also, as was already noted in Gunion () in the context of the “standard” 2HDMII (i.e., with four generations), we find that the simplest case of a light 125 GeV pseudoscalar of any 2HDM, with and without a 4th family, is not compatible with the Higgs data, irrespective of the 4th generation fermion masses. In particular, the signals of the 125 GeV Higgs decaying into a pair of vector bosons, and , excludes this possibility due to the absence of treelevel and couplings. We, therefore, focus below only on the case where the observed 125 GeV Higgslike particle is the lighter CPeven Higgs, .
We plot in Fig. 3 the resulting and pvalues in the 4G2HDM case (combining all the six reported Higgs decay channels above), with GeV, and 600 GeV, and 0.5 and for (this range is allowed by EWPD and flavor physics in the 2HDM 4th generation setups, see 4G2HDM (); AHEPrev ()). The value of the Higgs mixing angle is the one which minimizes the for each value of . The SM best fit is also shown in the plot. In Fig. 4 we further plot the resulting and pvalues as a function of , this time minimizing for each value of with respect to both and (in the 4G2HDM case). For comparison, we also show in Fig. 4 the and pvalues for a 125 GeV in the 2HDMII with a 4th generation and in the SM.
Looking at the pvalues in Figs. 3 and 4 (which “measure” the extent to which a given model can be successfully used to interpret the Higgs data in all the measured decay channels) we see that, of the 4G2HDM with and GeV is a good candidate for the recently observed 125 GeV Higgs, giving a fit comparable to the SM fit. The “standard” 2HDMII setup with GeV is also found to be consistent with the Higgs data in a narrower range of . We find that the fit favors a large mixing parameter , implying which completely changes the decay pattern 4G2HDM () and, therefore, significantly relaxing the current bounds on Geller (). This can be seen in Table 1 where we list 6 representative sets of best fitted values (to be used in the plots below) for in the 4G2HDM, that correspond to points on the best fitted 4G2HDM curves shown in Fig. 4.
In Fig. 5 we further test the goodness of fit for the 125 GeV of the 4G2HDM, where, in addition to the Higgs results, we explicitly imposed the constraints on the 4G2HDM parameter space from EWPD (from the S and T parameters and from ) using the results in 4G2HDM (); AHEPrev (). Evidently, our conclusions above do not change after adding the EWPD constraints to the analysis.
Finally, we note that we have also tested the 3 generations type II 2HDM and found that its lightest CPeven Higgs is also a good candidate for the observed 125 GeV Higgs particle, giving a fit which is also comparable to the SM fit for .
Point #  [GeV]  

P1  0.7  0.09  0.5  400 
P2  0.7  0.51  0.433  600 
P3  1.0  0.1  0.42  400 
P4  1.0  0.08  0.5  600 
P5  1.3  0.11  0.3  400 
P6  1.3  0.07  0.33  600 
Iv Higgs phenomenology in the 4G2HDM
In Fig. 6 we plot the individual pulls and the signal strengths for the various measured channels, and , respectively, as a function of , for the above best fitted 4G2HDM curve with GeV. We see that appreciable deviations from the SM are expected in the channels , and . In particular, the most notable effects are about a deviation (from the observed value) in the VBF diphoton channel and a deviation in the channel. The deviations in these channels are in fact a prediction of the 4G2HDM strictly based on the current Higgs data, which could play a crucial role as data with higher statistics becomes available. They can be understood as follows: the channels that dominate the fit (i.e., having a higher statistical significance due to their smaller errors) are . Thus, since the production vertex is generically enhanced by the loops, the fit then searches for values of the relevant 4G2HDM parameters which decrease the decays in the appropriate amount. This in turn leads to an enhanced (i.e., due to the enhancement in the production vertex) and to a decrease in the and , which are independent of the enhanced vertex but are sensitive to the decreased one. It is important to note that some of the characteristics of these “predictions” can change with more data collected.
We conclude with the implications of the above results for the other two neutral scalars of the 4G2HDM. For the heavier CPeven neutral Higgs, , we consider its decays to and , which are currently the most sensitive channels in which searches for a heavy SM Higgs were performed at the LHC. A useful approximation of the expected exclusion range on can be performed by comparing the calculated signal strengths:
(11) 
to the observed/measured values of this quantity, i.e., to (note that in the 4G2HDM we find for ). In Fig. 7 we plot as a function of for the 6 best fitted points of the relevant 4G2HDM parameter space, given in Table 1. We also show in Fig. 7 an approximate exclusion line for , i.e., for the observed signal strength , which we have extracted from the most recent CMS exclusion plot in this channel (see CMSZZ ()) and which is currently the most stringent observed exclusion limit for a heavy Higgs with a mass GeV. We see that GeV is excluded by the current data in the channel for points P1, P2, P3 and P5 (i.e., for GeV), while for point P4 and P6 GeV is allowed.
The current CMS and ATLAS Higgs data in the and channels are not sensitive to the pseudoscalar , due to the absence of a tree level and coupling (and due to the smallness of the corresponding and oneloop couplings gunionAZZ ()). Therefore, the only relevant search channels which are currently sensitive to the decays are and , for which a search for the Higgs was performed up to a Higgs mass slightly below by both CMS and ATLAS. Defining the signal strengths for the signals as:
(12) 
we plot in Figs. 8 and 9 and , respectively, as a function of (we assume that ), for points P1P6 of Table 1. Here also, we plot the existing approximate exclusion lines and , based on the most recent CMS analysis, which currently gives the most stringent limits in these two channels CMStt (); CMSgg (). We see that a pseudoscalar as light as 130 GeV is allowed by the current data, e.g., for for points P1 and P2.
V Summary
We have studied the recently measured Higgs signals in the framework of a specific 2HDM with a fourth generation of fermions (the 4G2HDM suggested in 4G2HDM ()), designed and motivated by the possibility that the subTeV Higgs particles are condensates of the heavy 4th generation fermions, which are therefore, viewed as the agents of dynamical electroweak symmetry breaking.
We find that the lightest CPeven Higgs state of this model, , is a good candidate for the recently discovered 125 GeV Higgs signals in all the measured channels, within a large portion of the 4G2HDM allowed parameter space, which is consistent with the current bounds from EWPD. In particular, for typical 4th generation fermion masses in the range GeV, and a large mixing (the parameter predicted by the model), the lightest 4G2HDM Higgs gives a good overall fit to the current 125 GeV Higgs data  roughly comparable to the SM fit.
For these values of the 4G2HDM parameter space, in particular with , the flavor changing decay dominates with , leading to different signatures (than the simple SM4) that can be searched for at the LHC using the methods suggested in Geller ().
We also find that, based on the current Higgs data, the 4G2HDM predicts large deviations from the SM in the channels , and , which remains to be tested with more data.
Finally, the heavier CPeven Higgs state, , is found to be excluded in this model up to GeV, while the pseudoscalar Higgs state, , can be as light as 130 GeV and can, therefore, be discovered (or ruled out in this small mass range) with more data collected in the channels.
Acknowledgments: SBS and MG acknowledge research support from the Technion. GE thanks R. Godbole and S. Vempati for hospitality and discussions. The work of AS was supported in part by the U.S. DOE contract #DEAC0298CH10886(BNL).
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 (59) The CMS collaboration, CMS Physics Analysis Summaries, Report Number: CMSPASHIG12018, available on the CERN CDS information server.
 (60) The CMS collaboration, CMS Physics Analysis Summaries, Report Number: CMSPASHIG12015, available on the CERN CDS information server.