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Exploring Two Higgs Doublet Models Through Higgs Production

We discuss the connections between the recently observed Higgs-like particle and rare B decays in the context of two Higgs doublet models (2HDMs). The measured decays of the Higgs boson to fermions and gauge bosons, along with the observation of the decay B_s ->\mu+ \mu-, place stringent restrictions on the allowed parameter space of 2 Higgs doublet models. Future measurements of h0 ->\gamma \gamma can potentially exclude type I 2HDMs, while the parameters of other 2HDMs are already severely restricted. The recent observations of the h0 ->\tau+ \tau- and h0 ->b bbar decays further constrain the models.


I. INTRODUCTION
The discovery of a Higgs-like particle at the LHC with a mass m h 0 ∼ 125 GeV is the beginning of the exploration of the source of electroweak symmetry breaking. The new particle has been observed in a number of different final states with rates roughly consistent with the Standard Model predictions, although the decay rate to γγ is slightly high. The crucial task now is to extract the properties (spin/parity and couplings to fermions and gauge bosons) of this particle as precisely as possible and determine whether they correspond to those predicted by the minimal Standard Model. It is also important to explore the possibility that there is a spectrum of Higgs-like states.
Many beyond the Standard Model (BSM ) scenarios have a Higgs-like particle which has Standard Model -like couplings to fermions and gauge bosons in the low energy limit, and precision measurements of the Higgs particle couplings can serve to limit the parameters of BSM models. A well motivated extension of the Standard Model is obtained by adding a second SU(2) L Higgs doublet, leading to 5 physical Higgs particles: h 0 , H 0 , A 0 , and H ± .
We will consider the possibility that the particle observed at the LHC is the lightest neutral Higgs particle, h 0 , of a 2 Higgs doublet model (2HDM.) 1 The 2HDM models generically have tree level flavor changing neutral currents (FCNCs) from Higgs exchanges unless there is a global or discrete symmetry which forbids such interactions [4,5] and therefore we consider only the class of models where there is a discrete Z 2 symmetry such that one of the fermions couples only to a single Higgs doublet. FCNCs are highly suppressed in this case and provide stringent limits on the parameters of the models. There are four possibilities for 2HDMs of this type which are typically called the Type I, Type II, Lepton Specific, and Flipped models [4]. We review the limits from FCNCs on these models, and determine the range of parameters consistent with the latest Higgs measurements at the LHC. Our goal is to study the extent to which LHC measurements in the Higgs sector can restrict the possibilities for 2HDMs. Previous works have examined the possibility of enhancing the branching ratio h 0 → γγ [1,6,7], and various other channels [8][9][10][11][12] in the 2HDMs and we discuss the implications of a measurement of h 0 → γγ which differs from the Standard Model prediction and demonstrate the impact of the h 0 → bb and 1 The possibility that the observed particle is the heavier neutral Higgs particle, H 0 , of a 2HDM has been examined elsewhere [1][2][3].
Finally, we show how the recent measurement of B s → µ + µ − [13] serves to further restrict 2HDMs.

II. REVIEW OF 2HDMS
The Higgs sector of the 2HDMs is parameterized in terms of tan β ≡ v 2 v 1 , where v 1 and v 2 are the vacuum expectation values of the two Higgs doublets and satisfy M 2 W = g 2 (v 2 1 +v 2 2 )/2, and the angle α which diagonalizes the neutral Higgs mass matrix. The couplings of the lightest Higgs boson, h 0 , to the Standard Model particles are parameterized as: where g iih = g hV V = 1 in the Standard Model and v = 246GeV . The h 0 coupling to gauge bosons is the same for all four models considered here, while the couplings to fermions differentiates between the models. The Higgs Yukawa couplings normalized to their Standard Model values are summarized in Table I. The Standard Model couplings are obtained for sin(β − α) = 1, sin α = − cos β, and cos α = sin β. The charged Higgs-fermion couplings can be written as, where P L,R = 1∓γ 5 2 , m l is the charged lepton mass and the coefficients λ f f are given in Table  II.
Perturbative unitarity of the Yukawa couplings is violated if For all models considered here this requires tan β > 0.28. Model II and the Flipped model require tan β < 140, while the Lepton-specific model has the limit tan β < 350 from perturbative unitarity. Other bounds on perturbative unitarity have been derived by requiring that the quartic couplings in the scalar potential remain positive up to a high scale [14] and by considering the perturbative unitarity of gauge boson scattering [15]. These bound typically give much lower upper bounds on tan β than those derived from perturbative unitarity of the Yukawa couplings, but we will not consider them further since these limits can be evaded by postulating new physics at some high scale.
There are also strong bounds on the 2HDMs from precision electroweak measurements, which can be parameterized by the oblique parameters, S, T and U. In the limit, M H 0 , M A , M H ± >> M Z and subtracting the Standard Model contribution [16,17], For M A = M H 0 = M H ± ∼ 1 T eV , ∆T provides no useful limit on sin(β − α), while ∆S requires cos(β − α) ∼ 1. The most significant restrictions come from B decays, as discussed in the next section.
The branching ratios to fermions in the 2HDMs are simply scaled from the couplings of The total widths in the 2HDMs are given by, 2 where we neglect other contributions which are smaller than the h 0 → γγ branching ratio and assume that there is no new physics beyond the 2HDM.
The decay width to γγ is found using the exact form factors of Refs. [19,20]. For 2 We assume g hW W = g hZZ .
The tri-linear h 0 H + H − coupling is not enhanced by a mass factor, and we neglect its negligible contribution [21].
Similarly, the decay to gluons proceeds predominantly through top and bottom quark loops, For large tan β, the b quark loop can contribute significantly to the gg → h 0 production channel in Model II and the Flipped model. In our numerical studies, we include both the b and t contributions exactly in all cases .
Using the results given above, the production from gluon fusion and the following decay to γγ or to f f pairs can be described by, The Higgs signal from gluon fusion with the subsequent decay to γγ is shown in Fig. 1 for √ S = 8 T eV 3 . It is interesting to note that in Model I, it is not possible to obtain R ggF γγ larger than ∼ 1.2, so a future measurement which confirms the current deviation of R ggF γγ from 1 could serve to exclude Model I 4 . For R ggF γγ > 1, only a narrow region of α ∼ −0.5 can be obtained. The Lepton Specific model is similar to Model I at small tan β, while at large tan β ( for fixed non-zero α) the total width is enhanced by the large branching ratio to τ + τ − , which decreases R ggF γγ . A value of R ggF γγ ∼ 1.2 is only consistent with the Lepton Specific model for α ∼ 0 and tan β > 8. Model II and the Flipped model have similar predictions for R ggF γγ with a wide range of α and tan β values consistent with R ggF γγ ∼ 1. The gluon fusion production with decay to τ + τ − is shown in Fig. 2. In Model I and the  Model rate for very specific values of α and tan β and hence a precise measurements of R ggF τ τ can serve to restrict these models significantly.
Preliminary LHC measurements of h 0 → bb and h 0 → τ + τ − in the vector boson fusion (VBF) and V h 0 channels are particularly interesting and will serve to distinguish between the different 2HDMs. Both VBF and V h 0 production follow the same simple scaling between the Standard Model rates and the 2HDM predictions, shown in Fig. 4. Note that in Models I and II, . This is because the h 0 coupling to bb is the same as the h 0 coupling to τ + τ − in these two models, as shown in Table I. As a result Fig. 3(a) is identical to Fig. 4(a) and similarly Fig. 3(b) and Fig. 4(b) are also identical to each other. One can also see that Fig. 3(a)  appears in Fig. 3(b) and Fig. 3(d) because the h 0 coupling to bb is the same for Model II and the Flipped model.

III. REVIEW OF LIMITS FROM FLAVOR PHYSICS
Limits on 2HDMs have been examined by many authors and we briefly update the results of Ref. [22] using the SuperIso program [23][24][25] in order to examine the restrictions on Stringent bounds also arise from the experimental measurement of B → X s γ [26,27], and are shown in Fig. 6  for the 2HDMs, in good agreement with the Standard Model prediction [32], New physics effects in B s → µ + µ − come predominantly from the charged Higgs exchanges.
The contributions to B s → µ + µ − in the type II two Higgs doublet model have been computed in the large tan β regime in Refs. [33][34][35], and adapted to the general Two Higgs doublet models considered here in the SuperIso program [24]. 5 The branching ratio for B s → µ + µ − in the Type I model is shown in Fig.7(a) as a function of M H + for various values of tan β. It is apparent that for M H + > 500 GeV, the branching ratio is almost a constant, independent of tan β. In Fig.7(b), the excluded region is shown In the Type II model, the branching ratio B s → µ + µ − has a significant dependence on tan β for small M H + , and goes to a constant for very large M H + . In this model high values of tan β are excluded at 3σ for small M H + , while there is a 2σ excluded region at large tan β, as shown in Fig. 8. The dependence of the excluded region on the choice of neutral Higgs masses, M H 0 and M A , is shown in Fig. 9 for α = −0.02 and tan β = 60, (which corresponds to the best fit to the Higgs data derived in Section IV).
For the Lepton Specific case, the dominant contribution to B s → µ + µ − is proportional to λ tt λ µµ and so the branching ratio is insensitive to tan β. In Fig. 10, we show the BR(B s → µ + µ − ) as a function of M H + and the regions which are excluded at 2 and 3σ from this decay. We see that the excluded region does not depend on tan β. For heavy charged Higgs masses, the branching ratio approaches a constant. The dependence on the choice of neutral Higgs masses is shown in Fig. 11. From Fig. 10(a), it is clear that the branching The branching ratio for B s → µ + µ − for the Flipped model is shown in Fig. 12 for several values of tan β and for M H 0 = M A = 300 GeV . For M H + > 300 GeV , the branching ratio is insensitive to the input parameters.

IV. RESULTS FROM HIGGS MEASUREMENTS
We do a simple χ 2 fit to the data shown in Tables III and IV assuming M h 0 = 125 GeV .
We follow the standard definition of , where R 2HDM represents predictions for the signal strength from the 2HDMs and R meas stands for the most recent results of the measured signal strength shown in Tables III and IV by the ATLAS and CMS collaborations at the LHC. σ meas denotes the uncertainty of R meas . 6 The results (with no constraints We perform a constrained fit to the data requiring tan β > 1, which is consistent with B physics data of the previous section. In all models, the results of Fig. 13 show that there are large regions of parameter space allowed at both the 2 and 3σ confidence levels and the results have only a mild dependence on tan β. In Model II and the Flipped model, α = 0 is not allowed, primarily due to the h 0 → bb measurement. In Model II, the Lepton Specific, and the Flipped model, only a small range of α is allowed and the χ 2 minimum occurs for large tan β (60, 54, and 77, respectively). In Model I, a fairly large range of α is consistent with the data and the χ 2 minimum is at tan β = 1.