Explaining 750 GeV diphoton excess from top/bottom partner cascade decay in two-Higgs-doublet model extension

In this paper, we interpret the 750 GeV diphoton excess in the Zee-Babu extension of the two-Higgs-doublet model by introducing a top partner ($T$)/bottom partner ($B$). In the alignment limit, the 750 GeV resonance is identified as the heavy CP-even Higgs boson ($H$), which can be sizably produced via the QCD process $pp \to T\bar{T}$ or $pp \to B\bar{B}$ followed by the decay $T\to Ht$ or $B \to Hb$. The diphoton decay rate of $H$ is greatly enhanced by the charged singlet scalars predicted in the Zee-Babu extension and the total width of $H$ can be as large as 7 GeV. Under the current LHC constraints, we scan the parameter space and find that such an extension can account for the observed diphoton excess.


I. INTRODUCTION
Very recently, both the ATLAS data with 3.2 fb −1 and the CMS data with 2.6 fb −1 [1] have reported an excess of the diphoton resonance (X) around 750 GeV. The local significances of their results are 3.6σ and 2.6σ in the respective experiments. Combining the 8 and 13 TeV data [2], the observed signal strength σ X × Br(X → γγ) is 10.6 ± 2.9 fb for the ATLAS and 4.47 ± 1.86 fb for the CMS. Since there are no excesses observed in the dijet [3], tt [4], diboson or dilepton channels, understanding such an excess becomes a challenging task. So far, many new physics models have been proposed for this excess [2,[5][6][7][8][9][10][11][12], among which, a singlet scalar is usually introduced as the 750 GeV resonance.
Different from the previous singlet scalar explanations, we attempt to interpret the 750 GeV resonance as a heavy Higgs boson from a second doublet, which is mainly originating from the QCD top partner (T ) or bottom partner (B) pair production process followed by the decay T → Ht or B → Hb. Obviously, such a scenario still needs the extra particles to enhance the 750 GeV Higgs decay into diphoton. Therefore, we introduce a top partner/bottom partner to the Zee-Babu extension [13] of the two-Higgs-doublet model , where two extra charged singlet scalars can enhance the decay of diphoton mode and generate the neutrino mass. Considering the LHC Higgs data, our study will be focused on an interesting limit of this model, in which one of the neutral Higgs mass eigenstates is almost aligned with the direction of the scalar field vacuum expectation values. In this limit, the 125 GeV Higgs boson tends to have the gauge couplings as in the Standard Model (SM) and is easily consistent with the current Higgs data, while the heavy CP-even Higgs boson has the very small couplings or no couplings to the SM particles.
Compared to the direct gg → H production process, there are several benefits for the production of H from the QCD process pp → TT /BB → HH + tt/bb. Since the production of T /B and the decay of H are generally unrelated, it is easy to obtain a large branching ratio of H → γγ by suppressing the 750 GeV Higgs coupling to the top quark. Although the cascade decays have other objects in the diphoton events, such as the additional top or bottom quark jets, the status of whether or not there are other objects in the event is unclear at the moment. So, currently, the cascade decay is still a feasible way to interpret the 750 GeV diphoton excess although not very likely.
Our work is organized as follows. In Sec. II we present the Zee-Babu extension of the 2HDM with the top/bottom partner. In Sec. III we perform the numerical calculations and discuss the 750 GeV diphoton production rate and the total width of the resonance in the allowed parameter space. Finally, we give our conclusion in Sec. IV.

II. MODEL
A. Two-Higgs-doublet model The general Higgs potential is written as [14] Here we focus on the CP-conserving case where all λ i and m 2 12 are real. In the Higgs basis, the two complex scalar doublets with the hypercharge Y = 1 can be written as The Φ 1 field has the vacuum expectation value (VEV) v =246 GeV, and the VEV of Φ 2 field is zero. The G 0 and G + are the Nambu-Goldstone bosons which are eaten by the gauge bosons. The H + and A are the mass eigenstates of the charged Higgs boson and CP-odd Higgs boson, and their masses are given by The physical CP-even Higgs bosons h and H are the linear combination of ρ 1 and ρ 2 , To satisfy the 125 GeV Higgs data, we focus on the so-called alignment limit [15], which corresponds to λ 6 = 0 and cos θ = 0. In this limit, the two CP-even Higgs masses are given as The general Yukawa interactions without the tree-level FCNC can be given by [16] − where Q T L = (u L , d L ), L T L = (ν L , l L ), and Φ 1,2 = iτ 2 Φ * 1,2 . y u , y d and y ℓ are 3 × 3 matrices in family space, and κ u , κ d and κ ℓ are the coupling constants. The couplings of neutral Higgs bosons normalized to the SM Higgs boson are give by where V denotes Z and W , and f denotes u, d and ℓ.

B. Zee-Babu Extension
In order to enhance the branching ratio of the 750 GeV Higgs boson decay to diphoton, we can suppress the total width by taking a small heavy CP-even Higgs coupling to the top quark. However, for this case the charged Higgs of 2HDM (H ± ) can not enhance the branching ratio of diphoton sizably. The perturbativity will give the upper bound of the the heavy CP-even Higgs coupling to the charged Higgs. A light H ± can enhance the width of H → γγ, but the decay H → H ± W ∓ will be open and enhance the total width more sizably. Therefore, some additional particles are needed to enhance the 750 GeV Higgs decay into diphoton, such as the vector-like fermions or the charged scalars. Since the amplitude of H → γγ is proportional to the square of electric charge of the particle in the loop, the multi-charged particle can enhance H → γγ sizably.
Here we take the approach of Zee-Babu model to introduce two SU(2) L singlet scalar fields π + and χ ++ with hypercharge 1 and 2 [13], respectively. In addition to enhancing the decay rate of H → γγ sizably, this model can naturally give rise to the small neutrino Majorana mass.
The potential of the two singlet scalars can be written as The gauge invariance precludes the singlet Higgs fields from coupling to the quarks. The Yukawa coupling of singlets to leptons are The trilinear µ term in Eq. (8) breaks the lepton number and gives rise to the neutrino Majorana mass contributions at the two-loop level. The detailed introductions on the neutrino mass can be found in [13]. Here we focus on the charged Higgs couplings to the heavy CPeven Higgs. Since the k 1 and k ′ 1 terms of Eq. (8) that contain the 125 GeV Higgs couplings to charged Higgs are proportional to sin θ, we assume k 1 and k ′ 1 to be very small and ignore them in our calculations. Then, after the Φ 1 acquires the VEV, the masses of π + and χ ++ are m π and m χ , and the CP-even Higgs couplings to the charged Higgses are determined by k 3 and k 4 terms, hπ + π − : −k 3 cos θv, hχ ++ χ −− : −k 4 cos θv, For cos θ = 0, the couplings of hπ + π − and hχ ++ χ −− are zero. Considering the constraints of perturbativity and stability of the potential, we simply take 0 k 3 = k 4 4π, and fix m π = m χ = 375 GeV, which will give the maximal value of the form factor of scalar loop in the H → γγ decay.

C. Top/Bottom Partners
Next, we introduce the top partner to interact with Φ 2 in the 2HDM. The Yukawa interaction is given as where Q T tL = (t L b L ) T and t R are the left-handed SU(2) doublet of third generation and the right-handed SU(2) singlet of top quark, respectively, while T R and T L are two SU (2) singlet top partners.
We obtain the mass matrix of top quark and the partner (t, T ), In this paper, we assume m ′ T to be very small so that there is no mixing between t and T . If the Φ 1 has the interactions with Q tL and T R , the mixing of t and T will appear. Here we do not consider this case. Due to the absence of the mixing of t and T , the top partner mass is m T . Using the Eq. (2), the Eq. (11) gives the Yukawa interactions, Using the Eq. (4), the Eq. (13) gives the top partner couplings to the Higgs bosons, Due to the absence of the mixing of t and T , there are not the diagonal couplings of HT T and hT T . For cos θ = 0, the T → th channel will be open, and some simulations on the channel at the LHC have been studied in [17]. In this paper we will take cos θ = 0 for which the coupling of htT is absent.
For the singlet T L and T R , the general neutral and charged current interactions are [18] Where c θ L = cos θ L and s θ L = sin θ L with θ L being the mixing angle of the left-handed top and the partner.
. In this paper we assume that there is no mixing of t and T , namely s θ L = 0. For this case, the Eq. (15) shows that the couplings of ZT t and W +T b are zero, and there are no decays of T → Zt and T → W + b.
Similarly, we can introduce the bottom partner and the Yukawa interaction is given as where B R and B L are two SU(2) singlet bottom partners. When m ′ B approaches to zero, there is no mixing between b and B. From the Eq. (16), we can obtain the bottom partner couplings to Higgses, Similar to the top partner, there are no couplings of hbB, hBB, HBB, ZBb and W −B t for cos θ = 0 and the absence of the mixing of b and B.

III. NUMERICAL CALCULATIONS AND DISCUSSIONS
The 2HDM is usually described in the physical basis and Higgs basis. In the physical basis, the two Higgs doublet Φ 1 and Φ 2 have the non-zero VEVs, and tan β is defined as v 2 /v 1 with v 1 and v 2 being the VEV of the first and second scalar doublet. In the Higgs basis, the VEV of Φ 2 is zero, therefore, the parameter tan β is absent. The coupling constants of Higgs potential in the Higgs basis as shown in the Eq. (1), can be expressed using the coupling constants and tan β in the physical basis [19].
In the Higgs basis, the Yukawa interactions of fermions are parameterized by the κ u , κ d and κ ℓ as shown in Eq. (6) and Eq. (7), and which can be mapped to the four traditional types of 2HDMs via the κ u , κ d and κ ℓ specified in Table I. However, here we take sin θ = 1, For this choice, the Eq. (7) shows that the 750 GeV Higgs (H) couplings to the down-type quark and lepton are zero, and the coupling to gauge boson is zero, which can naturally satisfy the bounds from the measurements of the diboson, dijet and dilepton. The 125 GeV Higgs (h) couplings to up-type quark, down-type quark, lepton and gauge boson A. T and B decay As discussed above, the partners T and B have no couplings to the gauge bosons and the 125 GeV Higgs in the parameter space taken in this paper. Therefore, T and B can be hardly constrained by the current experimental data of the exotic quark from the ATLAS [20] and CMS [21] searches. The main decay modes are T → tH, T → tA and T → bH + for the T quark, as well as B → bH, B → bA and B → tH − for the B quark. For m H = 750 GeV, the oblique parameters favor m H ± and m A to have the degenerate mass, especially for that their mass have sizable deviation from 750 GeV.
We take m B = 770 GeV and m T = 940 GeV, and plot their branching ratios versus m A in Fig. 1. Since the widths of T → tH, T → tA and T → bH + are proportional to y 2 T , their branching ratios are independent on y T , which also holds for the B quark and y B . Both decay modes.

B. The production rate of 750 GeV diphoton resonance
In order to obtain the maximal production rate, we assume m A = m H ± to be larger than For m H ± > m H , λ 4 and λ 5 are negative, which will be constrained by the vacuum stability to some extent. As discussed in the Section II, cos θ = 0 determines λ 6 = 0 and λ 1 = m 2 h 2v 2 , and λ 2 , λ 3 and λ 7 are the free parameters, which can be tuned to satisfy theoretical constraints from the vacuum stability, unitarity and perturbativity. Refs. [22][23][24][25] give the corresponding well-known classical formulas for the constrains on the coupling constants of the physical basis. We employ 2HDMC [26] to perform the theoretical constraints on the coupling constants in the physical basis, and then use the formulas of Eqs. (A16-A22) in the ref. [19] to transform the results into the constraints on λ 2 , λ 3 and λ 7 in the Higgs basis, namely expressing λ 2 , λ 3 and λ 7 with the allowed parameters of the physical basis. In the We define the production rate of the 750 GeV diphoton, At the LHC, the cross sections of gg → BB (TT ) with m B = 770 GeV (m T = 940 GeV) are approximate 240 (65) fb for √ s=13 TeV and 28 (5.5) fb for √ s=8 TeV [27].
Taking k 4 = 4π, m π = m χ = 375 GeV, m T = 940 GeV and m B = 770 GeV, we project the surviving samples on the plane of R γγ versus κ u in Fig. 3. Since the heavy CP-even Higgs coupling to top quark is proportional to κ u , the production rate from gg → H increases with κ u . Since the cross section of gg → BB (TT ) is independent on κ u , and the total width of 750 GeV Higgs increases with κ u , the production rate from gg → BB (TT ) decreases with increasing of κ u . The production rate from latter dominates over the former for the small κ u , and equals to the former for κ u = 0.8 (0.42). R γγ > 1 fb favors κ u to be smaller than For a very small top Yukawa coupling, the total width of 750 GeV Higgs is very narrow, which leads a large Br(H → γγ). Therefore, the very small κ u is mainly excluded by the the total width can reach 7 GeV for R γγ = 2 fb, and be larger than 2 GeV for R γγ < 6 fb.
For m T = 940 GeV, the total width can reach 2 GeV for R γγ = 2 fb, and be larger than 0.8 GeV for R γγ < 4 fb.
With the increasing of the mass of bottom partner and top partner, the cross section of gg → BB (TT ) will decrease rapidly and be around 2 fb for m B = m T = 1500 GeV. For the enough small top quark Yakawa coupling of the 750 GeV Higgs, the 750 GeV Higgs will mainly decay into γγ, Zγ and ZZ, and Br(H → γγ) is around 60%. Therefore, the diphoton production rate of the 750 GeV Higgs will reach 1.2 fb for m B = m T = 1500 GeV.
For m B and m T are smaller than 1500 GeV, the more large production rate can be obtained.
However, the total width of the 750 GeV Higgs is required to be very narrow to enhance the production rate. Therefore, the precise measurement of width at the LHC can be as a sensitive probe of the bottom partner and top partner.
For the 750 GeV resonance, the CMS slightly prefers a narrow width, and the ATLAS favors a width of 45 GeV. Such large width can be obtained by the enhancement of κ u and κ d which can enhance the widths of H →tt,bb. However, with the increasing of the total width, the branching ratio of the diphoton mode decreases, which will suppress the diphoton production rate. For the model with one singlet bottom partner (m B = 770 GeV), the total width of the 750 GeV Higgs is required to be smaller than 7 GeV in order to obtain R γγ > 2 fb. Some additional charged particles need be introduced to enhance the width of H → γγ in order to obtain R γγ > 2 fb and Γ H ≃ 45 GeV.
In this paper, we discussed the two different scenarios of the singlet top partner and the singlet bottom partner. Besides, one can attempt to introduce the doublet fields, The Yukawa interactions can be given as In order to avoid the experimental constraints of the ATLAS and CMS searches for the and the charged current of T and B still appears since they are the doublets of SU(2) L , In order to obtain the large cross sections of pp →BB/T T , one should take the small masses of B and T . For m T = m B = 770 GeV, the 750 GeV diphoton production rate from pp →BB → HHbb process is the same as the model with the singlet B L and B R . Also the 750 GeV diphoton resonance can be originating from the pp →T T followed by the off-shell decays T → t * H and T → W * B * (→ Hb). Since T will partly decay into the other objects, including the off-shell 750 GeV Higgs, the 750 GeV diphoton rate from the pp →T T is smaller than that of the pp →BB. This model predicts the existence of the top partner and bottom partner simultaneously, and the particle spectrum is more complicated than the model with one top partner and the model with one bottom partner which are studied in this paper.

IV. CONCLUSION
To accommodate the 750 GeV diphoton excess, we proposed an extension of 2HDM with the top and bottom partners. In addition, we took the approach of Zee-Babu model to introduce two scalar singlets (one is singly charged, and the other is doubly charged), which can naturally give a small neutrino Majorana mass and enhance the 750 GeV Higgs decay into diphoton. In this model, the production rate R γγ of the 750 GeV diphoton is from both gg → BB (TT ) and gg → H, and the former dominates over the latter for a small top quark coupling with the 750 GeV Higgs, and is comparable to the latter for a large top Yukawa coupling.
For m B = 770 GeV, R γγ > 2 fb favors κ u < 0.46 and k 4 > 0.05, and the total width of the 750 GeV Higgs can reach 7 GeV for R γγ = 2 fb. For m T = 940 GeV, R γγ > 2 fb favors κ u < 0.24 and k 4 > 1.0, and the total width can reach 2 GeV for R γγ = 2 fb. To obtain enough large production rate of the 750 GeV diphoton, the total width tends to decrease with the increasing of the bottom partner and top partner masses. Therefore, the precise measurement of the width of the resonance at the LHC can be as a sensitive probe of these bottom partner and top partner.

Acknowledgment
This work has been supported in part by the National Natural Science Foundation of China under grant Nos. 11575152, 11305049, 11275057, 11405047, 11275245,