LHC diphoton and Z+photon Higgs signals in the Higgs triplet model with Y=0

We study the implications of the LHC diphoton and Z+photon Higgs signals on the Higgs triplet model with Y=0. We discuss three different scenarios: (i) the observed boson is the light Higgs boson $h$; (ii) it is the heavy Higgs boson $H$; (iii) the observed signal is from the almost degenerate $h$ and $H$. We find that the inclusive Higgs diphoton rates in the first two scenarios can be enhanced or suppressed compared to the SM value, which can respectively fit the ATLAS and CMS diphoton data within $1\sigma$ range. The inclusive $ZZ^*$ rates are suppressed, which are outside $1\sigma$ range of ATLAS data and within $1\sigma$ range of CMS data. Meanwhile, another CP-even Higgs boson production rate can be suppressed enough not to be observed at the collider. For the third scenario, the Higgs diphoton rate is suppressed, which is outside $1\sigma$ range of ATLAS data, and the $ZZ^*$ rate equals to SM value approximately. In addition, we find that the two rates of $h\to \gamma\gamma$ and $h\to Z\gamma$ have the positive correlations for the three scenarios.


I. INTRODUCTION
Recently, the CMS and ATLAS collaborations have announced the observation of a new boson around 125. 5 GeV [1,2]. This observation is corroborated by the Tevatron search results which showed a 2.5σ excess in the range 115-135 GeV [3]. The diphoton rate is sizably higher than the SM expectation while the signal rates of ZZ * and W W * are consistent with the SM values. There are still large uncertainties on the V bb and ττ channels.
The recent Higgs data has been discussed in the SUSY models [4], little Higgs models [5] and the extensions of Higgs field models, such as the two-Higgs-doublet model [6], the Higgs triplet model (Y=2) [7], the models with septuplet [8] and color-octet scalar [9]. In this work, we will study the implications of the LHC diphoton Higgs signal on the Higgs triplet model with Y=0 [10], which predicts two neutral CP-even Higgs bosons h, H and a pair of charged Higgs H ± . The model has the more simplest particle spectrum than the two-Higgs-doublet model and the Higgs triplet model (Y=2). We will discuss three different scenarios: (i) the observed boson is the light Higgs h, and the heavy Higgs H is not observed at the LHC; (ii) it is the heavy Higgs H, and the light Higgs h is not observed at the LEP; (iii) the observed signal is from the almost degenerate h and H. Besides, we will study the correlations between h → Zγ and h → γγ. Since both of the rates are loop-induced by charged particles, they should be closely correlated. Any new physics effects manifested in the diphoton decay should also alter the Zγ decay [11,12] Our work is organized as follows. In Sec. II we recapitulate the Higgs triplet model with Y=0. In Sec. III we discuss the LHC diphoton Higgs signal and the correlations between h → Zγ and h → γγ. Finally, we give our conclusion in Sec. IV.

II. HIGGS TRIPLET MODEL WITH Y=0
In the Higgs triplet model with Y=0 (HTM0), a real SU(2) L triplet scalar field Σ with Y = 0 is added to the SM Lagrangian in addition to the doublet field Φ. These fields can be written as The renormalizable scalar potential can be written as [13] V where F ≡ (δ 0 ) 2 + 2δ + δ − and all the parameters are real. The Higgs doublet and triplet fields can acquire vacuum expectation values with After the spontaneous symmetry breaking, the Lagrangian of Eq. (2) predicts the four physical Higgs bosons, including two CP-even Higgs bosons h, H and a pair of charged Higgs H ± . These mass eigenstates are in general mixtures of the doublet and triplet fields. The mass matrixes of neutral and charged Higgs bosons are [13] The physical mass eigenstates and the unphysical electroweak eigenstates are related by rotations through two mixing angles θ 0 and θ + : Where the Goldstone boson G ± is eaten by the gauge bosons.
Since the experimental value of the ρ parameter is near unity [14], 4v 2 t /v 2 d is required to be much smaller than unity. In our calculation, v t is taken as 1 GeV. The mixing angle θ ± is proportional to vt v d , therefore it is very small. The charged Higgs mass is given as The neutral mixing angle θ 0 is given as Where The neutral Higgs boson masses are given as In our calculations, the involved Higgs couplings are listed as [13] hff Where s + = sin θ + and c + = cos θ + . All the momenta flow into the vertex.

III. THE HIGGS DIPHOTON AND Zγ RATES AT THE LHC
In our calculations, we take m h , m H , a 2 , b 4 and v d , v t as the input parameters, which can determine the values of λ 0 , a 1 , m H ± . As mentioned above, v t is taken as 1 GeV. The perturbativity can give the strong constraints on a 2 and b 4 , The electroweak T parameter can give the constraints on the splitting of m H and m H ± , 13]. Since the coupling H ±f i f j is sizably suppressed by s + , the search experiments through the top quark decay hardly give the constraints on H ± . The experimental data at the LEP gives the lower bound of the charged Higgs mass, m H ± > 79.3 GeV [15]. As shown in the Eq. (11), the h couplings to ff and W W are proportional to c 0 while these couplings of H are proportional to s 0 . Due to v t ≪ v d and s + → 0, the h couplings to W W and H + H − are sensitive to c 0 while these couplings of H are sensitive to s 0 . Therefore, the cross sections and the decay widths of h(H) normalized to SM values can be given as (13) where V denotes W, Z. Compared to SM, in addition to the modified htt and hW W couplings, the charged Higgs H ± will alter the decays h → γγ and h → Zγ via the one-loop.
The corresponding expressiones are given in the Appendix A.
The Higgs boson γγ, ZZ * and Zγ rates of HTM0 normalized to the SM values are respectively defined as Where σ ( pp → h(H) ) is the total cross section of Higgs boson. The analytic expressions in Eq. (13) and Eq. (14) may help us understand the Higgs production and decay well. In our numerical calculations, we take code Hdecay to consider the relevant higher order QCD and electroweak corrections [16].
R γγ = 1.8 ± 0.5, R ZZ = 1.2 ± 0.6. (ATLAS) The CMS collaboration has released their results of the measurement of Zγ and set an upper limit on the ratio R Zγ < 10 [17].

A. Scenario I
For the scenario I, the light Higgs h is the observed boson. Since the observed ZZ * rate is consistent with the SM value, c 0 can not be too small. Also, it is important to make sure that the production rate of H is small enough not to be detected at the LHC. Thus, to obtain a large c 0 and a small s 0 , we require C > A (see Eq. (9)).
In Fig. 1, we plot R h (γγ) versus a 2 , m H ± and c 2 0 , respectively. The h coupling to H + H − is sensitive to the parameter a 2 , which gives the additional contributions to the decay h → γγ via one-loop. The left panel shows that the H ± contributions to R h (γγ) can interfere constructively with W contributions for a 2 < 0 and interfere destructively for a 2 > 0, leading R h (γγ) > 1 and R h (γγ) < 1, respectively. The magnitude becomes sizable as the increasing of the absolute value of a 2 and the decreasing of m H ± . The ATLAS and CMS   The corresponding s 2 0 is smaller than 0.14, which will suppress the production rate of H at the LHC sizably, leading that H is not detected at the LHC.  The large m H ± favors the large c 2 0 , which leads that s 2 0 is small and H is difficult to be detected at the LHC. Fig. 3 shows R h (γγ) versus R h (Zγ). We find that the two rates are positively correlated, and the behavior of R h (Zγ) is similar to that of R h (γγ). Further, the prediction of R h (Zγ) equals to that of R h (γγ) approximately.

B. Scenario II
For the scenario II, the heavy Higgs H is the observed boson. The parameter s 0 can not be very small to make the observed ZZ * rate to be consistent with the experimental data.
Besides, it is important to make sure that the production rate of h is small enough not to be detected at the LEP. Thus, we require C < A to obtain a large s 0 and a small c 0 , (see Eq. (9)).
In Fig. 4, we plot R H (γγ) versus a 2 , m H ± and s 2 0 , respectively. Similar to R h (γγ), R H (γγ) is also larger than 1.0 for a 2 < 0 and smaller than 1.0 for a 2 > 0. R H (γγ) can reach 5.0 for a 2 ∼ −3.5 and m H ± ∼ 80 GeV, which is much larger than R h (γγ) since m H ± for the former is smaller than that for the latter. The right panel shows that the scatter plots lie in the region of s 2 0 > 0.92, For such values of s 0 , the ZZ * rate of H is consistent with the experimental data.
In Fig. 5, we plot a 2 and m H ± for which R H (γγ) is in the 1σ range of the LHC data (1. 2-2.3). The small m H ± favors a large s 2 0 , leading to a small c 2 0 . For example, c 2 0 is smaller than 0.02 for 80 GeV ≤ m H ± ≤ 100 GeV. The corresponding cross section of e + e − → Zh is below the upper limit presented by the LEP [18].
In Fig. 6, we plot R H (γγ) versus R H (Zγ). We find that the two rates are also positively correlated for the scenario II. The 1 σ range of diphoton experimental data will imply that R H (Zγ) should be in the range of 1.2 and 2.5.  (7) and (10).
In Fig. 7, we plot R h (γγ)+R H (γγ) versus a 2 and c 2 0 , respectively. We find that the Higgs diphoton rate is suppressed compared to SM value, 0.87 < R h (γγ)+R H (γγ) < 0.9, which is disfavored by the enhancement of diphoton data. Due to a 1 > 0, a 2 must be larger than zero to obtain a very small | B | (B = −a 1 v d /2 + a 2 v d v t ). Thus, R h (γγ)+R H (γγ) is smaller than 1.0 since the H ± contributions will interfere destructively with the W contributions for a 2 > 0. The right panel shows that the large mixing angle θ 0 may appear. The reason is that | A − C | still may be smaller than | B | although | B | is very small.
In Fig. 8, we plot R h (γγ) + R H (γγ) versus R h (Zγ) + R H (Zγ). We find that the two rates are also positively correlated and approximately equal.

IV. CONCLUSION
In the Higgs triplet model with Y=0, we study the Higgs boson γγ and Zγ rates at the LHC. We obtained the following observations: (i) For the observed boson is the light Higgs h, whose diphoton rate can be within the 1σ lower range of the ATLAS and CMS data. The heavy Higgs H production rate can be suppressed enough not to be observed at the LHC.
(ii) For the observed Higgs is the heavy Higgs H, whose diphoton rate can be within the whole 1σ range of the ATLAS and CMS data. The light Higgs h production rate can be suppressed enough not to be observed at the LEP. (iii) For the observed signal is from the almost degenerate h and H, the Higgs diphoton rate is suppressed compared to SM, which is disfavored the ATLAS and CMS data. (iv) The Zγ and γγ rates are positively correlated for the above three scenarios.

Acknowledgment
This work was supported by the National Natural Science Foundation of China (NNSFC) under grant Nos. 11105116, 11005089, and 11175151.