Higgs boson decays and production in the left-right twin Higgs model

The left-right twin Higgs model predicts one neutral Higgs boson $\phi_{0}$ and it acquires mass $m_{\phi_{0}}\sim \mu_{r}$ with the $\mu$ term, which can be lighter than half the SM-like Higgs boson mass in a portion of parameter space. Thus, the SM-like Higgs boson $h$ can dominantly decay into a pair of light neutral Higgs bosons especially when $m_{h}$ is below the $WW$ threshold. First, we examine the branching ratios of the SM-like Higgs boson decays and find that the new decay mode $h\rightarrow \phi_{0}\phi_{0}$ is dominant for the case of $m_{h}>2m_{\phi_{0}}$. Then we study the production via gluon fusion followed by the decay into two photons or two weak gauge bosons and found that the production rate can be significantly suppressed for some part of parameter space. Finally, we comparatively study the process $\gamma\gamma\rightarrow h \rightarrow b\bar{b}$ at ILC in the cases of $m_{h}>2m_{\phi_{0}}$ and $m_{h}<2m_{\phi_{0}}$, respectively. We find that these predictions can significantly deviated from the SM predictions, e.g., the gluon-gluon fusion channel, in the cases of $m_{h}>2m_{\phi_{0}}$ and $m_{h}<2m_{\phi_{0}}$, can be suppressed by about 80% and 45%, respectively. Therefor, it is possible to probe the left-right twin Higgs model via these Higgs boson production processes at the LHC experiment or in the future ILC experiment.


I. Introduction
The Higgs boson is the last ingredient of the standard model (SM) to be probed at experiments. The precision electroweak measurement data and direct searches suggest that the Higgs boson must be relatively light and its mass should be roughly in the range of 114.4 GeV∼186 GeV at 95% C.L. [1], but the SM suffers of the so-called hierarchy problem [2], which is due to the presence of quadratic divergences in the loop processes for the scalar Higgs boson self-energy. Therefore, the standard model with a light Higgs boson can be viewed as the lowenergy effective approximation of a fundamental theory. A wide variety of models have been introduced to address electroweak symmetry breaking (EWSB) and the hierarchy problem: supersymmetry [3], large extra-dimensions [4], topcolor models [5], and little Higgs models [6] et al.
Recently, the twin Higgs mechanism is proposed as a solution to the little hierarchy problem [7,8,9]. Instead of protecting the Higgs mass from receiving large radiative corrections by using several approximate global symmetries, twin Higgs theories use a discrete symmetry in combination with an approximate global symmetry to eliminate the quadratic divergences that arise at loop level. Together with the gauge symmetries of the model, the discrete symmetry mimics the effect of a global symmetry, thus stabilizing the Higgs mass. The twin Higgs mechanism can be implemented in left-right models with the discrete symmetry being identified with left-right symmetry [8]. In the left-right twin Higgs(LRTH) model, the leading quadratically divergent contributions of the SM gauge bosons to the Higgs boson mass are canceled by the loop involving the new gauge bosons, while those for the top quark can be canceled by the contributions from a heavy top quark. Besides, the other Higgs particles acquire large masses not only at quantum level but also at tree level. The phenomenology of the LRTH model are widely discussed in literature [10,11,12,13], and constraints on LRTH model parameters are studied in [14]. The LRTH model is also expected to give new significant signatures in future high energy colliders and studied in references [15].
Besides the SM-like Higgs boson h, there are two additional neutral Higgs bosons in the LRTH model, which areĥ 0 2 and φ 0 . The neutral Higgs bosonĥ 0 2 could be a good dark matter candidate [12]. The light neutral Higgs boson φ 0 is a pseudoscalar and charged under the spontaneously broken SU(2) R . Its mass is determined by µ r that can be anything below the scale f . Here we consider another possibility, in which the mass m φ 0 < m h /2. Therefore, in addition to the SM decay channels, the Higgs boson can then decay into two φ 0 bosons. This new decay channel can change other decay branching ratios and thus affect the strategy of searching for the Higgs boson at high energy colliders, which is the main aim of this paper.
Ref. [16] studied the Higgs phenomenology in LRTH model by paying special attention to the decay h →ŜŜ which is strongly corrected with the dark matter scattering on nucleon.
They found that such an invisible decay can severely suppress the conventional decay modes like h → V V (V = W, Z) and h → bb. Note that similar exotic decays for the SM-like Higgs boson may also be predicted by some other new physics models like the little Higgs models and SUSY or two Higgs-doublet models et al [17,18]. A common feature of their phenomenology is the suppression of the conventional visible channels of the Higgs boson. To distinguish between different models, all the channels of Higgs production should be jointly analyzed. In this work we first study the decay branching ratios of the Higgs boson in the LRTH model for small value of m φ 0 . Then we study the production via gluon fusion followed by the decay into two photons or two charged gauge bosons in the cases of m h > 2m φ 0 and m h < 2m φ 0 , respectively. We also study the process γγ → h → bb at ILC for these two cases.
This article is organized is as follows. In the next section, we briefly review the left-right twin Higgs model. In Sec. III, we calculate the decay branching ratios of the Higgs boson. In Sec. IV, we calculate the main production of the Higgs boson at the LHC via gluon fusion followed by the decay into two photons or two weak gauge bosons. In Sec. V we calculated the rate of γγ → h → bb at ILC. Finally, we give our conclusion in Sec.VI.

II. Review of the left-right twin Higgs model
Before our calculations we recapitulate the left-right twin Higgs (LRTH) model. The details of the LRTH model as well as the particle spectrum, Feynman rules, and some phenomenology analysis have been studied in Ref. [10]. Here we will briefly review the essential features of the LRTH model and focusing on the new particles and the couplings relevant to our computation.
The LRTH model is based on the global U(4) 1 × U(4) 2 symmetry with a locally gauged subgroup SU(2) L ×SU(2) R ×U(1) B−L . The twin symmetry is identified with the left-right symmetry which interchanges L and R, implying that the gauge couplings of SU(2) L and SU(2) R are identical (g 2L = g 2R = g 2 ). Two Higgs fields, H andĤ, are introduced and each transforms as (4,1) and (1,4) respectively under the global symmetry. They can be written as where H L,R andĤ L,R are two component objects which are charged under the SU(2) L × The global U(4) 1 (U(4) 2 ) symmetry is spontaneously broken down to its subgroup U (3)  The remaining Higgses are the SM Higgs doublet H L and an extra Higgs doubletĤ L = (Ĥ + 1 ,Ĥ 0 2 ) that only couples to the gauge boson sector. A residue matter parity in the model renders the neutral HiggsĤ 0 2 stable, and it could be a good dark matter candidate. In the LRTH model, the masse of charged gauge bosons and fermions are given by [10] The values of f andf will be bounded by electroweak precision measurements. Once f is fixed, the values off can be determined from the minimization of the Coleman-Weinberg potential of the SM Higgs. The mass parameter M is essential to the mixing between the SM-like top quark and the heavy T-quark.
At the leading order, the couplings expression forms of the Higgs boson with charged gauge bosons and fermions, which are related to our calculation can be written as [10] hW W : htt : where The Coleman-Weinberg potential, obtained by intefrating out the gauge bosons and top quarks, yields the SM Higgs potential, which determine the SM Higgs VEV and its mass, as well as the masses for the other Higgs. On the other hand, the µ-term, contributes to the Higgs masses at tree level. The mass of φ 0 and new scalar self-interactions are given by [10] here p1, p2, and p3 refer to the incoming momentum of the first, second, and third particle, respectively. From above we can see that the mass of the neutral Higgs boson φ 0 is a free parameter and is determined by µ r and f . Here we consider another possibility, in which the mass is in the low mass region where the new decay h → φ 0 φ 0 can be open.

III. Higgs decay branching ratios in LRTH model
In the LRTH model, the major decay modes of the Higgs boson are the SM-like ones: h → ff (f = b, c, τ ), W W and ZZ. The LRTH model gives corrections to these decay modes via the corresponding modified Higgs couplings where X denotes a SM particle, Γ(h → XX) SM is the decay width in the SM, and the g hXX and g SM hXX are the couplings of hXX in the LRTH model and SM, respectively. The loop-induced decays H → gg and H → γγ will be also important for a low Higgs mass. In the LRTH model, in addition to the corrections via the modified couplings htt and hW W , the new heavy T-quark and charged gauge bosons can also contribute to their decay widths [19]. For the decay h → Zγ, the W boson loop contribution is dominant [20] and thus we only consider the alteration of the Higgs coupling with the W boson. Because the QCD radiative corrections are rather small [21], our results is precise enough.
As discussed in [14], the mass of neutral Higgs boson φ 0 may be as low as 50GeV . Therefore, in addition to the SM decay channels, the new decay h → φ 0 φ 0 will open for m h ≥ 2m φ 0 , and the partial width is given by here g hφ 0 φ 0 is the couplings of hφ 0 φ 0 .
In the LRTH model, the SM-like Higgs mass can be obtained via the minimization of the Higgs potential, which depends slightly on M and Λ but is insensitive to f . Varying M between 0 and 150GeV , Λ between 2πf and 4πf , its mass is found to be in the range of 145 − 180GeV [10]. However, if we take a little smaller value of Λ, the lower bound on the SM-like Higgs mass will be relaxed. In our calculations, the free parameters involved are f , M, m φ 0 and the Higgs boson mass m h . For the Higgs boson mass, we will take it in the range of 110GeV − 200GeV .
Following Ref. [10], we will assume that the values of the free parameters f and M are in the ranges of 500GeV − 1500GeV and 0 ≤ M ≤ f , respectively.
A search strategy of the Higgs boson depends sensitively on its branching ratios(BR): In the SM, the major decay mode for m h < 2m W is into bb while that for m h > 2m W is into W + W − . In the LRTH model, there may be one new decay mode h → φ 0 φ 0 for Higgs boson. In table 1, we list the Higgs decay branching ratios normalized to the SM predictions for three main channels in the LRTH model. Table 1 shows that the deviation from the SM prediction for each decay mode becomes small as f gets large. The deviation from the SM prediction is also sensitive to the Higgs boson mass. For m h = 120GeV , and 500GeV ≤ f ≤ 1000GeV , the deviations for the decay h → bb and h → gg are in the ranges of 11% − 68%, 18% − 78%, respectively. For the decay modes h → gg and h → γγ, the deviations from the SM predictions are also sensitive to M, which are not shown here. We will show the dependence of these decay modes on M later.  In the SM the Higgs production at the LHC is dominated by gluon fusion process. The h → γγ channel shows very good sensitivity in the range of 114GeV < m h < 140GeV . Especially, the rate σ(gg → h) × BR(h → γγ) can be measured to 10%(30%) with an integrated luminosity 100f b −1 (10f b −1 ) from both ATLAS and CMS [22]. Once we find a light Higgs boson at the LHC, this channel can provide a test for different models. In the LRTH model, σ(gg → h) is strongly correlated with the decay width Γ(gg → h). In our results we use σ(gg → h) to denote the hadronic cross section of the Higgs production proceeding through gg → h at parton level. We use CTEQ6L [23] for parton distributions, with the renormalization scale µ R factorization scale µ F chosen to be µ R = µ R = m h .
In Fig. 2    When Higgs mass is relatively heavy (2m W < m h < 2m Z ), the decay h → W W → lνlν is an excellent channel for searching for Higgs boson [24]. In Fig. 4 we plot the rates of σ(gg → h) × BR(h → W + W − ) normalized to the SM prediction in the LRTH model versus the value of f for m h = 180GeV and m φ 0 = 50GeV . We see that, compared with the SM prediction, the LRTH model can suppress the rates significantly for a small of f . For M = 150GeV and 500GeV ≤ f ≤ 800GeV , the suppression of SM prediction is in the range of 37% − 14%, which can exceed the experimental uncertainty (10% − 20%) [25].
It has been shown [26] that, the Higgs boson can dominantly decay into a pair of pseudoscalar boson. Together with smaller g ZZh and B(h → bb) than in the SM, the LEP Higgs boson mass bound based on the limit (g ZZh /g SM ZZh ) 2 B(h → bb) can be reduced. In Ref. [27], the authors shown that h → ηη → bbbb is complementary and can be used to detect the intermediate Higgs boson at the LHC, via W h and Zh production. In the LRTH model, φ 0 mainly decays into bb, cc, or τ + τ − . The decay branching ratio of φ 0 → bb, cc, and τ + τ − are close to the corresponding SM Higgs decay branching ratios [10]. Thus the ultimate dominant decay mode of the Higgs can be h → φ 0 φ 0 → bbbb. Detailed study needs to be done to optimize the cuts and identify the signal from the background. Such study is beyond the scope of the current paper and we leave it for future work.

V. The process γγ → h → bb in the LRTH model
While the LHC is widely regarded as discovery machine for Higgs boson, a precision measurement of Higgs property can be only achieved at the proposed International Linear Collider (ILC) [28]. A unique feature of the ILC is that it can be transformed to γγ modes by the laserscattering method. Such an option of photon-photon collision can possibly measure the rates of the Higgs production with a precision of a few percent. Especially, for γγ → h → bb process, the production rate could be measured at about 2% for a light Higgs boson [29]. Such a process γγ → h → bb is a sensitive probe for new physics because the loop-induced hγγ coupling and the hbb coupling are sensitive to new physics [30].    ized to the SM prediction in the LRTH model, for m φ 0 = 50GeV , and m h < 2m φ 0 , respectively.
From Fig. 5, we can see that the rate have a sizable deviation from the SM prediction, and the magnitude of deviation is sensitive to the scale f . For M = 150GeV , m h = 120GeV , and 500GeV ≤ f ≤ 1000GeV , the suppression is in the range of 70% − 12%. The reason for such a serve suppression is similar to what have been discussed above, i.e., the opening of new decay mode. In the case of m h < 2m φ 0 , the new decay mode h → φ 0 φ 0 is kinematically forbidden. Fig.6 show that the LRTH model also suppresses the rate σ(γγ → h) × BR(h → bb), but the suppression can only reach about 4%. This is because the contribution from the LRTH model mainly come from the loops of new top partner and heavy charged gauge boson, in addition to the modified couplings htt and hW W at order v 2 /f 2 [19]. For a large value of f , the suppression is only a few percent.

VI. Conclusion
The twin Higgs mechanism provides an alternative method to solve the little hierarchy problem. The Left-right twin Higgs model is a concrete realization of the twin Higgs mechanism, which predicts one neutral scalar particle φ 0 . With the µ term introduced by hand, the φ 0 boson acquires mass m φ 0 ∼ µ r , which can be lighter than half the Higgs boson mass in a portion of parameter space. In this paper we focus on the case of m h ≥ 2m φ 0 so that the new decay h → φ 0 φ 0 can be open. From our numerical results we obtain the following observations: (i) For the Higgs decay, we found that, with f = 500GeV and 2m φ 0 < m h < 160GeV , the new decay h → φ 0 φ 0 can be the dominant mode and it can give very different branching ratios from the SM prediction. The branching ratios of the conventional decay modes of the Higgs boson, h → gg and h → bb, can be suppressed over 60%, 50%, respectively; (ii)For the rates σ(gg → h) × BR(h → γγ(W + W − )) at the LHC, the LRTH model can give severe suppression relative to the SM predictions, whenever the neutral scalar mass is less than the mass of the Higgs boson; (iii) For the process γγ → h → bb, the LRTH model can always suppress the rate for the cases of m h > 2m φ 0 and m h < 2m φ 0 , respectively. However, the production rate can be severely suppressed in some of the parameter space where the new decay mode is open and dominant for the case of m h > 2m φ 0 ; (iv) The Higgs production cross section times the branching ratios of the conventional decays can be all suppressed significantly for a small value of the scale f . Therefore, it is possible to probe the LRTH model via these Higgs boson production processes at the LHC experiment or in the future ILC experiment.