HZ associated production with decay in the Alternative Left-Right Model at CEPC and future linear colliders

In this study, Higgs and Z boson associated production with subsequent decay is attempted in the framework of alternative left-right model, which is motivated by superstring-inspired E6 model at CEPC and future linear colliders. We systematically analyze each decay channel of Higgs with theoretical constraints and latest experimental methods. Due to the mixing of scalars in the Higgs sector, charged Higgs bosons can play an essential role in the phenomenological analysis of this process. Even though the predictions of this model for the signal strengths of this process are close to the standard model expectations, it can be distinct under high luminosity.


Introduction
With the discovery of Higgs boson by ATLAS [1] and CMS [2] at Large Hadron Collider(LHC) in 2012, the standard model(SM) has made a great accomplishment. Higgs production with subsequent decay plays an essential role not only in the precision test of the Higgs property but also provides a window to new physics beyond the SM(BSM). The study of Higgs and Z boson associated production and decay at Higgs factory such as Circular Electron Positron Collider(CEPC) and future linear colliders is significantly important in measuring gauge and Yukawa interactions, so more and more theorists and experimenters are motivated to investigate this process in new physics scenarios [3][4][5][6]. CEPC was proposed by Chinese scientists at about 240 GeV center-ofmass energy mainly for Higgs studies with two detectors situated in a very long tunnel more than twice the size of the LHC at CERN. A future linear collider, such as International Linear Collider(ILC) or Compact Linear Collider(CLIC), at center-of-mass energy √ s = 500 GeV or even higher in the TeV energy scale, will allow the Higgs sector to be probed with high precision significantly beyond that at High-Luminosity LHC [7][8][9]. CEPC and future linear colliders are e + e − colliders and will be crucial facilities for precision Higgs physics research, outcome of which may be an order of magnitude more precise than that achievable at LHC. Such measurements may be necessary to reveal BSM effects in Higgs sector. Moreover, e + e − colliders provide an opportunity to measure Higgs couplings, rather than ratios, with a cleaner background. In addition, an e + e − collider operating at 1 TeV or above, for example CLIC or an upgraded ILC, will have the sensitivity to top quark Yukawa coupling and Higgs self-coupling parameters, and thus will provide a direct probe of Higgs potential.
As for the discovery of neutrino masses and neutrino oscillations, it confirmed that SM remains incomplete. To provide a proper explanation for the measured neutrino masses, theorists have made several attempts, such as supersymmetry, extra dimensions, Two Higgs Doublet Model(2HDM), and Left-Right Model (LRM), to expand the SM. The Alternative Left-Right Model(ALRM) [10][11][12][13], motivated by the superstring-inspired E 6 model, is a type of left-right model [14][15][16][17]. ALRM is based on can break at TeV scale, allowing several interesting signatures at LHC. In ALRM all non-SM particles can couple with SM fermions and Higgs bosons which will lead to low energy consequences. Due to the rich Higgs sector, there are four neutral CP-even and two CP-odd Higgs bosons, in addition to two charged Higgs bosons, which come from one bidoublet and two left-handed and right-handed doublets; most of these Higgs bosons can be light, falling in the electroweak scale. As for the couplings of the SM-like Higgs with the fermions and gauge bosons, there are small changes compared to the corresponding ones in SM. In the literature, many studies have been undertaken, which primarily focus on dark matter or hadron production of ALRM [13,[18][19][20].
In this study, we will mainly focus on the weak production of Z boson and Higgs. Each channel of Higgs decay modes has been analyzed in ALRM and compared with the recent results reported by ATLAS and CMS experiments [21][22][23][24][25]. There are possible discrepancies between the results of signal decay strengths in each channel. We analyze through five main Higgs decay channels: H→bb, cc, ττ, ZZ and WW in both ALRM and SM correspondingly. We find that the signal strength of Higgs decay channel H → ZZ is consistent with SM expectation. However, the decay channel H→bb is more sensitive to the mass of charged Higgs, where there may exist discrepancy with SM. Secondly, HZ associated production has been systematically explored in this model at CEPC and future e + e − colliders. The couplings of new heavy bosons to the known fundamental particles will be a crucial test of SM and may support an opportunity to establish physics BSM. We find that the discrepancies of cross-sections between ALRM and SM are of a few percent at √ s=240 GeV, 500 GeV, and 1 TeV. Finally, we study the subsequent decay of the final state Higgs into a pair of bottom quarks and Z boson into a leptonic pair, where l = e, µ and τ , associated with ALRM and the required integrated luminosity when the discovery significance is 5σ.
The organization of this paper is as follows: In Section 2 we briefly describe the related theory of ALRM. In Section 3, we perform the numerical analysis for Higgs and Z boson associated production with decay in ALRM. Finally, a short summary is provided in Section 4.

Alternative
left-right symmetric model ALRM is a standard model extension based on SU (3) C ×SU (2) L ×SU (2) R ×U (1) (B−L)/2 ×S gauge symmetry, the discrete symmetry S is to distinguish the scalar bidoublet from its dual scalars. The details of ALRM are reported in the literature [19]. Here, we only introduce the formulas used in our calculations.
Let us start from the most general left-right symmetric Yukawa Lagrangian: In Eq.(1), Φ and χ L,R are the duals of the bidoublet Φ and the doublets χ L,R , which are defined as Φ = τ 2 Φ * τ 2 and χ L,R = iτ 2 χ * L,R . From this Lagrangian, we can get the masses of the fermions, which are quarks u, d, d ′ , the charged leptons l, and the additional singlet fermion n called scotino.
The mixing angle and the vacuum expectation are set as tanβ = k/v L and v 2 L +k 2 = v ≡ 246 GeV. From Eq.(1), we also get the Yukawa couplings of the SM-like Higgs where the T Φ , T L and T R are the mixing parameters of the SM-like Higgs with the gauge eigenstates φ 0R 2 , χ 0R L and χ 0R R , respectively. Similar to the Yukawa coupling, the specific couplings of the SM-like Higgs with the massive EW gauge bosons can also be derived from the Lagrangian of the scale sector [19].
In the gauge sector, W ± L and W ∓ R cannot mix with each other as < φ 0 1 >= 0. We get the mass eigenstates W ± = W ± L , which are the SM gauge bosons, and the heavy charged bosons W ′± = W ± R . The masses of these bosons are given by: At present, numerous measurements focused on the heavy bosons have been conducted. Till date, a search for high-mass resonances using an integrated luminosity of 36.1 fb −1 by the ATLAS collaboration offers a lower mass limit of W ′ as M W ′ > ∼ 3.7 TeV [26][27][28]. This lower boundary on M W ′ is applicable in our following calculation in this study. For the neutral gauge bosons, the masses of two massive bosons can be calculated using where mixing angle ϑ is defined as 093107-2 and From Eqs. (6-7), we know that the mixing angle ϑ strongly influences the masses of Z and Z ′ , and when ϑ → 0, Z ≃ Z L and Z ′ ≃ Z R . The latest LHC experiments using a data sample corresponding to an integrated luminosity of 36.1 fb −1 from proton-proton collisions give a limitation for the Z ′ gauge boson as M Z ′ > ∼ 2.42 TeV [28][29][30], and we use the constraint in our numerical calculation.
Reference [17] gives the most general Higgs potential with the symmetry invariance, We follow the theorems reported earlier [31,32], to ensure that the matrix of the quartic terms, which are dominant at higher values of the fields, is copositive. The ref. [19] presents a detailed study on the conditions which keep the potential Eq. (8)  The lightest neutral eigenstate H is the SM-like Higgs, whose mass is fixed to be 125.09 GeV. For charged Higgs H ± 1 , the diagonalizable matrix is related to angle β with tanβ = k/v L . However, for H ± 2 , the diagonalizable matrix is related to angle ζ with tanζ = k/v R . The vevs of v R is much larger than v L . From this point, coupling of H ± 1 to the SM particles is stronger than that with H ± 2 . The LEP experiments have been conducted to search for charged bosons via pair charged Higgs production. The data statistically combined by four experiments (ALEPH, DELPHI, L3 and OPAL) [33] showed that the mass of charged Higgs boson must be greater than 80 GeV. This lower limit will be used as a reference in our calculations. In recent past, ATLAS and CMS have also searched for the charged boson masses ranging from 200 to 2000 GeV [34,35], and constraints for some models such as hMSSM are given.

ALRM effects in Higgs decay
Each channel of discovered Higgs has already been detected by CMS and ATLAS experiment groups. The decay signal strengths of Higgs to ZZ bosons and bb pair are given in Table 1, independently by CMS [21,22], ATLAS [23,24]. Due to the detectors' limits and the defects of hardron collider, the data in Table 1 may deviate from the real results, especially in H → bb. The Higgs signal strength in a particular final state XX µ XX is defined as where σ stands for the total Higgs production cross section at LHC and BR(H → XX) is the corresponding branching ratio. The total decay width of Higgs can be considered as the sum of some dominant Higgs partial decay widths. In Eq. (3), we can see that the Yukawa couplings Y Htt and Y Hbb in ALRM may be changed by adding a factor of T Φ sinβ and T L cosβ , respectively, from the SM values.
In Fig. 1, the effect of these two factors are plotted to show that both of them tend to be 1 while T L cosβ of Y Hdd is greater than 1 particularly in the region of small M H ± 1 with large tanβ. Y Hbb strongly depends on the mass of H ± 1 . However, the total decay width of Higgs boson remains very close to the SM result, κ tot ≃ 1, when the mass of H ± 1 is big enough. As for κ gg , this channel is mainly propagated through the top quark triangle loop diagram and the extra quark d ′ can be neglected due to the suppression of its coupling with SM-like Higgs. From Fig. 1, we can see that the adding factor to top Yukawa coupling can be almost 1, making the top Yukawa coupling unchanged from the SM result. Therefore, the ratio κ gg = Γ (H→ gg)/Γ (H→ gg) SM can be considered as 1. It is worth mentioning that the parameters λ 3 , α 12 and M H ± 2 are not sensitive in the numerical results, only 0 < λ 3 < √ 4π and α 12 > 0, to be consistent with the perturbative unitarity and the minimization and boundedness from below conditions Eqs. (21)(22)(23)(24) in ref. [19]. The relevant input parameters are chosen as [28]: We have used Feynrules [36,37] to generate the model files and MadGraph [38] to calculate the numerical values of the cross-sections. In Fig. 2   2 SM , respectively. Obviously, the results are the same in both the cases. In Fig. 2(b), with increase in M H ± 1 , the value rapidly increases and stabilizes when M H ± 1 200 GeV. Hence, in the following calculation M H ± 1 is equal to 200 GeV, unless otherwise stated. In this case, it is clear that the signal strength µ zz is also close to the SM expectation and can be consistent with CMS experimental results. It is remarkable that all signal strengths of Higgs decay channels in ALRM are close to SM results with MadWidth [39] automatically computing decay widths.
In Fig. 3(a), κ bb is plotted as a function of M H ± 1 . This figure shows that the decay channel H→bb is more sensitive to M H ± 1 than the channel H→ZZ. In addition, it is remarkable that the decay width of this channel in ALRM is slightly larger than that in SM. In Fig. 3(b), κ bb is plotted as a function of tanβ, it is clearly seen that tanβ has negligible impact on κ bb . From Fig. 3, we find that the decay channel H → bb is more sensitive to M H ±

ALRM effects in e + e − →HZ
In this subsection the production of e + e − → HZ at CEPC and future e + e − colliders is presented and Feynman diagrams of this process are displayed in Fig. 4. As the contributions from t channel are negligibly small, we only give the Feynman diagrams in s channel. As can be seen from Fig. 4, a new scalar A 2 and a heavy boson Z ′ are added in the propagators. The relevant input parameters are chosen as described above. The cross section as a function of tanβ with the mass of heavy boson W ′ varying from 4 TeV to 5 TeV and charged boson H ± 1 varying from 150 GeV to 300 GeV is shown in Fig. 5 at √ s = 240 GeV. Obviously, the total cross-sections are all less than those in SM from Fig. 5. From Ref. [19], the mass of A 2 become small when tanβ and M H ± 1 are small, and M W ′ influences the heavy boson Z ′ . In Fig. 5, due to the large M W ′ , the contribution from Z ′ propagator is small and the contribution from A 2 is mainly in small tanβ region. Fig. 5(b) shows the discrepancies from A 2 propagator become larger with smaller M H ± 1 . At the other two collision energies, the same tendency can be obtained which we did not show.  The total cross-sections and corresponding relative ALRM discrepancies are tabulated in Table 2 with tanβ =50, M H ± 1 =200 GeV and M W ′ =4 TeV at √ s=240 GeV, 500 GeV, and 1 TeV, respectively. The relative ALRM discrepancy is defined as δ=(σ ALRM −σ SM )/σ SM . In this table, we can see the relative ALRM discrepancies are increasing with √ s. It is worth mentioning that the Higgs sector in ALRM is very similar to that in 2HDM, where one Higgs doublet couples to up-quarks and the second couples to down-quarks. Therefore, it does not 093107-5 lead to any flavor changing neutral current problem and light charged Higgs is phenomenologically acceptable.
We next analyze the discovery significance, which is calculated using the formula n S √ ntot , where n S = Ldt× (σ ALRM −σ SM ) is the number of discrepancy events and n tot = Ldt×σ SM is the number of total events. The plot of discovery significance as a function of integrated luminosity for CEPC, ILC, and CLIC is depicted in Fig. 6. From Fig. 6, one can see that the integrated luminosity of all the three colliders can reach several hundreds, specifically at 619.72 fb −1 (CEPC), 553.80 fb −1 (ICL), and 443.93 fb −1 (CLIC) when the discovery significance is 5σ. By contrast, CLIC seems to have an advantage in detecting it. It is worth mentioning that the discovery significance shown in Fig. 6 is calculated with no kinetic cuts. It cannot be treated as a serious result.

ALRM effects in e
In this subsection we will analyze and compute the cross-section for production and subsequent decay at √ s= 240 GeV, 500 GeV and 1 TeV, respectively. Feynman diagrams for subsequent decay of the SM-like Higgs boson into a pair of bottom quarks and Z boson into opposite-sign dilepton, where l=e, µ and τ, are shown in Fig. 7 associated with ALRM. When doing the numerical calculation, the mass of fermions is chosen as follows: In dealing with the sequential Z boson leptonic decay and Higgs decay, the naive narrow-width approximation (NWA) method is used to acquire the total crosssection. Hence, cross-section for this process can be ap-proximately written as: σ e + e − →l + l − bb ≃σ(e + e − →HZ) ×BR H→bb ×BR(Z→l + l − ). (12) (1) In order to get the precise branch ratio of H→bb in ALRM, we set the K-factor of each channel the same as that in SM. By adopting HDECAY program [40], dominant Higgs partial decay widths are computed that are tabulated in Table 3. Here, the scale µ of the Yukawa coupling y Q (µ) = m Q (µ)/v is used as the mass of Higgs in the calculation, while m Q (µ) is the running mass of heavy quark. The total cross-section GeV. Obviously, the branch ratio of H→bb is 58.27% in SM and experiment shows that SM prediction for the decay branching fraction of Higgs boson with mass around 125.09 GeV to bb is 57.5% [25]. The leading order(LO) results in SM computed by MadWidth and the corresponding K-factors ( σ HDECAY σ MadWidth ) are also included in Table 3. The decay width of H→gg is directly used result in SM by HDECAY. In this manner, we can estimate the branch ratio of H→bb in ALRM as a function of M H ± 1 .
As for the branch ratio of Z→l + l − , the result is 10.31% in both SM and ALRM which is independent of M H ± 1 . The total cross-sections and corresponding relative discrepancies are shown in Table 4 at √ s = 240 GeV, 500 GeV and 1 TeV respectively, where the relative deviation is defined as δ=(σ ALRM −σ SM )/σ SM . From Table 4 one 093107-6 finds that with the increase of √ s, the cross-sections in both ALRM and SM decrease. While the corresponding relative discrepancies are increasing significantly, which will be phenomenologically accessible.   To analyze the feasibility of experiment, the discovery significance is chosen to be the same as last subsection: n S √ ntot , where n S = Ldt × BR(Z→l + l − ) × (σ ALRM × BR ALRM (H→bb) − σ SM × BR SM (H → bb)) is the number of discrepancy events and n tot = Ldt × BR(Z→l + l − )×σ SM ×BR SM (H → bb) is the total number of events. In Fig. 8, we depict the integrated luminosity needed for 5σ discovery significance as a function of M H ± 1 for CEPC, ILC and CLIC determined by n S √ ntot . For e + e − → HZ → l + l − bb process, the discrepancies between SM and ALRM are mainly influenced by the cross-section of e + e − → HZ and the branching ratio of Higgs to bb. The cross-sections of e + e − →HZ in ALRM is a little smaller than that in SM but the branching ratio of H→bb is opposite. In the middle of M H ± 1 region, two parts of the contribution counteract each other while the cross-section of e + e − →HZ→l + l − bb in ALRM and SM approach each other. Hence, in order to detect the discrepancies, the required integrated luminosity needs to be very large, which means that it is difficult to search new physics in the region. This corresponds to the peak in Fig. 8.

Summary
In the present paper, we have analyzed Higgs decay in each channel, Higgs and Z boson associated production and decay at CEPC and future e + e − colliders in ALRM, motivated by superstring inspired E 6 model. We found that the contribution of charged Higgs boson M H ± 2 to Higgs decay is negligible due to the large tanβ, while M H ± 1 plays an essential role in the decay channel of H → bb due to the mixing of scalars. In addition, the model predicts the signal strengths of Higgs decay, of H→ZZ in particular, that are consistent with SM expectations. We also analyzed the discrepancies of crosssections about Higgs and Z boson production between ALRM and SM and found that it can be enhanced to 6.78% when √ s is increased to 1 TeV. Finally, we studied the sequential decay of Higgs and Z boson to bb and l + l − , respectively, where l = e, µ, and τ , with NWA method. We found that the cross-sections of sequential decay are significantly dependent on the branch ratio of H → bb. We have also shown that the typical values of cross-sections are of O(1) fb which can be measured using future colliders.