# Single Top and Higgs Associated Production in the MinimalB-L Model at the LHC

Authors: Bingfang Yang; Zhiyong Liu; Jinzhong Han; Guang Yang
Journal: Advances in High Energy Physics
 (2016)

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## Abstract

We study the single top production in association with a Higgs boson in theU(1)B-L extension of the Standard Model at the LHC. We calculate the production cross sections of the processes pp→thX(h=H1,H2;X=j,b,W) in this model. We further study the observability of the process pp→tH2j through pp→t(→qq-′b)H2(→4l)j and find that it is still challenging for the 14 TeV LHC with high luminosity to detect this signal.


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## Body

## 1. Introduction

In July 2012, a Higgs-like resonance with massmh~125GeV has been discovered by the ATLAS and CMS experiments at the Large Hadron Collider (LHC) [1, 2]. So far, all the measurements of the discovered new particle [3–10] are well compatible with the scalar boson predicted by the Standard Model (SM) [11–15].It is well known that the SM cannot be the final theory of nature. Theoretically, successful explanation of some problems, such as the hierarchy problem, requires new physics beyond the SM near the TeV scale. Experimentally, the solid evidence for neutrino oscillation is one of the firm hints for new physics. The minimal extension of the SM that we consider in this paper is that the SM gauge groups are augmented by aU(1)B-L symmetry, where B and L represent the baryon number and lepton number, respectively. The B-L gauge symmetry can explain the presence of three right-handed neutrinos and provide a natural framework for the seesaw mechanism [16, 17]. In addition, it is worth noting that B-L symmetry breaking can take place at the TeV scale, hence giving rise to new and interesting TeV scale phenomenology.The Yukawa couplings play an important role in probing the new physics since they are sensitive to new flavor dynamics. The top quark is the heaviest particle discovered and owns the strongest Yukawa coupling. The top quark Yukawa coupling is speculated to be sensitive to the electroweak symmetry breaking (EWSB) mechanism and new physics. Thett-h production process is a golden channel for directly probing the top Yukawa coupling; however, this process cannot provide the information on the relative sign between the coupling of the Higgs to fermions and to vector bosons. As a beneficial supplement, the thj production process can bring a unique possibility [18–21] and many relevant works have been carried out [22–34].TheU(1)B-L model predicts heavy neutrinos, a TeV scale extra neutral gauge boson, and an additional heavy neutral Higgs, which makes the model phenomenologically rich. The heavy Higgs state mixes with the SM Higgs boson so that some Higgs couplings are modified and this effect can also influence the process of single top and Higgs associated production. Besides, the process of single top and heavy Higgs associated production deserves attention, which is equally important for understanding the EWSB and probing new physics. Performing the detailed analysis on this process may provide a good opportunity to probe the U(1)B-L model signal.The paper is structured as follows. In Section2 we review the U(1)B-L model related to our work. In Section 3 we first calculate the production cross sections of the single top and h(=H1,H2) associated production at the LHC and then explore the observability of t-channel process pp→tH2j through pp→t(→qq-′b)H2(→4l)j by performing a parton-level simulation. Finally, we make a summary in Section 4.


## 2. A Brief Review of theU(1)B-L Model

The minimalB-L extension of the SM [35–42] is based on the gauge group SU(3)C×SU(2)L×U(1)Y×U(1)B-L with the classical conformal symmetry. Under this gauge symmetry, the invariance of the Lagrangian implies the existence of a new gauge boson. In order to make the model free from all the gauge and gravitational anomalies, three generations of right-handed neutrinos are necessarily introduced.The Lagrangian for Yang-Mills and fermionic sectors is given by(1)LYM+f=-14FμνFμν-14F′μνFμν′+∑k=13iqkL¯γμDμqkL+iukR¯γμDμukR+idkR¯γμDμdkR+ilkL¯γμDμlkL+iekR¯γμDμekR+iνkR¯γμDμνkR,where Fμν=∂μBν-∂νBμ, Fμν′=∂μBν′-∂νBμ′, Bμ and Bμ′ are, respectively, the U(1)Y and U(1)B-L gauge fields, and the fields’ charges are the usual SM and B-L ones. The non-Abelian field strengths not included here are the same as in the SM. In this field basis, the covariant derivative is (2)Dμ≡∂μ+igsTαGμα+igTaWμa+ig1YBμ+ig~Y+g1′YB-LBμ′.In this model, the most general gauge-invariant and renormalizable scalar Lagrangian can be expressed as(3)Ls=DμH†DμH+Dμχ†Dμχ-Vχ,H,with the scalar potential given by (4)Vχ,H=MH2H†H+mχ2χ2+λ1H†H2+λ2χ4+λ3H†Hχ2.To determine the condition for the potential to be bounded from below, the couplings λ1, λ2, and λ3 should be related as (5)4λ1λ2-λ3>0,λ1,2≥0.We denote the vacuum expectation values (VEVs) of H and χ by v and v′, respectively, and the nonzero minimums are given by (6)v2=4λ2m12-2λ3m22λ32-4λ1λ2,v′2=-2m12+λ1v2λ3,where v and v′ are the EWSB scale and the B-L symmetry breaking scale, respectively.From the mass terms in the scalar potential, the mass matrix between the two Higgs bosons in the basis(H,χ) can be given by (7)M2H,χ=2λ1v2λ32vv′λ32vv′λ2v′2.The mass eigenstates are related via the mixing matrix (8)H1H2=cos⁡αsin⁡α-sin⁡αcos⁡αHχ,where the mixing angle α (-π/2<α<π/2) satisfies (9)tan⁡2α=λ3v′vλ2v′2-λ1v2.The masses of the physical Higgs bosons H1 and H2 are given by (10)mH1,H22=λ1v2+λ2v′2∓λ1v2-λ2v′22+λ3vv′2,where H1 and H2 are light SM-like and heavy Higgs bosons, respectively.To complete the discussion on the Lagrangian, we write down the Yukawa term, which in addition to the SM terms has interactions involving the right-handed neutrinosNR: (11)LY=-yijdQLi¯dRjH-yijuQLi¯uRjH~-yijeLLi¯eRjH-yijνLLi¯NRjH~-yijMNRic¯NRjχ+h.c.,where H~=iσ2H∗ and i,j run within 1~3. The VEV of the χ field breaks the B-L symmetry and generates the Majorana masses for the right-handed neutrinos and the Dirac masses for the light neutrinos.In terms of the mixing angleα, the couplings of H1 and H2 with the fermions and gauge bosons can be expressed as follows: (12)H1ff-:-eMfcos⁡α2MWsW,H2ff-:-eMfsin⁡α2MWsW,H1W+W-:eMWcos⁡αsW,H2W+W-:eMWsin⁡αsW,H1ZZ:eMWcos⁡αcW2sW,H2ZZ:eMWsin⁡αcW2sW,where f denotes the SM fermions and sW=sin⁡θW with θW is the usual Weinberg angle.


## 3. Numerical Results and Discussions

For the single top and Higgs associated production, the three processes of interest are characterized by the virtuality of theW boson in the process [43]: (i) t-channel, where the W is spacelike; (ii) s-channel, where the W is timelike; (iii) W-associated production channel, where there is emission of a real W boson. In the U(1)B-L model, the lowest-order Feynman diagrams of the t-channel process pp→tH1(H2)j(j≠b) are shown in Figure 1, the s-channel process pp→tH1(H2)b- is shown in Figure 2 and the W-associated production channel process pp→tH1(H2)W- is shown in Figure 3. We can see that the Feynman diagrams for these processes are the same as the corresponding SM processes. Moreover, the conjugate processes where t is replaced by t- have been included in our calculations.Figure 1
Lowest-order Feynman diagrams forpp→tH1(H2)j in the U(1)B-L model.
(a) (b) (c)Figure 2
Lowest-order Feynman diagrams forpp→tH1(H2)b- in the U(1)B-L model.
(a) (b) (c)Figure 3
Lowest-order Feynman diagrams forpp→tH1(H2)W- in the U(1)B-L model.
(a) (b) (c) (d) (e) (f) (g) (h)We compute the cross sections by usingCalcHEP  3.6.25 [44] with the parton distribution function CTEQ6L [45] and set the renormalization scale μR and factorization scale μF to be μR=μF=(mt+mh+mX)/2, (h=H1,H2;X=j,b,W). The SM input parameters are taken as follows [46]: (13)mt=173.2GeV,mZ=91.1876GeV,αmZ=1128,sin2⁡θW=0.231,mH1=125GeV,αsmZ=0.1185.In our calculations, the relevantU(1)B-L model parameters are the mixing parameter α and the heavy Higgs mass mH2. Considering the constraints in [47–50], we choose the parameter space as follows: 0.01<sin⁡α<0.4, 250GeV≤mH2≤1000GeV.


### 3.1. Single Top andH1 Associated Production

In Figure4, we show the production cross sections of the processes pp→tH1j, pp→tH1b-, and pp→tH1W- as a function of sin⁡α at the 8 and 14 TeV LHC in the U(1)B-L model, respectively. For clarity, we marked the corresponding SM process cross sections on the figures. We can see that the cross sections in the U(1)B-L model decrease with increasing sin⁡α. Besides, the behavior of these three processes is similar for the 8 TeV and 14 TeV. This is easy to understand because there is the same change factor cos⁡α in the light Higgs H1 couplings in (12) so that the production cross sections are suppressed by cos2⁡α; that is, σB-L=σSMcos2⁡α. When sin⁡α→0, the mixing between the light Higgs H1 and the heavy Higgs H2 will decouple so that the cross sections go back to the SM values.Figure 4
The production cross sectionsσtH1j, σtH1b, σtH1W as a function of sin⁡α at 8, 14 TeV LHC in the U(1)B-L model.


### 3.2. Single Top andH2 Associated Production

In Figures5 and 6, we show the production cross sections of the processes pp→tH2j, pp→tH2b-, and pp→tH2W- as a function of sin⁡α at the 8 and 14 TeV LHC in the U(1)B-L model, respectively. In order to see the influence of the heavy Higgs mass mH2 on the production cross sections, we take mH2=250,500,750,1000GeV as example. We can see that the cross sections increase with increasing sin⁡α, which is because the heavy Higgs H2 couplings in (12) are proportional to sin⁡α so that the cross sections are proportional to sin2⁡α.Figure 5
The production cross sectionsσtH2j, σtH2b, σtH2W as a function of sin⁡α at 8 TeV LHC in the U(1)B-L model.Figure 6
The production cross sectionsσtH2j, σtH2b, σtH2W as a function of sin⁡α at 14 TeV LHC in the U(1)B-L model.


### 3.3. Observability ofpp→tH2j

Thet-channel process dominates amongst these three production modes at the LHC, so we will explore the observability through the t-channel pp→tH2j at 14 TeV LHC in the following section. The three most dominant decay modes of the heavy Higgs H2 are WW, H1H1, and ZZ [51]. Though the branching fraction of H2→ZZ is smaller than the branching fractions of H2→WW and H2→H1H1, the ZZ signal is much easier to separate from SM backgrounds. For the ZZ decay modes, the leptonic decay mode of ZZ offers the cleanest possible signatures though the dijet and semileptonic decay modes of ZZ are larger. This leptonic decay mode has been studied in the heavy Higgs production at the LHC and it found that a heavy Higgs boson of mass smaller than 500 GeV can be discovered at the LHC with high luminosity (HL-LHC) [50]. In our work, we concentrate on the channel pp→t(→W+b→qq-′b)H2(→ZZ→l1+l1-l2+l2-)j as shown in Figure 7, where H2 decays to two Z bosons and the two Z bosons subsequently decay to four leptons. The signal is characterized by (14)3-j+b-jet+4l,where j denotes the light jets and l=e,μ. The largest background for this process comes from the tZZj production mode that will generate the same final state.Figure 7
Feynman diagrams for signalpp→tH2j (a) and background pp→tZZj (b) including the decay chain with hadronic top quark, leptonic Z boson decay, and Higgs decay H2→ZZ→l1+l1-l2+l2- at the LHC.
(a) (b)We generate the signal and background events withMadGraph5 [52] and perform the parton shower and the fast detector simulations withPYTHIA [53] andDelphes [54]. To simulate b-tagging, we take moderate single b-tagging efficiency ϵb=0.7 for b-jet in the final state. Following the analysis on tt-h signature by ATLAS and CMS collaborations [55, 56] at the LHC Run-I, the events are selected to satisfy the criteria as follows: (15)ΔRik>0.4,i,k=b,jorl,pTb>25GeV,ηb<2.5,pTl>10GeV,ηl<2.5,pTj>25GeV,ηj<5.Due to the small signal cross section, this process has a low signal-to-background ratioS/B at the LHC. In this case, we will focus on enhancing the systematic significance S/B. Considering the transverse momentum of the leptons has little effect on the signal-to-background ratio and the systematic significance, we do not use it as selection cuts here. After analysis, we will adopt the following two cuts; the relevant normalized distributions of the kinematic variables for mH2=250 GeV, sin⁡α=0.3 with respect to the background are shown in Figure 8.Figure 8
The normalized distributions ofHT,M4l in the signal and background at 14 TeV LHC for mH2=250 GeV, sin⁡α=0.3, where HT(=∑hadronicparticles‍p→T) is the total transverse hadronic energy.Firstly, we impose the cutHT<380 GeV to separate signal from background. This cut can improve both the signal-to-background ratio S/B and the systematic significance S/B.After that, we apply the invariant mass of the four-lepton system to further isolate the signal and letM4l lie in the range mH2±20 GeV. We can see that the signal-to-background ratio S/B is improved and the systematic significance S/B is enhanced obviously.The cut-flow cross sections of the signal and background for 14 TeV LHC are summarized in Table1. For clarity, we also give the cut efficiency of the signal events in Table 1. After all cuts above, we can see that the systematic significance S/B is substantially improved. For the HL-LHC with a final integrated luminosity of L=3000fb-1, the signal-to-background ratio S/B can reach 1.6σ and systematic significance S/B can reach 2.86 for mH2=250 GeV, sin⁡α=0.3. Furthermore, we can compute the number of of signal events NS and background events NB and find that NS≃0.9 and NB≃0.3 for the luminosity of L=3000fb-1. Unfortunately, we can see that the number of signal events is very small because of the small leptonic branching ratio of the Z boson, which will be a trouble for detecting this signal at the LHC.Table 1
Cutflow of the cross sections for the signal and backgrounds at 14 TeV LHC on the benchmark point (mH2=250 GeV, sin⁡α=0.3). All the conjugate processes of the signal and background have been included.
Cuts σ (×10-4 fb) S / B S / B S-cut efficiency Signal Background 3000 fb−1 % t H 2 j t Z Z j No cuts 34.3 103.9 1.84 0.33 Basic cuts 15.6 50.2 1.20 0.31 45.5 H T < 380 GeV 11.3 19.5 1.40 0.58 72.4 | M 4 l - 250 | < 20 GeV 2.97 1.04 1.60 2.86 26.3


## 3.1. Single Top andH1 Associated Production

In Figure4, we show the production cross sections of the processes pp→tH1j, pp→tH1b-, and pp→tH1W- as a function of sin⁡α at the 8 and 14 TeV LHC in the U(1)B-L model, respectively. For clarity, we marked the corresponding SM process cross sections on the figures. We can see that the cross sections in the U(1)B-L model decrease with increasing sin⁡α. Besides, the behavior of these three processes is similar for the 8 TeV and 14 TeV. This is easy to understand because there is the same change factor cos⁡α in the light Higgs H1 couplings in (12) so that the production cross sections are suppressed by cos2⁡α; that is, σB-L=σSMcos2⁡α. When sin⁡α→0, the mixing between the light Higgs H1 and the heavy Higgs H2 will decouple so that the cross sections go back to the SM values.Figure 4
The production cross sectionsσtH1j, σtH1b, σtH1W as a function of sin⁡α at 8, 14 TeV LHC in the U(1)B-L model.


## 3.2. Single Top andH2 Associated Production

In Figures5 and 6, we show the production cross sections of the processes pp→tH2j, pp→tH2b-, and pp→tH2W- as a function of sin⁡α at the 8 and 14 TeV LHC in the U(1)B-L model, respectively. In order to see the influence of the heavy Higgs mass mH2 on the production cross sections, we take mH2=250,500,750,1000GeV as example. We can see that the cross sections increase with increasing sin⁡α, which is because the heavy Higgs H2 couplings in (12) are proportional to sin⁡α so that the cross sections are proportional to sin2⁡α.Figure 5
The production cross sectionsσtH2j, σtH2b, σtH2W as a function of sin⁡α at 8 TeV LHC in the U(1)B-L model.Figure 6
The production cross sectionsσtH2j, σtH2b, σtH2W as a function of sin⁡α at 14 TeV LHC in the U(1)B-L model.


## 3.3. Observability ofpp→tH2j

Thet-channel process dominates amongst these three production modes at the LHC, so we will explore the observability through the t-channel pp→tH2j at 14 TeV LHC in the following section. The three most dominant decay modes of the heavy Higgs H2 are WW, H1H1, and ZZ [51]. Though the branching fraction of H2→ZZ is smaller than the branching fractions of H2→WW and H2→H1H1, the ZZ signal is much easier to separate from SM backgrounds. For the ZZ decay modes, the leptonic decay mode of ZZ offers the cleanest possible signatures though the dijet and semileptonic decay modes of ZZ are larger. This leptonic decay mode has been studied in the heavy Higgs production at the LHC and it found that a heavy Higgs boson of mass smaller than 500 GeV can be discovered at the LHC with high luminosity (HL-LHC) [50]. In our work, we concentrate on the channel pp→t(→W+b→qq-′b)H2(→ZZ→l1+l1-l2+l2-)j as shown in Figure 7, where H2 decays to two Z bosons and the two Z bosons subsequently decay to four leptons. The signal is characterized by (14)3-j+b-jet+4l,where j denotes the light jets and l=e,μ. The largest background for this process comes from the tZZj production mode that will generate the same final state.Figure 7
Feynman diagrams for signalpp→tH2j (a) and background pp→tZZj (b) including the decay chain with hadronic top quark, leptonic Z boson decay, and Higgs decay H2→ZZ→l1+l1-l2+l2- at the LHC.
(a) (b)We generate the signal and background events withMadGraph5 [52] and perform the parton shower and the fast detector simulations withPYTHIA [53] andDelphes [54]. To simulate b-tagging, we take moderate single b-tagging efficiency ϵb=0.7 for b-jet in the final state. Following the analysis on tt-h signature by ATLAS and CMS collaborations [55, 56] at the LHC Run-I, the events are selected to satisfy the criteria as follows: (15)ΔRik>0.4,i,k=b,jorl,pTb>25GeV,ηb<2.5,pTl>10GeV,ηl<2.5,pTj>25GeV,ηj<5.Due to the small signal cross section, this process has a low signal-to-background ratioS/B at the LHC. In this case, we will focus on enhancing the systematic significance S/B. Considering the transverse momentum of the leptons has little effect on the signal-to-background ratio and the systematic significance, we do not use it as selection cuts here. After analysis, we will adopt the following two cuts; the relevant normalized distributions of the kinematic variables for mH2=250 GeV, sin⁡α=0.3 with respect to the background are shown in Figure 8.Figure 8
The normalized distributions ofHT,M4l in the signal and background at 14 TeV LHC for mH2=250 GeV, sin⁡α=0.3, where HT(=∑hadronicparticles‍p→T) is the total transverse hadronic energy.Firstly, we impose the cutHT<380 GeV to separate signal from background. This cut can improve both the signal-to-background ratio S/B and the systematic significance S/B.After that, we apply the invariant mass of the four-lepton system to further isolate the signal and letM4l lie in the range mH2±20 GeV. We can see that the signal-to-background ratio S/B is improved and the systematic significance S/B is enhanced obviously.The cut-flow cross sections of the signal and background for 14 TeV LHC are summarized in Table1. For clarity, we also give the cut efficiency of the signal events in Table 1. After all cuts above, we can see that the systematic significance S/B is substantially improved. For the HL-LHC with a final integrated luminosity of L=3000fb-1, the signal-to-background ratio S/B can reach 1.6σ and systematic significance S/B can reach 2.86 for mH2=250 GeV, sin⁡α=0.3. Furthermore, we can compute the number of of signal events NS and background events NB and find that NS≃0.9 and NB≃0.3 for the luminosity of L=3000fb-1. Unfortunately, we can see that the number of signal events is very small because of the small leptonic branching ratio of the Z boson, which will be a trouble for detecting this signal at the LHC.Table 1
Cutflow of the cross sections for the signal and backgrounds at 14 TeV LHC on the benchmark point (mH2=250 GeV, sin⁡α=0.3). All the conjugate processes of the signal and background have been included.
Cuts σ (×10-4 fb) S / B S / B S-cut efficiency Signal Background 3000 fb−1 % t H 2 j t Z Z j No cuts 34.3 103.9 1.84 0.33 Basic cuts 15.6 50.2 1.20 0.31 45.5 H T < 380 GeV 11.3 19.5 1.40 0.58 72.4 | M 4 l - 250 | < 20 GeV 2.97 1.04 1.60 2.86 26.3


## 4. Summary

In the minimalB-L extension of the SM, we investigated the single top and Higgs associated production at the LHC. We computed the production cross sections of the processes pp→tH1(H2)X(X=j,b,W) for 8, 14 TeV LHC, and displayed the dependance of the cross sections on the relevant U(1)B-L model parameter. Moreover, we investigated the observability of process pp→tH2j followed by the decays t→qq-′b and H2(→ZZ→l1+l1-l2+l2-) at 14 TeV LHC for mH2=250 GeV, sin⁡α=0.3. We performed a simple parton-level simulation and found that it is challenging for the 14 TeV LHC and future HL-LHC with the integrated luminosity L=3000fb-1 to observe the effect of the process pp→tH2j through this final state. So, we have to expect a collider with higher energy and higher luminosity to probe this effect. Maybe, a 100 TeV proton-proton collider with integrated luminosities of 3ab-1~30ab-1 can provide us with a potential opportunity [57].



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