Advances in High Energy Physics
Volume 2016 (2016), Article ID 2613187, 9 pages
http://dx.doi.org/10.1155/2016/2613187

Research Article

Single Top and Higgs Associated Production in the Minimal Model at the LHC

Bingfang Yang,¹ Zhiyong Liu,¹ Jinzhong Han,² and Guang Yang³

¹College of Physics & Electronic Engineering, Henan Normal University, Xinxiang 453007, China
²School of Physics and Electromechanical Engineering, Zhoukou Normal University, Henan 466001, China
³Basic Teaching Department, Jiaozuo University, Jiaozuo 454000, China

Received 17 April 2016; Accepted 31 July 2016

Academic Editor: Juan José Sanz-Cillero

Copyright © 2016 Bingfang Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP³.

Abstract.

We study the single top production in association with a Higgs boson in the extension of the Standard Model at the LHC. We calculate the production cross sections of the processes in this model. We further study the observability of the process through and find that it is still challenging for the 14 TeV LHC with high luminosity to detect this signal.

1. Introduction

In July 2012, a Higgs-like resonance with mass 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 a symmetry, where and represent the baryon number and lepton number, respectively. The 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 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. The 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 production process can bring a unique possibility [18–21] and many relevant works have been carried out [22–34].

The 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 model signal.

The paper is structured as follows. In Section 2 we review the model related to our work. In Section 3 we first calculate the production cross sections of the single top and associated production at the LHC and then explore the observability of -channel process through by performing a parton-level simulation. Finally, we make a summary in Section 4.

2. A Brief Review of the Model

The minimal extension of the SM [35–42] is based on the gauge group 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

where , , and are, respectively, the and gauge fields, and the fields’ charges are the usual SM and ones. The non-Abelian field strengths not included here are the same as in the SM. In this field basis, the covariant derivative is

In this model, the most general gauge-invariant and renormalizable scalar Lagrangian can be expressed as

with the scalar potential given by

To determine the condition for the potential to be bounded from below, the couplings , , and should be related as

We denote the vacuum expectation values (VEVs) of and by and , respectively, and the nonzero minimums are given by

where and are the EWSB scale and the symmetry breaking scale, respectively.

From the mass terms in the scalar potential, the mass matrix between the two Higgs bosons in the basis can be given by

The mass eigenstates are related via the mixing matrix

where the mixing angle () satisfies

The masses of the physical Higgs bosons and are given by

where and 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 neutrinos :

where and run within 1~3. The VEV of the field breaks the symmetry and generates the Majorana masses for the right-handed neutrinos and the Dirac masses for the light neutrinos.

In terms of the mixing angle , the couplings of and with the fermions and gauge bosons can be expressed as follows:

where denotes the SM fermions and with 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 the boson in the process [43]: (i) -channel, where the is spacelike; (ii) -channel, where the is timelike; (iii) -associated production channel, where there is emission of a real boson. In the model, the lowest-order Feynman diagrams of the -channel process are shown in Figure 1, the -channel process is shown in Figure 2 and the -associated production channel process 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 is replaced by have been included in our calculations.

(a)

(b)

(c)

Figure 1: Lowest-order Feynman diagrams for in the model.

(a)

(b)

(c)

Figure 2: Lowest-order Feynman diagrams for in the model.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Figure 3: Lowest-order Feynman diagrams for in the model.

We compute the cross sections by using CalcHEP  3.6.25 [44] with the parton distribution function CTEQ6L [45] and set the renormalization scale and factorization scale to be , . The SM input parameters are taken as follows [46]:

In our calculations, the relevant model parameters are the mixing parameter and the heavy Higgs mass . Considering the constraints in [47–50], we choose the parameter space as follows: , .

3.1. Single Top and Associated Production

In Figure 4, we show the production cross sections of the processes , , and as a function of at the 8 and 14 TeV LHC in the model, respectively. For clarity, we marked the corresponding SM process cross sections on the figures. We can see that the cross sections in the model decrease with increasing . 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 in the light Higgs couplings in (12) so that the production cross sections are suppressed by ; that is, . When , the mixing between the light Higgs and the heavy Higgs will decouple so that the cross sections go back to the SM values.

Figure 4: The production cross sections , , as a function of at 8, 14 TeV LHC in the model.

3.2. Single Top and Associated Production

In Figures 5 and 6, we show the production cross sections of the processes , , and as a function of at the 8 and 14 TeV LHC in the model, respectively. In order to see the influence of the heavy Higgs mass on the production cross sections, we take as example. We can see that the cross sections increase with increasing , which is because the heavy Higgs couplings in (12) are proportional to so that the cross sections are proportional to .

Figure 5: The production cross sections , , as a function of at 8 TeV LHC in the model.

Figure 6: The production cross sections , , as a function of at 14 TeV LHC in the model.

3.3. Observability of

The -channel process dominates amongst these three production modes at the LHC, so we will explore the observability through the -channel at 14 TeV LHC in the following section. The three most dominant decay modes of the heavy Higgs are , , and [51]. Though the branching fraction of is smaller than the branching fractions of and , the signal is much easier to separate from SM backgrounds. For the decay modes, the leptonic decay mode of offers the cleanest possible signatures though the dijet and semileptonic decay modes of 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 as shown in Figure 7, where decays to two bosons and the two bosons subsequently decay to four leptons. The signal is characterized by

where denotes the light jets and . The largest background for this process comes from the production mode that will generate the same final state.

(a)

(b)

Figure 7: Feynman diagrams for signal (a) and background (b) including the decay chain with hadronic top quark, leptonic boson decay, and Higgs decay at the LHC.

We generate the signal and background events with MadGraph5 [52] and perform the parton shower and the fast detector simulations with PYTHIA [53] and Delphes [54]. To simulate -tagging, we take moderate single -tagging efficiency for -jet in the final state. Following the analysis on signature by ATLAS and CMS collaborations [55, 56] at the LHC Run-I, the events are selected to satisfy the criteria as follows:

Due to the small signal cross section, this process has a low signal-to-background ratio at the LHC. In this case, we will focus on enhancing the systematic significance . 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  GeV, with respect to the background are shown in Figure 8.

Figure 8: The normalized distributions of in the signal and background at 14 TeV LHC for  GeV, , where is the total transverse hadronic energy.

Firstly, we impose the cut  GeV to separate signal from background. This cut can improve both the signal-to-background ratio and the systematic significance .

After that, we apply the invariant mass of the four-lepton system to further isolate the signal and let lie in the range  GeV. We can see that the signal-to-background ratio is improved and the systematic significance is enhanced obviously.

The cut-flow cross sections of the signal and background for 14 TeV LHC are summarized in Table 1. 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 is substantially improved. For the HL-LHC with a final integrated luminosity of , the signal-to-background ratio can reach 1.6 and systematic significance can reach 2.86 for  GeV, . Furthermore, we can compute the number of of signal events and background events and find that and for the luminosity of . Unfortunately, we can see that the number of signal events is very small because of the small leptonic branching ratio of the 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 ( GeV, ). All the conjugate processes of the signal and background have been included.

Cuts
(× fb)

-cut efficiency

Signal
Background
3000 fb⁻¹
%

No cuts
34.3
103.9
1.84
0.33

Basic cuts
15.6
50.2
1.20
0.31
45.5

 GeV
11.3
19.5
1.40
0.58
72.4

 GeV
2.97
1.04
1.60
2.86
26.3

4. Summary

In the minimal 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 for 8, 14 TeV LHC, and displayed the dependance of the cross sections on the relevant model parameter. Moreover, we investigated the observability of process followed by the decays and at 14 TeV LHC for  GeV, . 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 to observe the effect of the process 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 ~ can provide us with a potential opportunity [57].

Competing Interests

The authors declare that they have no competing interests.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (NNSFC) under Grant no. 11405047, the Startup Foundation for Doctors of Henan Normal University under Grant no. qd15207, the Joint Funds of the National Natural Science Foundation of China (U1404113), the Education Department Foundation of Henan Province (14A140010), the Aid Project for the Mainstay Young Teachers in Henan Provincial Institutions of Higher Education of China (2014GGJS-283), and colleges and universities in Henan province key scientific research project for 2016 (16B140002).

References

G. Aad, B. Abbott, J. Abdallah et al., “Combined search for the Standard Model Higgs boson using up to 4.9 fb⁻¹ of pp collision data at  TeV with the ATLAS detector at the LHC,” Physics Letters B, vol. 710, no. 1, pp. 49–66, 2012.

S. Chatrachyan, V. Khachatryan, A. M. Sirunyan et al., “Combined results of searches for the standard model Higgs boson in pp collisions at  TeV,” Physics Letters B, vol. 710, pp. 26–48, 2012.

G. Aad, T. Abajyan, B. Abbott et al., “Evidence for the spin-0 nature of the Higgs boson using ATLAS data,” Physics Letters B, vol. 726, no. 1–3, pp. 120–144, 2013.

G. Aad, B. Abbott, J. Abdallah et al., “Measurement of Higgs boson production in the diphoton decay channel in pp collisions at center-of-mass energies of 7 and 8 TeV with the ATLAS detector,” Physical Review D, vol. 90, Article ID 112015, 2014.

G. Aad, B. Abbott, J. Abdallah et al., “Measurements of Higgs boson production and couplings in the four-lepton channel in pp collisions at center-of-mass energies of 7 and 8 TeV with the ATLAS detector,” Physical Review D, vol. 91, Article ID 012006, 2015.

The ATLAS collaboration, “Search for the decay of the Standard Model Higgs boson in associated (W/Z)H production with the ATLAS detector,” Journal of High Energy Physics, vol. 2015, article 69, 2015.

V. Khachatryan, A. M. Sirunyan, A. Tumasyan et al., “Observation of the diphoton decay of the Higgs boson and measurement of its properties,” The European Physical Journal C, vol. 74, article 3076, 2014.

S. Chatrchyan, V. Khachatryan, A. M. Sirunyan et al., “Evidence for the direct decay of the 125 GeV Higgs boson to fermions,” Nature Physics, vol. 10, pp. 557–560, 2014.

S. Chatrchyan, V. Khachatryan, A. M. Sirunyan et al., “Measurement of the properties of a Higgs boson in the four-lepton final state,” Physical Review D, vol. 89, no. 9, Article ID 092007, 2014.

The CMS Collaboration, “Measurement of Higgs boson production and properties in the WW decay channel with leptonic final states,” Journal of High Energy Physics, vol. 2014, articlr 96, 2014.

P. W. Higgs, “Broken symmetries, massless particles and gauge fields,” Physics Letters, vol. 12, no. 2, pp. 132–133, 1964.

P. W. Higgs, “Broken symmetries and the masses of gauge bosons,” Physical Review Letters, vol. 13, pp. 508–509, 1964.

F. Englert and R. Brout, “Broken symmetry and the mass of gauge vector mesons,” Physical Review Letters, vol. 13, pp. 321–323, 1964.

G. S. Guralnik, C. R. Hagen, and T. W. B. Kibble, “Global conservation laws and massless particles,” Physical Review Letters, vol. 13, no. 20, pp. 585–587, 1964.

T. W. B. Kibble, “Symmetry breaking in n-Abelian gauge theories,” Physical Review, vol. 155, no. 5, pp. 1554–1561, 1967.

S. Khalil, “Low-scale B–L extension of the standard model,” Journal of Physics G: Nuclear and Particle Physics, vol. 35, no. 5, Article ID 055001, 2008.

S. Khalil, “TeV-scale gauged symmetry with inverse seesaw mechanism,” Physical Review D, vol. 82, Article ID 077702, 2010.

G. Bordes and B. van Eijk, “On the associate production of a neutral intermediate-mass Higgs boson with a single top quark at the LHC and SSC,” Physics Letters B, vol. 299, no. 3-4, pp. 315–320, 1993.

T. M. Gould and E. R. Poppitz, “Complex time solutions with nontrivial topology and multiparticle scattering in Yang-Mills theory,” Physics Letters. B, vol. 312, no. 3, pp. 299–304, 1993.

W. J. Stirling and D. J. Summers, “Production of an intermediate-mass Higgs boson in association with a single top quark at LHC and SSC,” Physics Letters B, vol. 283, no. 3-4, pp. 411–415, 1992.

J. L. Diaz-Cruz and O. A. Sampayo, “Associated production of the Higgs boson with tb at hadron colliders,” Physics Letters B, vol. 276, no. 1-2, pp. 211–213, 1992.

V. Barger, M. McCaskey, and G. Shaughnessy, “Single top and Higgs associated production at the LHC,” Physical Review D, vol. 81, Article ID 034020, 2010.

M. Farina, C. Grojean, F. Maltoni, E. Salvioni, and A. Thamm, “Lifting degeneracies in Higgs couplings using single top production in association with a Higgs boson,” Journal of High Energy Physics, vol. 2013, article 22, 2013.

L. Wu, “Enhancing thj production from Top-Higgs FCNC couplings,” Journal of High Energy Physics, vol. 2015, article 61, 2015.

A. Kobakhidze, L. Wu, and J. Yue, “Anomalous top-Higgs couplings and top polarisation in single top and Higgs associated production at the LHC,” Journal of High Energy Physics, vol. 2014, article 100, 2014.

A. Greljo, J. F. Kamenik, and J. Kopp, “Disentangling flavor violation in the top-Higgs sector at the LHC,” Journal of High Energy Physics, vol. 2014, no. 7, article 046, 2014.

S. Khatibi and M. M. Najafabadi, “Probing the anomalous FCNC interactions in a top-Higgs boson final state and the charge ratio approach,” Physical Review D, vol. 89, Article ID 054011, 2014.

D. Atwood, S. K. Gupta, and A. Soni, “Constraining the flavor changing Higgs couplings to the top-quark at the LHC,” Journal of High Energy Physics, vol. 2014, article 57, 2014.

J. Chang, K. Cheung, J. S. Lee, and C.-T. Lu, “Probing the top-Yukawa coupling in associated Higgs production with a single top quark,” Journal of High Energy Physics, vol. 2014, article 62, 2014.

B. F. Yang, J. Z. Han, and N. Liu, “Associated production of single top and Higgs at the LHC in the littlest Higgs model with T-parity,” Journal of High Energy Physics, vol. 2015, article 148, 2015.

Y. M. Zhang and B. F. Yang, “Single-top and Higgs associated production via the Formula and tHW-channels at the LHC in the LHT model,” EPL, vol. 110, no. 2, Article ID 21001, 2015.

F. Demartin, F. Maltoni, K. Mawatari, and M. Zaro, “Higgs production in association with a single top quark at the LHC,” European Physical Journal C, vol. 75, no. 6, p. 267, 2015.

J. Campbell, K. Ellis, and R. Röntsch, “Single top production in association with a Z boson at the LHC,” Physical Review D, vol. 87, Article ID 114006, 2013.

P. Agrawal, S. Mitra, and A. Shivaji, “Effect of anomalous couplings on the associated production of a single top quark and a Higgs boson at the LHC,” Journal of High Energy Physics, vol. 2013, article 77, 2013.

R. N. Mohapatra and R. E. Marshak, “Local B−L symmetry of electroweak interactions, majorana neutrinos, and neutron oscillations,” Physical Review Letters, vol. 44, no. 20, pp. 1316–1319, 1980.

R. E. Marshak and R. N. Mohapatra, “Quark-lepton symmetry and as the U(1) generator of the electroweak symmetry group,” Physics Letters B, vol. 91, no. 2, pp. 222–224, 1980.

C. Wetterich, “Neutrino masses and the scale of B-L violation,” Nuclear Physics B, vol. 187, no. 2, pp. 343–375, 1981.

A. Masiero, J. F. Nieves, and T. Yanagida, “B-L violating proton decay and late cosmological baryon production,” Physics Letters B, vol. 116, no. 1, pp. 11–15, 1982.

R. N. Mohapatra and G. Senjanovic, “Spontaneous breaking of global B-L symmetry and matter-antimatter oscillations in grand unified theories,” Physical Review D, vol. 27, no. 1, pp. 254–263, 1983.

W. Buchmüller, C. Greub, and P. Minkowski, “Neutrino masses, neutral vector bosons and the scale of breaking,” Physics Letters B, vol. 267, no. 3, pp. 395–399, 1991.

L. Basso, A. Belyaev, S. Moretti, and C. H. Shepherd-Themistocleous, “Phenomenology of the minimal B-L extension of the standard model: Z ′ and neutrinos,” Physical Review D, vol. 80, Article ID 055030, 2009.

L. Basso, S. Moretti, and G. M. Pruna, “A renormalisation group equation study of the scalar sector of the minimal extension of the standard model,” Physical Review D, vol. 82, Article ID 055018, 2010.

F. Maltoni, K. Paul, T. Stelzer, and S. Willenbrock, “Associated production of the Higgs boson and a single top quark at hadron colliders,” Physical Review D, vol. 64, Article ID 094023, 2001.

A. Belyaev, N. D. Christensen, and A. Pukhov, “CalcHEP 3.4 for collider physics within and beyond the standard model,” Computer Physics Communications, vol. 184, no. 7, pp. 1729–1769, 2013.

J. Pumplin, D. R. Stump, J. Huston, H. L. Lai, P. M. Nadolsky, and W. K. Tung, “New generation of Parton distributions with uncertainties from global QCD analysis,” Journal of High Energy Physics, vol. 2002, article 07, 2002.

K. A. Olive, K. Agashe, C. Amsler et al., “Review of particle physics,” Chinese Physics C, vol. 38, no. 9, Article ID 090001, 2014.

T. Robens and T. Stefaniak, “Status of the Higgs singlet extension of the standard model after LHC run 1,” The European Physical Journal C, vol. 75, no. 3, article 104, 2015.

L. Basso, S. Moretti, and G. M. Pruna, “Theoretical constraints on the couplings of non-exotic minimal Z ′ bosons,” Journal of High Energy Physics, vol. 2011, no. 8, article 122, 2011.

L. Basso, A. Belyaev, S. Moretti, and G. M. Pruna, “Tree-level unitarity bounds for the minimal model,” Physical Review D, vol. 81, no. 9, Article ID 095018, 2010.

S. Banerjee, M. Mitra, and M. Spannowsky, “Searching for a heavy Higgs boson in a Higgs-portal B-L model,” Physical Review D, vol. 92, Article ID 055013, 2015.

L. Basso, S. Moretti, and G. M. Pruna, “Phenomenology of the minimal extension of the Standard Model: the Higgs sector,” Physical Review D, vol. 83, Article ID 055014, 2011.

J. Alwall, R. Frederix, S. Frixione et al., “The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations,” Journal of High Energy Physics, vol. 2014, no. 7, article 079, 2014.

T. Sjöstrand, S. Mrenna, and P. Skands, “PYTHIA 6.4 physics and manual,” Journal of High Energy Physics, vol. 2006, no. 5, article 026, 2006.

J. de Favereau, C. Delaere, P. Demin et al., “DELPHES 3: a modular framework for fast simulation of a generic collider experiment,” Journal of High Energy Physics, vol. 2014, no. 2, article 57, 2014.

G. Aad, B. Abbott, J. Abdallah et al., “Search for the standard model Higgs boson produced in association with top quarks in proton-proton collisions at  TeV using the ATLAS detector,” ATLAS-CONF-2012-135

S. Chatrchyan, G. Hmayakyan, V. Khachatryan et al., “Search for Higgs boson production in association with top quark pairs in pp collisions,” CMS-PAS-HIG-12-025

N. Arkani-Hamed, T. Han, M. Mangano, and L.-T. Wang, “Physics opportunities of a 100 TeV proton-proton collider,” https://arxiv.org/abs/1511.06495