Search for signal via associated production at LHC
Abstract
A variety of new physics models predict the existence of extra charged gauge bosons (). It is verified that and top quark associated production is a promising process to search for signal at the LHC. We study the collider signatures of multijetslepton by reconstructing the intermediate state through the decay modes of , and respectively. An angular distribution related to charged lepton and top quark moving direction is provided to distinguish alternative lefthanded or righthanded chiral couplings of to quarks in the hadronic decay modes. The superiority on the search of is demonstrated in the leptonic decay channel for the lefthanded type interaction, which is forbidden for the righthanded type interaction in the most theories. To be more realistic, the relevant standard model backgrounds are simulated. We adopt various kinematic cuts to suppress the backgrounds and collect the integral luminosity needed for the corresponding process detected at the LHC with sensitivity. We also provide a forwardbackward asymmetry which is related to the chirality of . The successive studies can shed light on the potential searching for signal as well as distinguishing typical new physics models.
pacs:
12.60.Cn, 14.70.Pw, 14.65.HaI Introduction
Though the standard model (SM) has gained great success and SMlike Higgs boson is discovered at the LHC, it is still in progress to investigate the new phenomena induced by many new physics models, such as extra dimensional models Klein:1926tv (); ArkaniHamed:1998rs (); Randall:1999vf (); ArkaniHamed:2001ca (), grand unified theories Pati:1973uk (); Georgi:1974sy (); Fritzsch:1974nn () and leftright symmetric models Pati:1974yy (); Mohapatra:1974hk (); Mohapatra:1974gc (); Senjanovic:1975rk (); Mohapatra:1977mj (), etc. Among this kind of models, a new extra charged gauge boson is proposed. To discriminate different new physics models beyond the SM, it is crucial to search for the production signal and study its properties at the LHC.
Recently, the latest experimental results have explored the potential to observe the heavy gauge bosons at the LHC. Searching for a boson with a signature of lepton and missing transverse energy has been performed by ATLAS and CMS collaborations. The results show that no significant excess over the SM expectation has been observed through or decay Aad:2012dm (); Chatrchyan:2013lga (). On the other hand, the signature of has also been investigated at the center of mass energy of 7 and 8 TeV, and the observed limits are displayed on the cross section as well as mass Aad:2012ej (); Chatrchyan:2012gqa (); atlas8tev ().
In general, is the most prospective channel for its research at the LHC due to the unambiguous backgrounds, while decay channel also becomes important, especially within the models in which the couplings of to leptons are extremely suppressed. The collider signature of a topphilic , which couples only to the third generation quarks of the SM, produced in association with a top quark is investigated at the LHC Berger:2011xk (). In addition, the investigation on the properties of also contributes to searching for its signal at the LHC, such as the chirality of coupling to SM particles. In reference Gopalakrishna:2010xm (), process is analyzed and the authors propose that the angular distribution for the charged lepton decayed from the top quarks can be a feature of the chirality of with decay mode. The extensively studies on the chiral property are carried out in the gauge interaction of decaying into and Higgs boson, which can be used to distinguish from the charged Higgs boson Bao:2011nh (); Bao:2011sy ().
In this paper we study the production in association with top quark at the LHC and the future hadron colliders. The dominant three decay modes of , ( stands for the light quark) and are investigated with the collider signature of , and . Searching for a massive signature with the electroweak coupling to fermions through the decay channel is hard due to the large backgrounds. The channel shows evidence in the search of at TeV. Because the highly boosted charged lepton decayed from differs from the backgrounds, the investigation of channel contributes to the search of signal. Moreover, we provide the charged lepton angular distribution to distinguish the chirality of .
This paper is organized as follows. The couplings of to SM particles are discussed in Sec. II together with the mass constraints. In Sec. III, the numerical results with , and decay modes are listed respectively and the corresponding SM backgrounds are simulated. Finally, we give a brief summary in Sec. IV.
Ii Theoretical Framework and Mass Constraints
The heavy charged gauge boson appears in various models with different couplings. We extract the couplings to quark and lepton () from the following general formula,
(1) 
where is the coupling constant, () is a unitary matrix representing the fermion flavor mixing, and is the left, righthanded chiral projection operator. To give a simplified result, we set with the pure lefthanded gauge boson , with the pure righthanded gauge boson , where is the electroweak coupling constant in the SM.
The mass parameter is one of the most crucial factors in the search of as well as the interaction couplings. From the proton antiproton collisions, CDF and D collaborations obtain the lower bound for a SMlike at 0.8 and 1 TeV Aaltonen:2009qu (); Abazov:2007ah (), respectively. The investigations on the K and B meson demonstrate that the lower mass limit is around 2.5 TeV Zhang:2007da (). The recent searches of have been performed by the ATLAS and CMS detectors at the LHC. Based on the results of decay channel, a with sequential SM couplings is excluded at the 95 credibility level for masses up to 2.55 and 2.90 TeV Aad:2012dm (); Chatrchyan:2013lga (). As discussed in the references Mohapatra:1974hk (); Mohapatra:1974gc (); Senjanovic:1975rk (); Mohapatra:1977mj (), one can imagine neutrino being Dirac particle. In this case, would have the usual leptonic decay channel, which implies a lower limit on its mass about 3 TeV. Independent of the nature of neutrino mass, the leftright symmetric theory implies a theoretical lower limit on the mass of about 2.5 TeV Zhang:2007da (); Beall:1981ze (); Maiezza:2010ic (). Additionally, the righthanded with the mass below 1.13 and 1.85 TeV is excluded through the reconstructed resonances Aad:2012ej (); Chatrchyan:2012gqa (); atlas8tev (). The search for the dijet mass spectrum, including quarkquark, quarkgluon, and gluongluon pairs, also presents mass bound TeV Chatrchyan:2011ns (). In particular, the CMS detector illustrates the mass of righthanded should be larger than 0.84 TeV through the associated production Chatrchyan:2012su ().
The branching fractions of decay into fermions are shown in Fig. 1. Whatever the lefthanded or righthanded decay into light quarks leads to more than a half fractions in the massive region. A disparate decay mode between the lefthanded and righthanded is that the is forbidden due to only lefthanded neutrino existed in the SM. We completely study the signatures of production in association with top quarks via the three decay modes, , and in the following section.
Iii Numerical Results and discussion
The tree level predominant partonic subprocess for production is the following process
(2) 
as depicted in Fig. 2, where denotes the 4momentum of the corresponding particle. The process is not referred in this paper for the similar character under the invariance. The LHC leads to a large probability to study the for the larger gluon parton distribution than Tevatron.
The total cross section for the process can be expressed as
(3) 
where is the parton distribution function (PDF) of gluon (quark), is the partonic center of mass energy squared, and is the partonic level cross section for process. To obtain the numerical results we set , GeV, and GeV. For PDF, we use CTEQ6L1Pumplin:2002vw (). The total cross section for process is displayed in Fig. 3, as a function of representing the mass of and at the LHC with 14 TeV and 33 TeV. In addition, we also give the results at the future hadron collider with 50 TeV and 80 TeV as a reference. There is no discrepancy in the cross section of lefthanded production from righthanded. The cross section can be up to 15 (300) for TeV with (33) TeV at the LHC. While the observation of the signal at 14 TeV LHC for the mass heavier than 3.3 TeV is difficult in the associated production on the condition of the couplings chosen in this paper. The and top quark can not be observed directly at the LHC, thus we analyze the multijets plus lepton and missing transverse energy signal with different decay modes as the follows.
iii.1 channel for production
First we explore the channel for the process at the LHC with and 33 TeV as the following process
(4) 
(5) 
where the charged lepton is an excellent trigger for the event search. Corresponding to process (4), the associated top quark semileptonically decays as and the antitop quark hadronically decays as . While in process (5), the decay modes of top and antitop quark are exchanged.
To be more realistic, the simulation at the detector is performed by smearing the leptons and jets energies according to the assumption of the Gaussian resolution parameterization
(6) 
where is the energy resolution, is a sampling term, is a constant term, and denotes a sum in quadrature. We take , for leptons and , for jets respectivelyatlas0901 ().
The transverse momentum distributions of jets and charged lepton are shown in Fig. 4 (a) and (b) as well as the missing transverse energy for the precess . In order to identify the isolated jet (lepton), the angular distribution between particle i and particle j is defined by
(7) 
where denotes the difference between the particles’ azimuthal angle, and the difference between the particles’ rapidity. In Fig. 4 (c), we display the differential distributions for .
The analysis of the whole process including the reconstruction of the intermediate resonances is propitious to select the production process from the substantial backgrounds. Theoretically, the top (antitop) quark with semileptonical decay can be reconstructed by one of the five jets, the charged lepton and the neutrino, while three of remaining jets can be used to reconstruct the antitop (top) quark with hadronical decay. Although the momentum of neutrino can not be directly recorded at the detector, one can resolve it by the kinematical constraint. The neutrinos’ transverse momentum is determined by the sum of the observable particles’ transverse momentum according to the momentum conservation, and the longitudinal part can be solved through the on shell condition for the Wboson,
(8) 
Once the neutrino’s momentum reconstructed, we can reconstruct the top or antitop quark invariant mass
(9) 
where j refers to any one of the five jets that makes the be closest to the top quark mass. Based on the above discussion, we employ the basic cuts to outstand the process as

Cut :
Then the mass peak can be reconstructed through the momentum of all the particles except the ones used to reconstruct the associated top or antitop quark. The distributions of are shown in Fig. 5. The resonance peak is significant in the invariant mass distribution of , which will be a direct signal in the search of . In order to further purify the signal, we require the following cut

Cut : or ,
together with the remaining jet that not be used to reconstruct top or antitop quark tagged as a bjet. The tagging efficiency is assumed to be 60% while the misstagging efficiency of a light jet as a jet is taken as transverse momentum dependent atlas0901 ():
(10) 
The cross section of process (4) at the LHC with and TeV after Cut and are displayed as a function of in Fig. 6 (a), which deriving from is larger than due to the discrepancy of the branching fraction . If the mass of is larger than 1 TeV, it will be negative to observe from the process at the 14 TeV LHC, while the cross section can be enhanced more than one order of magnitude at 33 TeV. Considering the effect from the background of , we give the integral luminosity needed at the LHC with for various in Fig .6 (b). The result shows that the with mass below 1 TeV can be observed from the process (4) at the LHC with TeV. For a with mass up to 3 TeV, only with the sizable couplings it can be detected in the associated production via the decay at the future LHC. It makes no difference to the results for the process (5) as displayed in Fig. 7.
iii.2 channel for production
According to Fig. 1, the search of is in favor of decay modes for the large branch fraction. Then we focus on the following process
(11) 
where the charged lepton is from the associated top quark. The differential distributions with the transverse momentum of the three jets and charged lepton are shown in Fig. 8 (a) and (b) as well as the missing transverse energy. The first two jets with the largest transverse momentum mostly derive from so that two peaks appear nearby 1.5 TeV which is half of the mass. The normalized differential distributions with which are displayed in Fig. 8 (c) for process is broader than that in processes (4) and (5).
We use the same methods as in Sec. III A to obtain the momentum of neutrino and reconstruct the intermediate resonances. The following relation is adopted,
(12) 
with j named refers to any one of the three jets which makes be closest to the top quark mass and for the left two.
Considering the unlike transverse momentum distributions of jet with the center of mass energy at 14 and 33 TeV, we employ the basic cuts as

Cut :
Once the jet derived from top quark is confirmed by the reconstruction of top quark, the two remaining jets are absolutely from the heavy charged gauge boson . As presented in Fig. 9, the resonance peak is obvious around the mass in the differential distribution with .
Hence the further cut is

Cut :.
Comparing the signal to the main SM backgrounds , and , one can find that btagging can help to purify the signal, so we require the jet used to reconstruct top quark to be a bjet.
We show the total cross section after all the cuts for the signal process (11) at the LHC with TeV and TeV in Fig. 10 (a), as well as the integral luminosity as a function of assuming the significance is in Fig. 10 (b). The cross section is up to 0.003 (0.005) for a mass of 2 TeV () with 14 TeV, as well as 0.118 (0.165) with 33 TeV, while it is obviously suppressed by the strictly kinematic cuts for the mass lighter than 2 TeV with 33 TeV. The main backgrounds with the same detector signal including , , and are simulated by MadEvent program MadEvent (). One can find that the luminosity need to be up to if the charged bosons with TeV can be detected at TeV. However, there are about forty events can be detected for a TeV with the luminosity of at TeV.
Once a heavy charged boson is discovered at the LHC, it will be imperative to determine its chiral couplings to SM fermions. Accounting for different chiral couplings between and , we investigate the charged lepton angular distribution which depends on the chiral couplings of to light quarks. The chirality of the coupling to the light quarks can be translated to the angular distribution of the charged lepton and a forwardbackward asymmetry is defined as follows
(13) 
with
(14) 
Here is the 3momentum of charged lepton in the top quark rest frame, and is the 3momentum of the top quark in center of mass frame.
The charged lepton angular distributions with respect to before and after cuts are displayed in Fig. 11 corresponding to the process (11) at 33 TeV LHC. The result shows that most charged leptons moving against the direction of the top quark for the lefthanded type interaction, while it leads to the inverse tendency for the righthanded type interaction. Thus we can separate the hemisphere of top quark direction from the opposite hemisphere according to or , then the forwardbackward asymmetry leads to inverse sign which is listed in Table. 1. Although the distributions after the cuts in the region are severely distorted by the acceptance cuts, due to the charged leptons moving against the top quark direction carry less energy than those in the remaining region, the forwardbackward asymmetry with is also an excellent characteristic quantity to distinguish from .
iii.3 channel for production
The leptonic decay modes of depend on the lepton spectrum and the flavor mixing in the given model. Although the righthanded boson can couple to a charged lepton and righthanded neutrino in some new physics models, the decay modes of is not considered due to the mass of larger than or the different signal comparing to . In this section, we focus on the process
(15) 
with decay mode, which provides the charged lepton with large transverse momentum as an excellent trigger at the LHC.
The distributions of with the transverse momentum of the three jets and lepton are shown in Fig. 12 (a) and (b). There is an obvious jacobian peak at in the charged lepton transverse momentum distribution. In Fig. 12 (c), we display the corresponding distributions for .
We employ the basic acceptance cuts as

Cut :
And we require the top quark mass be reconstructed by all of the three jets as well as boson mass reconstructed by two of the jets as the further cut

Cut :
where
(16) 
In addition, the jet which is not used to reconstruct boson is tagged as a bjet to suppress the background processes.
The differential distributions for process (15) are shown in Fig. 13, where
(17) 
One can see that a peak appears around the mass which is a significant excess comparing to the SM backgrounds.
In Fig. 14, we present the total cross section for the pure lefthanded with and without cuts at the LHC with TeV and TeV. The cross section reaches 0.02 for TeV with TeV. Corresponding to the process (15) with final states , the dominant backgrounds from SM are , , and , which are simulated by MadEvent. Supposing the integral luminosity to be at TeV, a with mass up to 1.7 TeV can be found at significance, which can be enlarged to 4 TeV on the condition of integral luminosity of at the LHC with TeV.
In a more appealing seesaw version Minkowski:1977sc (); Mohapatra:1979ia () of the theory, as in the papers below, decays into the heavy righthanded neutrino with the spectacular signatures of lepton number violation Keung:1983uu (). In this case, there have been dedicated searches and theoretical discussions Ferrari:2000sp (); Nemevsek:2011hz (); Han:2012vk (). Perhaps the can be first detected at the LHC associated with the heavy righthanded neutrino.
Iv Summary
The observation of a new charged vector boson is an unambiguous signal for new physics beyond the SM. As a result, it is important to search for production signal and its related phenomena via different production and decay channels at the LHC. In this paper, we focus on investigating the collider signature for the associated production with , and respectively at the LHC. It is found that with the most common coupling parameters and present mass constraints for , due to the limited cross section, it is difficult to observe production signal via associated production at 14 TeV. However, if the center of mass energy of the LHC is updated to 33 TeV or even higher, a distinct signal for production can be observed via and after adopting proper kinematic cuts, e.g., large transverse momentum cut to the jets/leptons, etc. Once the production is observed at the LHC, it will become important to study the interactions between and fermions. For this aim, as an example, we analyze the angular distribution of the charged lepton for process and the related forwardbackward asymmetry induced by top quark spin. Our results show that the charged lepton angular distribution is related to the chiral couplings of to fermions and the forwardbackward asymmetry depending on this angular distribution. These observables can be used to distinguish from . If the LHC can served as a discovery machine for the new charged gauge boson , our work will be useful to search for its production signal and to explore its properties.
Acknowledgments
We would like to thank Profs. ShiYuan Li and ShouShan Bao for their helpful discussions and comments. This work is supported in part by National Science Foundation of China (NSFC) under grant Nos.11305075, 11325525, 11275114, 10935012 and 11375200. Li is also supported in part by Natural Science Foundation of Shandong Province under grant No.ZR2013AQ006.
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