Search for tZ^{\prime} associated production induced by tcZ^{\prime} couplings at the LHC

Search for associated production induced by couplings at the LHC

Wei-Shu Hou Department of Physics, National Taiwan University, Taipei 10617, Taiwan    Masaya Kohda Department of Physics, National Taiwan University, Taipei 10617, Taiwan    Tanmoy Modak Department of Physics, National Taiwan University, Taipei 10617, Taiwan

The and anomalies, recently observed by the LHCb collaboration in transitions, may indicate the existence of a new boson, which may arise from gauged symmetry. Flavor-changing neutral current couplings, such as , can be induced by the presence of extra vector-like quarks. In this paper we study the LHC signatures of the induced right-handed coupling that is inspired by, but not directly linked to, the anomalies. The specific processes studied are and its conjugate process each followed by . By constructing an effective theory for the coupling, we first explore in a model-independent way the discovery potential of such a at the 14 TeV LHC with 300 and 3000 fb integrated luminosities. We then reinterpret the model-independent results within the gauged model. In connection with , the model also implies the existence of a flavor-conserving coupling, which can drive the process. Our study shows that existing LHC results for dimuon resonance searches already constrain the coupling, and that the can be discovered in either or both of the and processes. We further discuss the sensitivity to the left-handed coupling and find that the coupling values favored by the anomalies lie slightly below the LHC discovery reach even with 3000 fb.

I Introduction

Recent measurements performed by the LHCb experiment Aaij:2013qta (); Aaij:2015oid (); Aaij:2014ora () exhibit anomalous transitions. One is the measurement Aaij:2013qta (); Aaij:2015oid () of angular observables for the decay, which shows a discrepancy from the Standard Model (SM) prediction at 3.4 level, mainly driven by the observable. In another measurement Aaij:2014ora () of decays ( or ), LHCb found a further hint for lepton flavor universality violation, namely a 2.6 deviation of the observable from its SM value. These LHCb results are supported by a recent Belle analysis Wehle:2016yoi (), where the angular observables were separately measured for the muon and electron modes of decays, and the muonic was found to show the largest discrepancy (at 2.6 level) from the SM prediction. Although these anomalies can well be due to statistical fluctuations and/or hadronic uncertainties, it is interesting to investigate whether they can be attributed to physics beyond the SM (BSM). Model-independent analyses by various groups have found that a BSM contribution to the Wilson coefficient , associated with the effective operator , can explain both the  Descotes-Genon:2013wba (); Altmannshofer:2013foa (); Beaujean:2013soa (); Horgan:2013pva (); Hurth:2013ssa () and  Alonso:2014csa (); Hiller:2014yaa (); Ghosh:2014awa () anomalies, by a similar amount in BSM effect Hurth:2014vma (); Altmannshofer:2014rta ().

Given the data suggest BSM effects in the muon modes rather than the electron modes, an interesting BSM candidate is a new gauge boson of the gauged symmetry He:1990pn (); Foot:1990mn (), the difference between the muon and tau numbers. The boson couples to the muon but not to the electron. In Ref. Altmannshofer:2014cfa (), an extension of the gauged symmetry was constructed for sake of introducing flavor-changing neutral current (FCNC) couplings to the quark sector. In the model, the SM quarks mix with new vector-like quarks, that are charged under the new gauge symmetry, leading to effective FCNC couplings of with SM quarks. Among these, the left-handed (LH) coupling gives rise to . The model provides a viable explanation for both the and anomalies.

The gauged model is, however, just one possibility among many options for a UV theory. Hence, the model should be cross-checked by other ways, in particular, by direct searches at colliders. LHC phenomenology within the minimal version of the gauged model has been studied in Refs. Altmannshofer:2014cfa (); Harigaya:2013twa (); Altmannshofer:2014pba (); delAguila:2014soa (); Elahi:2015vzh (), where is searched in . The search is sensitive to lighter than the boson and can probe the new gauge coupling as well as the mass . On the other hand, the extended model Altmannshofer:2014cfa () gives effective couplings to SM quarks, and these couplings could offer new ways to produce the boson at colliders. In particular, the model predicts the existence of not only a LH coupling that is directly related to the LH coupling by SU(2) gauge symmetry, but also a right-handed (RH) coupling. Refs. Altmannshofer:2014cfa (); Fuyuto:2015gmk () have studied decay induced by these couplings. This decay can be searched for in the huge number of events at the LHC; however, it becomes kinematically forbidden if the mass is greater than the mass difference between the top and charm quarks, i.e. for .111 For , Arhrib:2006sg (); Cakir:2010rs (); Aranda:2010cy () may happen, but its branching ratio is highly suppressed due to mixings between the heavy vector-like and SM quarks, in addition to rather low production cross sections in the model we consider.

In this paper we consider another unique production mechanism of the boson via the couplings, namely, . To be specific, we study the following processes at the 14 TeV LHC: (hereafter denoted as the process) and its conjugate (denoted as ) process, each followed by and (or its conjugate). A model-independent study of such -induced processes at the LHC has been performed in Ref. Gupta:2010wt ().222 A -induced process has also been studied with decays to quarks in Ref. Gresham:2011dg () () and Ng:2011jv () (). We improve the treatment of SM background processes by including the ones missed in the previous study and find that the process is better suited for discovery than due to lower background. Combining the two signal processes (also referred to as the process collectively if there is no confusion), we present first the model-independent discovery potential of the process, aiming for the high-luminosity LHC (HL-LHC). In detailing our collider analysis, we choose two representative mass values: just below (150 GeV) and above (200 GeV) the top-quark mass. We then extend the latter case to masses up to 700 GeV, and reinterpret the model-independent results for RH coupling within the gauged model Altmannshofer:2014cfa (). It turns out that the LH coupling implied by the anomalies is rather small, and lies slightly beyond the discovery reach of the LHC even with 3000 fb data. Therefore, we mainly focus on the RH coupling, which is hardly probed by B physics. Yet our results can be easily translated into the case of the LH coupling.

The model implies a flavor-conserving effective coupling along with , while the effective couplings containing the up quark, i.e. , and , are suppressed by meson constraints. The coupling offers another production channel for at the LHC, i.e. (hereafter denoted as the dimuon process). Analogous to the case, we first perform a model-independent study, which is then reinterpreted within the gauged model. We find that the can be discovered in either or both of the and dimuon processes. We show that the dimuon process has a better chance for discovery in most of the model parameter space, while simultaneously measuring the process can confirm the flavor structure of the model.

The paper is organized as follows. In Sec. II, we briefly introduce the gauged model of Ref. Altmannshofer:2014cfa () and give the effective Lagrangian for and couplings. We detail our collider analysis in Sec. III, which is divided into two subsections: the and processes induced by coupling in Sec. III.1, and the dimuon process induced by coupling in Sec. III.2. In Sec. III.1, we also utilize an existing LHC data Sirunyan:2017kkr () to illustrate its implication for coupling. Three subsections are assigned to Sec. IV. In Sec. IV.1 we present the model-independent discovery reaches for RH and couplings at the HL-LHC. In Sec. IV.2, we reinterpret the model-independent results within the gauged model. In Sec. IV.3 we discuss collider sensitivities to the LH coupling, which is directly linked to the anomalies. We summarize and offer further discussions in Sec. V.

Ii Model

Let us briefly introduce the gauged model of Ref. Altmannshofer:2014cfa (), where a new U(1) gauge group associated with symmetry is introduced. The gauge and Higgs sectors of the U(1) consist of the gauge field and the SM gauge singlet scalar field , which carries unit charge under the U(1). The field acquires a nonzero vacuum expectation value (VEV) , which spontaneously breaks the U(1) and gives mass to , . In the minimal model, the couples to the SM fermions through


In Ref. Altmannshofer:2014cfa (), an extended model was constructed by the addition of vector-like quarks , , and their chiral partners , , . The vector-like quarks carry U(1) charge for , and for and , with gauge invariant mass terms given by


The vector-like quarks mix with SM quarks via Yukawa interactions given by


The SU(2) symmetry relates the Yukawa couplings of LH up-type quarks to those of the LH down-type quarks:


where and is an element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix.

At energy scales well below the heavy vector-like quark masses, the above Yukawa couplings generate an effective Lagrangian for FCNC couplings to SM quarks,




Among these, the couplings and affect the transitions. In particular, gives a new contribution to the Wilson coefficient of the operator , given by


which can explain both and anomalies. If the LH coupling exists, the SU(2) relation in Eq. (4) would imply the existence of the LH coupling . Unfortunately, the strength of favored by the and anomalies turns out to be below the discovery reach at HL-LHC, as we discuss in Sec. IV.3.

Figure 1: Feynman diagrams that generate the effective RH [left] and [right] couplings.

The model, however, predicts the existence of the RH coupling . The coupling is not directly linked to transitions and is therefore hardly probed by and physics. But this coupling and its effect on top physics should be viewed as on the same footing as the and anomalies. Because there is no gauge anomaly, it could even happen that the and quarks are absent, or equivalently rather heavy, but the quark could cause effects in the top/charm sector that are analogous to the current and “anomalies” in decay, even if the latter “anomalies” disappear with more data. We therefore focus on the LHC phenomenology of the RH coupling.

The RH coupling is generated by the diagram shown in the left panel of Fig. 1 and is given by


which is nonzero only if . One sees then that the diagram in the right panel of Fig. 1 generates RH coupling with


This means that if the RH coupling exists, the RH coupling should also exist. We shall therefore also consider the RH coupling for LHC phenomenology.

In short, we consider the following effective couplings in the collider study:


with the model-dependent expressions of and in Eq. (8) and (9). But, our collider results can be straightforwardly applied to the LH counterparts, and .

In principle, the model could also give the effective couplings containing the up quark, i.e. the RH , and couplings, if is nonzero. In this case, is constrained by -meson mixing and decays. We assume for simplicity, while RH coupling is discussed in Sec. V. The presence of the quark with nonzero and also leads to couplings of neutral SM bosons to the currents. and couplings are induced at tree level, while and couplings, forbidden at tree level due to gauge symmetry, are generated at one-loop level. In Ref. Altmannshofer:2014cfa (), it is claimed that the branching ratios of rare top quark decays induced by these FCNC couplings with the SM bosons are suppressed over by roughly a loop factor, with the latter assumed to be kinematically allowed.

We shall consider the mass range of 150 GeV 700 GeV, where the branching ratios and total width for decay are nicely approximated by


In this mass range, dominant constraints on the () plane comes from neutrino trident production and mixing Altmannshofer:2014cfa (). These can be recast into constraints on the VEV of the field , which can be summarized as Fuyuto:2015gmk ()


regardless of the value of . The lower limit comes from neutrino trident production Altmannshofer:2014pba () with range of the CCFR result Mishra:1991bv (),333 The presence of the boson affects couplings of the boson to the muon, tau and corresponding neutrinos via loop effect, which are constrained by experimental data taken at the resonance. A study in Ref. Altmannshofer:2014cfa () shows that combining results from the LEP and SLC ALEPH:2005ab () can provide competitive or slightly better limits than the CCFR for GeV. while the upper limit is set by mixing Crivellin:2015mga () with BSM effects allowed within and the assumption of TeV. The upper limit becomes tighter for larger , e.g. for TeV.

It is convenient to introduce the mixing parameters Fuyuto:2015gmk () between vector-like quark and RH top or charm quark defined by


Small mixing parameters are assumed in obtaining the effective couplings of Eq. (8) and (9). In the following analysis, we allow the mixing strengths up to the Cabibbo angle, i.e. , and the RH coupling is constrained as


If the Yukawa couplings are hierarchical, e.g., , this is further suppressed by . A similar constraint holds for . These set the target ranges for the LHC study.

Iii Search for at the LHC

iii.1 and processes

Figure 2: Feynman diagrams contributing to .

The RH coupling in Eq. (10) generates the parton-level process through the Feynman diagrams in Fig. 2, leading to at the LHC. We assume subsequent decays of and with or . In this subsection, we study the FCNC-induced process ( process) and its conjugate process ( process) at the 14 TeV LHC, and analyze the prospect of discovering such a boson. The RH coupling also generates processes with an extra charm quark in the final states, i.e. or . We will veto extra jets in the following analysis, but the latter processes can contribute to the signal region if the charm jet escapes detection. Hence, we also include the contributions from as a signal.

For sake of our collider analysis, we take two benchmark points for the effective theory defined by Eq. (10):

  • Case A: , GeV;

  • Case B: , GeV.

In Case A, where , the decay is kinematically allowed with , and it contributes to via . On the other hand, in Case B with , the decay is kinematically forbidden.444 For , a three-body decay may still happen through an off-shell , and can contribute to the signal region via the events. In this case, the mass cannot be reconstructed from the dimuon invariant mass, but the top quark mass reconstruction may help discriminate signal and backgrounds. In Case B with GeV, such a contribution is very tiny and is not included in our analysis, although it could be important for a mass nearby the top quark mass. Moreover, behavior of event distributions for SM backgrounds is qualitatively different depending on whether the mass is below or above the top-quark mass. The coupling value is in the range of Eq. (14) implied by the gauged model.

The signal cross sections are proportional to if the width is narrow. We assume , motivated by the gauged model, and GeV for each case. Besides these assumptions, the analysis in this subsection is model-independent. Effects of different branching ratios can be taken into account by rescaling .

A similar BSM process induced by couplings has been studied by the CMS experiment with 8 TeV data Sirunyan:2017kkr (). Our study closely follows this analysis. There exist several non-negligible SM backgrounds for the signal ( process) and ( process):

  • and backgrounds: The background predominantly originates from


    with smaller contributions from - or -initiated processes, while is generated by the charge-conjugate processes


    The cross section is larger than , as the parton distribution function (PDF) of the quark is larger than the quark in collisions Campbell:2013yla (). Thus, the process suffers from larger background.

  • background: becomes background for the () process, if the () decays hadronically and the () decays leptonically, i.e. [], with some of the jets undetected. Indeed, constitutes a major part of the overall background.

  • background: is another leading source of background. If the , and all decay leptonically and a jet goes undetected, it can give the event topology with trilepton (), missing transverse energy () and -tagged jet. The production cross section is larger than  Campbell:2012dh () for collisions. Thus, the process again suffers larger background.

  • +heavy-flavor jets and +light jets: The or production in association with heavy-flavor (h.f.) or light jets also contribute to background, if both and decay leptonically and a jet gets misidentified as a -tagged jet. Here, the h.f. jet refers to the -jet. The rejection factors for the -jet and the light jet are taken to be and , respectively ATLAS:2014ffa (). The cross section for +light jets is larger than +light jets, while the production cross sections in association with h.f.-jets are identical. This also gives larger background to the process than .

We do not consider processes such as , Drell-Yan (DY), +jets, which could contribute to background if one or two nonprompt leptons are produced and reconstructed. These backgrounds are not properly modeled in simulation and require data for better estimation. The analysis of the similar process by CMS Sirunyan:2017kkr () shows that such processes provide subdominant contributions to the total background. In the case of the process, stricter cuts on the transverse momenta of the muons may reduce such contributions. These are beyond the scope of this paper.

Figure 3: Normalized distributions of the dimuon invariant mass for the process in Case A ( GeV) and B ( GeV), and for the corresponding backgrounds, with close-to-default cuts in MadGraph.

The signal and background samples are generated at leading order (LO) in the collision with center of mass energy TeV, by the Monte Carlo event generator MadGraph5_aMC@NLO Alwall:2014hca (), interfaced to PYTHIA 6.4 Sjostrand:2003wg () for showering. To include inclusive contributions, we generate the matrix elements of signal and backgrounds with up to one additional jet in the final state, followed by matrix element and parton shower merging with the MLM matching scheme Alwall:2007fs (). Due to computational limitation, we do not include processes with two or more additional jets in the final state. The event samples are finally fed into the fast detector simulator Delphes 3.3.3 deFavereau:2013fsa () for inclusion of (ATLAS-based) detector effects. The effective theory defined by Eqs. (1) and (10) is implemented by FeynRules 2.0 Alloul:2013bka (). We adopt the PDF set CTEQ6L1 Pumplin:2002vw (). The LO and cross sections are normalized to the next-to-leading order (NLO) ones by -factors of 1.7 and 1.56, respectively Campbell:2013yla (). For simplicity, we assume has the same NLO -factor as . The NLO -factor for the () process is taken to be 1.35 (1.27) Campbell:2012dh (). The LO cross section for the +light jets background is normalized to the next-to-next-to-leading order (NNLO) one by a factor of 2.07 Grazzini:2016swo (). We assume the same correction factor for +light jets and +h.f. jets for simplicity.

The signal cross sections for the and processes are identical, while some of the dominant (and the total) background cross sections are smaller for the latter process. The process is, therefore, better suited for discovering the . It turns out that combining the and processes can improve discovery potential. In the following, we primarily investigate the process in showing details of our analysis, and finally give combined results of the and processes.

We present, in Fig. 3, the normalized event distributions of the dimuon invariant mass for the process in Case A and B, and for the corresponding background contributions. The distributions are obtained by applying default cuts in MadGraph with minor modifications. In Figs. 4 and 5, the normalized distributions are similarly shown for the leading and subleading muons, the third lepton and the -tagged jet, respectively.

Figure 4: Normalized distributions for the leading [left] and subleading [right] muons, for the process and its backgrounds as in Fig. 3.
Figure 5: Normalized distributions for the third lepton [left] and -tagged jet [right], for the process and its backgrounds as in Fig. 3.
Cuts Signal (Case A) +light jets +h.f. jets Total BG
Pre-selection cuts 0.410 0.872 (1.552) 1.672 0.514 (1.384) 0.641 (0.868) 4.55 8.25 (10.03)
Selection cuts 0.090 0.012 (0.022) 0.026 0.023 (0.071) 0.012 (0.015) 0.017 0.090 (0.151)
(No jet veto)
Selection cuts 0.085 0.011 (0.020) 0.014 0.014 (0.039) 0.005 (0.007) 0.014 0.058 (0.094)
Table 1: Effects of two sets of cuts on cross sections (in fb) for the and SM background processes in Case A ( GeV). The effect of the selection cuts without the subleading jet veto is also shown. (See text for details.) The second column gives the signal process, while the effects on individual backgrounds are tabulated in third to seventh columns. Cross sections for backgrounds of the conjugate process are given in parentheses, if they differ from the case of the process: (third column), (fifth column) and +light jets (sixth column), where similar sets of cuts as the process are applied. The last column shows the sum of all background cross sections.
Cuts Signal (Case B) +light jets +h.f. jets Total BG
Pre-selection cuts 0.186 0.872 (1.552) 1.672 0.514 (1.384) 0.641 (0.868) 4.55 8.25 (10.03)
Selection cuts 0.040 0.006 (0.010) 0.014 0.012 (0.035) 0.005 (0.007) 0.008 0.045 (0.074)
(No jet veto)
Selection cuts 0.037 0.005 (0.009) 0.007 0.008 (0.021) 0.002 (0.003) 0.007 0.029 (0.047)
Table 2: Same as Table 1, but for Case B ( GeV).

We use two sets of cuts on the signal and background processes as explained below.

Pre-selection cuts: This set of cuts is used at the generator level. The leading, subleading and third leptons in an event are required to have minimum of 60 GeV, 30 GeV and 15 GeV, respectively, in both Case A and B. The maximum pseudo-rapidity of all leptons are required to be . The transverse momentum of jets are required to be greater than 20 GeV. The minimum separation between the two oppositely-charged muons are required to be . The rest of the cuts are set to their default values in MadGraph.

Selection cuts: Utilizing the signal and background distributions in Figs. 3, 4 and 5, we impose a further set of cuts. Events are selected such that each should contain three (at least two muon type) leptons and at least one -tagged jet. Jets are reconstructed by the anti- algorithm with radius parameter . Stricter cuts on lepton transverse momenta are applied: the leading muon, subleading muon and third lepton in an event are required to have minimum of 60 (75) GeV, 30 (45) GeV and 20 (20) GeV, respectively, in Case A (B). The third lepton is assumed to arise from the top-quark decay accompanied by missing transverse energy and jet. We require that GeV and the reconstructed boson mass GeV. The leading -tagged jet is required to have GeV. An event is rejected if the of the subleading jet or subleading -tagged jet is greater than GeV. This veto significantly reduces the and backgrounds, as both processes contain two -jets from decay of the and . We will also analyze the impact of removing such a jet veto shortly. We finally apply the invariant mass cut GeV on two oppositely-charged muons. If an event contains three muons, there are two ways to make a pair of two oppositely-charged muons. In such a case, we identify the pair having the invariant mass closer to as the one coming from the decay, and impose the above invariant mass cut on this pair.

The effects of these two sets of cuts on the signal and background processes are illustrated in Table 1 for Case A, and Table 2 for Case B. From these tables, we see that the selection cuts significantly reduce the number of background events (), and the number of signal events () becomes larger than for the process in both Case A and B. The expected numbers of events with integrated luminosity fb are and in Case A (B) for the process. For comparison, the effects of removing the veto on the subleading jet are also shown in the tables. Without the jet veto, the signal events slightly increases as , but the background events increase more as in Case A (B) for the process. This illustrates the advantage of imposing the veto on the subleading jet.

To estimate the signal significance, we use Cowan:2010js ()


This becomes the well-known form for , but it does not hold in the current case. We require for 5 discovery. In Case A (B), therefore, the can be discovered at in the process with integrated luminosity fb. Discovery in the process would require more data: fb in Case A (B). Combining the and processes, one could discover the with lower integrated luminosities: fb in Case A (B). Therefore, better discovery potential is attained with the combined and processes. In the following, we will give results for this combined case and also call it process collectively if there is no confusion.

Before closing this subsection, we briefly discuss the use of some existing LHC data to search for the coupling. CMS Sirunyan:2017kkr () has studied the SM process in the three lepton (electron or muon) final state with 8 TeV data, measuring the cross section of fb, which is consistent with SM prediction of 8.2 fb. Taking this as background, CMS has also searched for the BSM process induced by () couplings; no evidence was found, resulting in the 95% CL upper limits of % and %.

In the CMS analysis Sirunyan:2017kkr (), production has been searched for with the invariant mass cut of GeV GeV on two oppositely-charged same-flavor leptons. Hence, the search is sensitive to the process if the mass falls into this window. The measured cross section for the three muon channel is fb, while the SM prediction is around 2.1 fb with an uncertainty of less than 10%. Following the same event selection cuts as the CMS analysis, we calculate the contribution to be 17.4 fb for GeV by MadGraph followed by showering and incorporating CMS based detector effects. Symmetrizing the experimental uncertainties by naive average and allowing the effect to enhance the cross section up to 2 of the measured value, we obtain an upper limit of for .

Figure 6: Normalized distributions of dimuon invariant mass for the dimuon process in Case I ( GeV), II ( GeV) and for the backgrounds, with close to default cuts in MadGraph.
Figure 7: Normalized distributions for leading [left] and subleading [right] muons, for the dimuon process and its backgrounds as in Fig. 6.

iii.2 Dimuon process:

The flavor conserving coupling in Eq. (10) gives rise to the parton-level process . Thus, the can also be searched for via (dimuon process), where existing dimuon resonance search results at the LHC can already constrain . The experimental searches do not veto extra activities ; hence, we also include subdominant contributions from and processes, induced by the RH coupling. In the following analysis, we adopt the 13 TeV results by ATLAS ATLAS:2016cyf () and CMS CMS:2016abv () (both based on 13 fb data). The ATLAS analysis puts 95% CL upper limits on production cross section times branching ratio for 150 GeV 5 TeV, while the CMS analysis provides 95% CL upper limits on the quantity , which is defined as the ratio of dimuon production cross section via to the one via or (in the dimuon-invariant mass window of 60–120 GeV), for 400 GeV 4.5 TeV. We interpret the latter as the limits on


and convert them into the limits on by multiplying the SM prediction of pb CMS:2015nhc (). With parameters allowed by these searches, we study the prospect of discovering the dimuon process at the 14 TeV LHC.

As in the previous subsection, we choose two benchmark points:

  • Case I: , GeV;

  • Case II: , GeV.

We assume narrow width ( GeV) and for each case. The benchmark points are allowed by the dimuon resonance searches, as can be seen from the right panel of Fig. 8 in the next section.

For treatment of SM backgrounds, we follow the analysis by ATLAS ATLAS:2016cyf (). There are multiple sources of backgrounds. The dominant contribution arises from the DY process, where the muon pair is produced via /. Other nonnegligible contributions arise from , and production, while contributions from and production are less significant. As in the case, we do not include backgrounds associated with nonprompt leptons.

The signal and background samples for the dimuon process are generated in a similar way as in the previous subsection, except the treatment of additional jets. In this case, we generate matrix elements of signal and backgrounds with up to two additional jets, followed by showering. The LO (DY) cross section is normalized to the NNLO QCD+NLO EW one with LO photon-induced channel by the correction factor 1.27. The latter is obtained by FEWZ 3.1 Li:2012wna () in the dimuon-invariant mass range of GeV. The LO and cross sections are normalized to the NNLO+NNLL ones by the factors  twiki () and  Kidonakis:2010ux (), respectively. As for , and , the LO cross sections are normalized to the NNLO QCD ones by the factors  Gehrmann:2014fva (),  Grazzini:2016swo () and  Cascioli:2014yka (), respectively.

Normalized distributions of the dimuon invariant mass are given in Fig. 6 for the dimuon process in Case I, II and the backgrounds, obtained by close-to-default cuts in MadGraph. The distributions of the leading and subleading muons are given in Fig. 7. We apply two sets of cuts on signal and background events as in the previous subsection.

Cuts Signal (Case I) Total BG
Pre-selection cuts 38.65 19980 1785 166 212 128.44 74.82 22346
Selection cuts 20.96 1677 163 16 24 0.22 0.02 1880
Table 3: Same as Table 1 (cross sections in fb), but for the dimuon process in Case I ( GeV).
Cuts Signal (Case II) Total BG
Pre-selection cuts 17.77 19980 1785 166 212 128.44 74.82 22346
Selection cuts 10.22 532 117 12 14 0.12 0.01 675
Table 4: Same as Table 1, but for the dimuon process in Case II ( GeV).

Figure 8: [Left] 5 discovery reach in strength vs for the combination of the and processes at the 14 TeV LHC with 300 fb (upper red solid line) or 3000 fb (lower blue solid line) data, and corresponding 3 reach shown by dashed lines. [Right] Same as left panel, but for vs for the dimuon process . The gray (semi-transparent blue) shaded region is excluded at 95% CL by the dimuon resonance search of ATLAS ATLAS:2016cyf () (CMS CMS:2016abv ()) with fb data at the 13 TeV LHC. and % are assumed in both panels.

Pre-selection cuts: The two muons in an event are required to have transverse momenta GeV, maximum pseudo-rapidity , with minimum separation .

Selection cuts: Events are selected such that each event contains two oppositely-charged muons with leading muon transverse momentum 60 (75) GeV, and subleading muon 55 (60) GeV in Case I (II). We impose an invariant-mass cut of GeV on the two muons in both Case I and II.

The effects of the two sets of cuts on the signal and backgrounds are tabulated in Table 3 for Case I, and in Table 4 for Case II. From these tables, we see that the number of background events is significantly larger than signal events in both Case I and II, even after the selection cuts. In this case, the signal significance of Eq. (17) becomes , which we use to estimate the discovery potential of the dimuon process. We find that the in benchmark Case I (II) can be discovered in the dimuon process at with integrated luminosity of fb. We remark that in actual experimental searches the mass would be scanned over a certain range and the look-elsewhere effect would be included. The latter effect will reduce the signal significance we estimated, pushing the integrated luminosities required for discovery to higher values.

Iv Discovery potential

In this section, we first extend the results of the previous section to higher masses within the effective theory framework of the RH and couplings, then give the discovery potential of the in the and dimuon processes at the 14 TeV LHC. We then reinterpret these model-independent results based on the gauged model Altmannshofer:2014cfa (). We also discuss the sensitivity on the LH coupling, directly linked to the and anomalies.

iv.1 Model-independent results

In the previous section, we studied the and dimuon processes for and 200 GeV with benchmark values of the effective couplings and . In this subsection, we extend the analysis to higher masses up to 700 GeV and to arbitrary values of and , and illustrate the discovery potential at the 14 TeV LHC with 300 and 3000 fb integrated luminosities.

For and 200 GeV, we simply rescale the results of the previous section by and . For higher masses from 300 to 700 GeV, in steps of 100 GeV, we follow the same ways as the 200 GeV case for the generation of events and the application of cuts. In particular, we adopt the same dimuon-invariant mass cut of GeV. We choose a width such that % is satisfied for each mass. We assume .

We do not consider lower masses, as control of SM backgrounds becomes more difficult toward