Search for tZ' associated production induced by tcZ' couplings at the LHC
SSearch for tZ (cid:48) associated production induced by tcZ (cid:48) couplings at the LHC Wei-Shu Hou, Masaya Kohda, and Tanmoy Modak
Department of Physics, National Taiwan University, Taipei 10617, Taiwan
The P (cid:48) and R K anomalies, recently observed by the LHCb collaboration in B → K ( ∗ ) transitions,may indicate the existence of a new Z (cid:48) boson, which may arise from gauged L µ − L τ symmetry.Flavor-changing neutral current Z (cid:48) couplings, such as tcZ (cid:48) , can be induced by the presence of extravector-like quarks. In this paper we study the LHC signatures of the induced right-handed tcZ (cid:48) coupling that is inspired by, but not directly linked to, the B → K ( ∗ ) anomalies. The specific pro-cesses studied are cg → tZ (cid:48) and its conjugate process each followed by Z (cid:48) → µ + µ − . By constructingan effective theory for the tcZ (cid:48) coupling, we first explore in a model-independent way the discoverypotential of such a Z (cid:48) at the 14 TeV LHC with 300 and 3000 fb − integrated luminosities. Wethen reinterpret the model-independent results within the gauged L µ − L τ model. In connectionwith tcZ (cid:48) , the model also implies the existence of a flavor-conserving ccZ (cid:48) coupling, which can drivethe c ¯ c → Z (cid:48) → µ + µ − process. Our study shows that existing LHC results for dimuon resonancesearches already constrain the ccZ (cid:48) coupling, and that the Z (cid:48) can be discovered in either or bothof the cg → tZ (cid:48) and c ¯ c → Z (cid:48) processes. We further discuss the sensitivity to the left-handed tcZ (cid:48) coupling and find that the coupling values favored by the B → K ( ∗ ) anomalies lie slightly below theLHC discovery reach even with 3000 fb − . I. INTRODUCTION
Recent measurements performed by the LHCb exper-iment [1–3] exhibit anomalous B → K ( ∗ ) transitions.One is the measurement [1, 2] of angular observablesfor the B → K ∗ µ + µ − decay, which shows a discrep-ancy from the Standard Model (SM) prediction at 3.4 σ level, mainly driven by the P (cid:48) observable. In anothermeasurement [3] of B + → K + (cid:96) + (cid:96) − decays ( (cid:96) = e or µ ), LHCb found a further hint for lepton flavor uni-versality violation, namely a 2.6 σ deviation of the ob-servable R K ≡ B ( B + → K + µ + µ − ) / B ( B + → K + e + e − )from its SM value. These LHCb results are supportedby a recent Belle analysis [4], where the angular observ-ables were separately measured for the muon and electronmodes of B → K ∗ (cid:96) + (cid:96) − decays, and the muonic P (cid:48) wasfound to show the largest discrepancy (at 2.6 σ level) fromthe SM prediction. Although these anomalies can wellbe due to statistical fluctuations and/or hadronic uncer-tainties, it is interesting to investigate whether they canbe attributed to physics beyond the SM (BSM). Model-independent analyses by various groups have found thata BSM contribution to the Wilson coefficient C µ , associ-ated with the effective operator O µ = (¯ s L γ α b L )(¯ µγ α µ ),can explain both the P (cid:48) [5–9] and R K [10–12] anomalies,by a similar amount in BSM effect [13, 14].Given the B → K ( ∗ ) (cid:96) + (cid:96) − data suggest BSM effectsin the muon modes rather than the electron modes, aninteresting BSM candidate is a new gauge boson Z (cid:48) ofthe gauged L µ − L τ symmetry [15, 16], the differencebetween the muon and tau numbers. The Z (cid:48) boson cou-ples to the muon but not to the electron. In Ref. [17],an extension of the gauged L µ − L τ symmetry was con-structed for sake of introducing flavor-changing neutralcurrent (FCNC) Z (cid:48) couplings to the quark sector. In themodel, the SM quarks mix with new vector-like quarks,that are charged under the new gauge symmetry, lead-ing to effective FCNC couplings of Z (cid:48) with SM quarks. Among these, the left-handed (LH) bsZ (cid:48) coupling givesrise to C µ . The model provides a viable explanation forboth the P (cid:48) and R K anomalies.The gauged L µ − L τ model is, however, just one possi-bility among many options for a UV theory. Hence, themodel should be cross-checked by other ways, in particu-lar, by direct searches at colliders. LHC phenomenologywithin the minimal version of the gauged L µ − L τ modelhas been studied in Refs. [17–21], where Z (cid:48) is searchedin Z → µ + µ − Z (cid:48) ( → µ + µ − ). The search is sensitive to Z (cid:48) lighter than the Z boson and can probe the new gaugecoupling g (cid:48) as well as the Z (cid:48) mass m Z (cid:48) . On the otherhand, the extended model [17] gives effective Z (cid:48) couplingsto SM quarks, and these couplings could offer new waysto produce the Z (cid:48) boson at colliders. In particular, themodel predicts the existence of not only a LH tcZ (cid:48) cou-pling that is directly related to the LH bsZ (cid:48) coupling bySU(2) L gauge symmetry, but also a right-handed (RH) tcZ (cid:48) coupling. Refs. [17, 22] have studied t → cZ (cid:48) de-cay induced by these tcZ (cid:48) couplings. This decay can besearched for in the huge number of t ¯ t events at the LHC;however, it becomes kinematically forbidden if the Z (cid:48) mass is greater than the mass difference between the topand charm quarks, i.e. for m Z (cid:48) > m t − m c . In this paper we consider another unique produc-tion mechanism of the Z (cid:48) boson via the tcZ (cid:48) couplings,namely, cg → tZ (cid:48) . To be specific, we study the follow-ing processes at the 14 TeV LHC: pp → tZ (cid:48) (hereafterdenoted as the tZ (cid:48) process) and its conjugate pp → ¯ tZ (cid:48) (denoted as ¯ tZ (cid:48) ) process, each followed by Z (cid:48) → µ + µ − and t → bW + ( → (cid:96) + ν (cid:96) ) (or its conjugate). A model-independent study of such tcZ (cid:48) -induced processes at the For m Z (cid:48) > m t + m c , Z (cid:48) → tc [23–25] may happen, but itsbranching ratio is highly suppressed due to mixings between theheavy vector-like and SM quarks, in addition to rather low Z (cid:48) production cross sections in the model we consider. a r X i v : . [ h e p - ph ] S e p LHC has been performed in Ref. [26]. We improve thetreatment of SM background processes by including theones missed in the previous study and find that the ¯ tZ (cid:48) process is better suited for discovery than tZ (cid:48) due tolower background. Combining the two signal processes(also referred to as the tZ (cid:48) process collectively if thereis no confusion), we present first the model-independentdiscovery potential of the tZ (cid:48) process, aiming for thehigh-luminosity LHC (HL-LHC). In detailing our collideranalysis, we choose two representative Z (cid:48) mass values:just below (150 GeV) and above (200 GeV) the top-quarkmass. We then extend the latter case to Z (cid:48) masses upto 700 GeV, and reinterpret the model-independent re-sults for RH tcZ (cid:48) coupling within the gauged L µ − L τ model [17]. It turns out that the LH tcZ (cid:48) coupling im-plied by the B → K ( ∗ ) anomalies is rather small, andlies slightly beyond the discovery reach of the LHC evenwith 3000 fb − data. Therefore, we mainly focus on theRH tcZ (cid:48) coupling, which is hardly probed by B physics.Yet our results can be easily translated into the case ofthe LH tcZ (cid:48) coupling.The model implies a flavor-conserving effective ccZ (cid:48) coupling along with tcZ (cid:48) , while the effective Z (cid:48) couplingscontaining the up quark, i.e. uuZ (cid:48) , cuZ (cid:48) and tuZ (cid:48) , aresuppressed by D meson constraints. The ccZ (cid:48) couplingoffers another production channel for Z (cid:48) at the LHC, i.e. c ¯ c → Z (cid:48) → µ + µ − (hereafter denoted as the dimuonprocess). Analogous to the tZ (cid:48) case, we first performa model-independent study, which is then reinterpretedwithin the gauged L µ − L τ model. We find that the Z (cid:48) can be discovered in either or both of the tZ (cid:48) and dimuonprocesses. We show that the dimuon process has a bet-ter chance for discovery in most of the model parameterspace, while simultaneously measuring the tZ (cid:48) processcan confirm the flavor structure of the Z (cid:48) model.The paper is organized as follows. In Sec. II, we brieflyintroduce the gauged L µ − L τ model of Ref. [17] and givethe effective Lagrangian for tcZ (cid:48) and ccZ (cid:48) couplings. Wedetail our collider analysis in Sec. III, which is dividedinto two subsections: the ¯ tZ (cid:48) and tZ (cid:48) processes inducedby tcZ (cid:48) coupling in Sec. III A, and the dimuon processinduced by ccZ (cid:48) coupling in Sec. III B. In Sec. III A, wealso utilize an existing LHC data [29] to illustrate itsimplication for tcZ (cid:48) coupling. Three subsections are as-signed to Sec. IV. In Sec. IV A we present the model-independent discovery reaches for RH tcZ (cid:48) and ccZ (cid:48) cou-plings at the HL-LHC. In Sec. IV B, we reinterpret themodel-independent results within the gauged L µ − L τ model. In Sec. IV C we discuss collider sensitivities tothe LH tcZ (cid:48) coupling, which is directly linked to the B → K ( ∗ ) anomalies. We summarize and offer furtherdiscussions in Sec. V. A tuZ (cid:48) -induced process ug → tZ (cid:48) has also been studied with Z (cid:48) decays to quarks in Ref. [27] ( Z (cid:48) → tj ) and [28] ( Z (cid:48) → b ¯ b ). II. MODEL
Let us briefly introduce the gauged L µ − L τ modelof Ref. [17], where a new U(1) (cid:48) gauge group associatedwith L µ − L τ symmetry is introduced. The gauge andHiggs sectors of the U(1) (cid:48) consist of the gauge field Z (cid:48) andthe SM gauge singlet scalar field Φ, which carries unitcharge under the U(1) (cid:48) . The Φ field acquires a nonzerovacuum expectation value (VEV) (cid:104) Φ (cid:105) = v Φ / √
2, whichspontaneously breaks the U(1) (cid:48) and gives mass to Z (cid:48) , m Z (cid:48) = g (cid:48) v Φ . In the minimal model, the Z (cid:48) couples tothe SM fermions through L ⊃ − g (cid:48) (¯ µγ α µ + ¯ ν µL γ α ν µL − ¯ τ γ α τ − ¯ ν τL γ α ν τL ) Z (cid:48) α . (1)In Ref. [17], an extended model was constructed bythe addition of vector-like quarks Q L = ( U L , D L ), U R , D R and their chiral partners ˜ Q R = ( ˜ U R , ˜ D R ), ˜ U L , ˜ D L .The vector-like quarks carry +1 U(1) (cid:48) charge for Q ≡ Q L + ˜ Q R , and − U ≡ U R + ˜ U L and D ≡ D R + ˜ D L ,with gauge invariant mass terms given by −L mass = m Q ¯ QQ + m U ¯ U U + m D ¯ DD. (2)The vector-like quarks mix with SM quarks via Yukawainteractions given by −L mix = Φ (cid:88) i =1 (cid:16) ¯˜ U R Y Qui u iL + ¯˜ D R Y Qdi d iL (cid:17) + Φ † (cid:88) i =1 (cid:16) ¯˜ U L Y Uui u iR + ¯˜ D L Y Ddi d iR (cid:17) + h . c . (3)The SU(2) L symmetry relates the Yukawa couplings ofLH up-type quarks to those of the LH down-type quarks: Y Qu i = (cid:88) i =1 V ∗ u i d j Y Qd j , (4)where i = 1 , , V u i d j is an element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix.At energy scales well below the heavy vector-like quarkmasses, the above Yukawa couplings generate an effectiveLagrangian for FCNC Z (cid:48) couplings to SM quarks,∆ L eff = − Z (cid:48) α (cid:88) i,j =1 (cid:16) g Lu i u j ¯ u iL γ α u jL + g Ru i u j ¯ u iR γ α u jR + g Ld i d j ¯ d iL γ α d jL + g Rd i d j ¯ d iR γ α d jR (cid:17) , (5)with g Lu i u j = g (cid:48) Y ∗ Qu i Y Qu j v m Q , g Ru i u j = − g (cid:48) Y ∗ Uu i Y Uu j v m U ,g Ld i d j = g (cid:48) Y ∗ Qd i Y Qd j v m Q , g Rd i d j = − g (cid:48) Y ∗ Dd i Y Dd j v m D . (6) Z ′ < Φ > < Φ >U Ut R c R Z ′ < Φ > < Φ >c R c R U U
FIG. 1. Feynman diagrams that generate the effective RH tcZ (cid:48) [left] and ccZ (cid:48) [right] couplings.
Among these, the bsZ (cid:48) couplings g Lsb and g Rsb affect the b → sµ + µ − transitions. In particular, g Lsb gives a newcontribution to the Wilson coefficient of the operator(¯ s L γ α b L )(¯ µγ α µ ), given by∆ C µ = g Lsb g (cid:48) m Z (cid:48) , (7)which can explain both P (cid:48) and R K anomalies. If the LH bsZ (cid:48) coupling g Lsb exists, the SU(2) L relation in Eq. (4)would imply the existence of the LH tcZ (cid:48) coupling g Lct .Unfortunately, the strength of g Lct favored by the P (cid:48) and R K anomalies turns out to be below the discovery reachat HL-LHC, as we discuss in Sec. IV C.The model, however, predicts the existence of the RH tcZ (cid:48) coupling g Rct . The coupling is not directly linked to B → K ( ∗ ) transitions and is therefore hardly probed by B and K physics. But this coupling and its effect on topphysics should be viewed as on the same footing as the P (cid:48) and R K anomalies. Because there is no gauge anomaly,it could even happen that the Q and D quarks are ab-sent, or equivalently rather heavy, but the U quark couldcause effects in the top/charm sector that are analogousto the current P (cid:48) and R K “anomalies” in B decay, evenif the latter “anomalies” disappear with more data. Wetherefore focus on the LHC phenomenology of the RH tcZ (cid:48) coupling.The RH tcZ (cid:48) coupling is generated by the diagramshown in the left panel of Fig. 1 and is given by g Rct = (cid:0) g Rtc (cid:1) ∗ = − g (cid:48) Y ∗ Uc Y Ut v m U , (8)which is nonzero only if Y Uc (cid:54) = 0. One sees then that thediagram in the right panel of Fig. 1 generates RH ccZ (cid:48) coupling with g Rcc = − g (cid:48) | Y Uc | v m U . (9)This means that if the RH tcZ (cid:48) coupling exists, the RH ccZ (cid:48) coupling should also exist. We shall therefore alsoconsider the RH ccZ (cid:48) coupling for LHC phenomenology.In short, we consider the following effective Z (cid:48) cou-plings in the collider study:∆ L eff ⊃ − g Rcc ¯ c R γ α c R Z (cid:48) α − (cid:0) g Rct ¯ c R γ α t R Z (cid:48) α + h . c . (cid:1) , (10) with the model-dependent expressions of g Rct and g Rcc inEq. (8) and (9). But, our collider results can be straight-forwardly applied to the LH counterparts, g Lct and g Lcc .In principle, the model could also give the effectivecouplings containing the up quark, i.e. the RH uuZ (cid:48) , cuZ (cid:48) and tuZ (cid:48) couplings, if Y Uu is nonzero. In this case, g Ruc ∝ | Y ∗ Uu Y Uc | is constrained by D -meson mixing anddecays. We assume Y Uu = 0 for simplicity, while RH ttZ (cid:48) coupling is discussed in Sec. V. The presence of the U quark with nonzero Y Ut and Y Uc also leads to cou-plings of neutral SM bosons to the t → c currents. tcZ and tch couplings are induced at tree level, while tcγ and tcg couplings, forbidden at tree level due to gauge sym-metry, are generated at one-loop level. In Ref. [17], itis claimed that the branching ratios of rare top quarkdecays induced by these FCNC couplings with the SMbosons are suppressed over B ( t → cZ (cid:48) ) by roughly a loopfactor, with the latter assumed to be kinematically al-lowed.We shall consider the mass range of 150 GeV ≤ m Z (cid:48) ≤
700 GeV, where the branching ratios and total width for Z (cid:48) decay are nicely approximated by B ( Z (cid:48) → µ + µ − ) (cid:39) B ( Z (cid:48) → τ + τ − ) (cid:39) B ( Z (cid:48) → ν ¯ ν ) (cid:39) , Γ Z (cid:48) (cid:39) m Z (cid:48) πv (cid:39) .
75 GeV (cid:16) m Z (cid:48)
150 GeV (cid:17) (cid:18)
600 GeV v Φ (cid:19) . (11)In this mass range, dominant constraints on the ( m Z (cid:48) , g (cid:48) )plane comes from neutrino trident production and B s mixing [17]. These can be recast into constraints on theVEV of the Φ field v Φ (= m Z (cid:48) /g (cid:48) ), which can be summa-rized as [22]0 .
54 TeV (cid:46) v Φ (cid:46) . (cid:18) (34 TeV) − | ∆ C µ | (cid:19) , (12)regardless of the value of m Z (cid:48) . The lower limit comesfrom neutrino trident production [19] with 2 σ range ofthe CCFR result [30], while the upper limit is set by B s mixing [31] with BSM effects allowed within 15% andthe assumption of m Q (cid:46)
10 TeV. The upper limit be-comes tighter for larger m Q , e.g. v Φ (cid:46) . .
9) TeV × [(34 TeV) − / | ∆ C µ | ] for m Q = 20 (50) TeV.It is convenient to introduce the mixing parameters [22]between vector-like quark U and RH top or charm quarkdefined by δ Uq ≡ Y Uq v Φ √ m U , ( q = t, c ) . (13) The presence of the Z (cid:48) boson affects couplings of the Z boson tothe muon, tau and corresponding neutrinos via loop effect, whichare constrained by experimental data taken at the Z resonance.A study in Ref. [17] shows that combining results from the LEPand SLC [32] can provide competitive or slightly better limitsthan the CCFR for m Z (cid:48) (cid:38)
600 GeV. c c tZ ′ g c Z ′ t tg g Rct ( g Lct ) g Rct ( g Lct ) FIG. 2. Feynman diagrams contributing to pp → tZ (cid:48) . Small mixing parameters are assumed in obtaining theeffective couplings of Eq. (8) and (9). In the follow-ing analysis, we allow the mixing strengths up to theCabibbo angle, i.e. | δ Ut | , | δ Uc | ≤ λ (cid:39) .
23, and the RH tcZ (cid:48) coupling is constrained as | g Rct | = m Z (cid:48) v Φ | δ Uc || δ Ut | (cid:46) . × (cid:16) m Z (cid:48)
150 GeV (cid:17) (cid:18)
600 GeV v Φ (cid:19) . (14)If the Yukawa couplings are hierarchical, e.g., | Y Ut | (cid:29)| Y Uc | , this is further suppressed by | Y Uc /Y Ut | . A similarconstraint holds for g Rcc . These set the target ranges forthe LHC study.
III. SEARCH FOR Z (cid:48) AT THE LHCA. tZ (cid:48) and ¯ tZ (cid:48) processes The RH tcZ (cid:48) coupling in Eq. (10) generates the parton-level process cg → tZ (cid:48) through the Feynman diagramsin Fig. 2, leading to pp → tZ (cid:48) at the LHC. We assumesubsequent decays of Z (cid:48) → µ + µ − and t → bW + ( → ν (cid:96) (cid:96) + )with (cid:96) = e or µ . In this subsection, we study the FCNC-induced process pp → tZ (cid:48) → bν (cid:96) (cid:96) + µ + µ − ( tZ (cid:48) process)and its conjugate process pp → ¯ tZ (cid:48) → ¯ b ¯ ν (cid:96) (cid:96) − µ + µ − (¯ tZ (cid:48) process) at the 14 TeV LHC, and analyze the prospectof discovering such a Z (cid:48) boson. The RH tcZ (cid:48) couplingalso generates processes with an extra charm quark in thefinal states, i.e. gg → t ¯ cZ (cid:48) or ¯ tcZ (cid:48) . We will veto extrajets in the following analysis, but the latter processes cancontribute to the signal region if the charm jet escapesdetection. Hence, we also include the contributions from gg → t ¯ cZ (cid:48) / ¯ tcZ (cid:48) as a signal.For sake of our collider analysis, we take two bench-mark points for the effective theory defined by Eq. (10): • Case A: (cid:12)(cid:12) g Rct (cid:12)(cid:12) = 0 . m Z (cid:48) = 150 GeV; • Case B: (cid:12)(cid:12) g Rct (cid:12)(cid:12) = 0 . m Z (cid:48) = 200 GeV.In Case A, where m Z (cid:48) < m t , the t → cZ (cid:48) decay is kine-matically allowed with B ( t → cZ (cid:48) ) (cid:39) × − , and itcontributes to gg → t ¯ cZ (cid:48) / ¯ tcZ (cid:48) via gg → t ¯ t . On the otherhand, in Case B with m Z (cid:48) > m t , the t → cZ (cid:48) decay is kinematically forbidden. Moreover, behavior of eventdistributions for SM backgrounds is qualitatively differ-ent depending on whether the Z (cid:48) mass is below or abovethe top-quark mass. The coupling value is in the rangeof Eq. (14) implied by the gauged L µ − L τ model.The signal cross sections are proportional to | g Rct | ×B ( Z (cid:48) → µ + µ − ) if the Z (cid:48) width is narrow. We assume B ( Z (cid:48) → µ + µ − ) = 1 /
3, motivated by the gauged L µ − L τ model, and Γ Z (cid:48) (cid:46) Z (cid:48) branching ratios canbe taken into account by rescaling | g Rct | .A similar BSM process pp → tZ → (cid:96)νb(cid:96) + (cid:96) − inducedby tcZ couplings has been studied by the CMS exper-iment with 8 TeV data [29]. Our study closely fol-lows this analysis. There exist several non-negligible SMbackgrounds for the signal bν (cid:96) (cid:96) + µ + µ − ( tZ (cid:48) process) and¯ b ¯ ν (cid:96) (cid:96) − µ + µ − (¯ tZ (cid:48) process): • tZj and ¯ tZj backgrounds : The tZj backgroundpredominantly originates from u + b → t + Z + d or ¯ d + b → t + Z + ¯ u, (15)with smaller contributions from c - or ¯ s -initiatedprocesses, while ¯ tZj is generated by the charge-conjugate processes d + ¯ b → ¯ t + Z + u or ¯ u + ¯ b → ¯ t + Z + ¯ d. (16)The tZj cross section is larger than ¯ tZj , as theparton distribution function (PDF) of the u quarkis larger than the d quark in pp collisions [33]. Thus,the tZ (cid:48) process suffers from larger background. • t ¯ tZ background : t ¯ tZ becomes background forthe ¯ tZ (cid:48) ( tZ (cid:48) ) process, if the t (¯ t ) decays hadron-ically and the ¯ t ( t ) decays leptonically, i.e. t ¯ tZ → ( bq ¯ q (cid:48) )(¯ b ¯ ν (cid:96) (cid:96) − )( µ + µ − ) [(¯ bq (cid:48) ¯ q )( bν (cid:96) (cid:96) + )( µ + µ − )], withsome of the jets undetected. Indeed, t ¯ tZ consti-tutes a major part of the overall background. • t ¯ tW background : t ¯ tW is another leading sourceof background. If the t , ¯ t and W all decay lep-tonically and a jet goes undetected, it can givethe event topology with trilepton ( µ + µ − (cid:96) ), missingtransverse energy ( (cid:0) E T ) and b -tagged jet. The t ¯ tW + production cross section is larger than t ¯ tW − [34]for pp collisions. Thus, the tZ (cid:48) process again suf-fers larger background. For m Z (cid:48) > m t , a three-body decay t → cµ + µ − may still happenthrough an off-shell Z (cid:48) , and can contribute to the signal regionvia the t ¯ t events. In this case, the Z (cid:48) mass cannot be recon-structed from the dimuon invariant mass, but the top quark massreconstruction may help discriminate signal and backgrounds. InCase B with m Z (cid:48) = 200 GeV, such a contribution is very tiny andis not included in our analysis, although it could be importantfor a Z (cid:48) mass nearby the top quark mass. N o r m a li z ed d i s t r i bu t i on Invariant mass m µµ in GeV signal (m Z' = 150 GeV)signal (m Z' = 200 GeV)WZ+h.f. jets backgroundWZ+light jets backgroundt ‾ Zj backgroundtt ‾ Z backgroundtt ‾ W background
FIG. 3. Normalized distributions of the dimuon invariantmass for the ¯ tZ (cid:48) process in Case A ( m Z (cid:48) = 150 GeV) andB ( m Z (cid:48) = 200 GeV), and for the corresponding backgrounds,with close-to-default cuts in MadGraph. • W Z +heavy-flavor jets and
W Z +light jets :The
W Z or W γ ∗ production in association withheavy-flavor (h.f.) or light jets also contribute tobackground, if both W and Z/γ ∗ decay leptoni-cally and a jet gets misidentified as a b -tagged jet.Here, the h.f. jet refers to the c -jet. The rejectionfactors for the c -jet and the light jet are taken tobe 5 and 130, respectively [35]. The cross sectionfor W + Z +light jets is larger than W − Z +light jets,while the W ± Z production cross sections in asso-ciation with h.f.-jets are identical. This also giveslarger background to the tZ (cid:48) process than ¯ tZ (cid:48) .We do not consider processes such as t ¯ t , Drell-Yan(DY), W +jets, which could contribute to background ifone or two nonprompt leptons are produced and recon-structed. These backgrounds are not properly modeled insimulation and require data for better estimation. Theanalysis of the similar process pp → tZ by CMS [29]shows that such processes provide subdominant contri-butions to the total background. In the case of the tZ (cid:48) process, stricter cuts on the transverse momenta of themuons may reduce such contributions. These are beyondthe scope of this paper.The signal and background samples are generatedat leading order (LO) in the pp collision with centerof mass energy √ s = 14 TeV, by the Monte Carloevent generator MadGraph5 aMC@NLO [36], interfacedto PYTHIA 6.4 [37] for showering. To include inclu-sive contributions, we generate the matrix elements ofsignal and backgrounds with up to one additional jet inthe final state, followed by matrix element and partonshower merging with the MLM matching scheme [38].Due to computational limitation, we do not include pro-cesses with two or more additional jets in the final state.The event samples are finally fed into the fast detectorsimulator Delphes 3.3.3 [39] for inclusion of (ATLAS-based) detector effects. The effective theory defined byEqs. (1) and (10) is implemented by FeynRules 2.0 [40]. We adopt the PDF set CTEQ6L1 [41]. The LO ¯ tZj and t ¯ tZ cross sections are normalized to the next-to-leadingorder (NLO) ones by K -factors of 1.7 and 1.56, respec-tively [33]. For simplicity, we assume tZj has the sameNLO K -factor as ¯ tZj . The NLO K -factor for the t ¯ tW − ( t ¯ tW + ) process is taken to be 1.35 (1.27) [34]. The LOcross section for the W − Z +light jets background is nor-malized to the next-to-next-to-leading order (NNLO) oneby a factor of 2.07 [42]. We assume the same correctionfactor for W + Z +light jets and W ± Z +h.f. jets for sim-plicity.The signal cross sections for the tZ (cid:48) and ¯ tZ (cid:48) processesare identical, while some of the dominant (and the to-tal) background cross sections are smaller for the latterprocess. The ¯ tZ (cid:48) process is, therefore, better suited fordiscovering the Z (cid:48) . It turns out that combining the tZ (cid:48) and ¯ tZ (cid:48) processes can improve discovery potential. Inthe following, we primarily investigate the ¯ tZ (cid:48) process inshowing details of our analysis, and finally give combinedresults of the tZ (cid:48) and ¯ tZ (cid:48) processes.We present, in Fig. 3, the normalized event distribu-tions of the dimuon invariant mass m µµ for the ¯ tZ (cid:48) pro-cess in Case A and B, and for the corresponding back-ground contributions. The distributions are obtained byapplying default cuts in MadGraph with minor modifica-tions. In Figs. 4 and 5, the normalized p T distributionsare similarly shown for the leading and subleading muons,the third lepton and the b -tagged jet, respectively.We use two sets of cuts on the signal and backgroundprocesses as explained below. Pre-selection cuts : This set of cuts is used at the gen-erator level. The leading, subleading and third leptonsin an event are required to have minimum p T of 60 GeV,30 GeV and 15 GeV, respectively, in both Case A and B.The maximum pseudo-rapidity of all leptons are requiredto be | η (cid:96) | < .
5. The transverse momentum of jets arerequired to be greater than 20 GeV. The minimum sep-aration between the two oppositely-charged muons arerequired to be ∆
R > .
4. The rest of the cuts are set totheir default values in MadGraph.
Selection cuts : Utilizing the signal and background dis-tributions in Figs. 3, 4 and 5, we impose a further set ofcuts. Events are selected such that each should containthree (at least two muon type) leptons and at least one b -tagged jet. Jets are reconstructed by the anti- k T al-gorithm with radius parameter R = 0 .
5. Stricter cutson lepton transverse momenta are applied: the leadingmuon, subleading muon and third lepton in an event arerequired to have minimum p T of 60 (75) GeV, 30 (45)GeV and 20 (20) GeV, respectively, in Case A (B). Thethird lepton is assumed to arise from the top-quark decayaccompanied by missing transverse energy (cid:0) E T and b jet.We require that (cid:0) E T >
30 GeV and the reconstructed W boson mass m WT >
10 GeV. The leading b -tagged jet isrequired to have p T >
20 GeV. An event is rejected ifthe p T of the subleading jet or subleading b -tagged jet isgreater than 20 GeV. This veto significantly reduces the t ¯ tZ and t ¯ tW backgrounds, as both processes contain two N o r m a li z ed d i s t r i bu t i on p T of leading muon ( µ ) in GeV signal (m Z' = 150 GeV)signal (m Z' = 200 GeV)WZ+h.f. jets backgroundWZ+light jets backgroundt ‾ Zj backgroundtt ‾ Z backgroundtt ‾ W background N o r m a li z ed d i s t r i bu t i on p T of subleading muon ( µ ) in GeV signal (m Z' = 150 GeV)signal (m Z' = 200 GeV)WZ+h.f. jets backgroundWZ+light jets backgroundt ‾ Zj backgroundtt ‾ Z backgroundtt ‾ W background
FIG. 4. Normalized p T distributions for the leading [left] and subleading [right] muons, for the ¯ tZ (cid:48) process and its backgroundsas in Fig. 3. N o r m a li z ed d i s t r i bu t i on p T of third lepton (l ) in GeV signal (m Z' = 150 GeV)signal (m Z' = 200 GeV)WZ+h.f. jets backgroundWZ+light jets backgroundt ‾ Zj backgroundtt ‾ Z backgroundtt ‾ W background 0 0.02 0.04 0.06 0.08 0.1 20 40 60 80 100 120 140 160 180 200 N o r m a li z ed d i s t r i bu t i on p T of b-tagged jet in GeV signal (m Z' = 150 GeV)signal (m Z' = 200 GeV)WZ+h.f. jets backgroundWZ+light jets backgroundt ‾ Zj backgroundtt ‾ Z backgroundtt ‾ W background
FIG. 5. Normalized p T distributions for the third lepton [left] and b -tagged jet [right], for the ¯ tZ (cid:48) process and its backgroundsas in Fig. 3. b -jets from decay of the t and ¯ t . We will also analyze theimpact of removing such a jet veto shortly. We finallyapply the invariant mass cut | m µµ − m Z (cid:48) | <
15 GeVon two oppositely-charged muons. If an event containsthree muons, there are two ways to make a pair of twooppositely-charged muons. In such a case, we identifythe pair having the invariant mass m µµ closer to m Z (cid:48) asthe one coming from the Z (cid:48) decay, and impose the aboveinvariant mass cut on this pair.The effects of these two sets of cuts on the signal andbackground processes are illustrated in Table I for CaseA, and Table II for Case B. From these tables, we seethat the selection cuts significantly reduce the number ofbackground events ( B ), and the number of signal events( S ) becomes larger than B for the ¯ tZ (cid:48) process in bothCase A and B. The expected numbers of events with in-tegrated luminosity L = 300 fb − are S (cid:39)
26 (11) and B (cid:39)
17 (9) in Case A (B) for the ¯ tZ (cid:48) process. For com-parison, the effects of removing the veto on the sublead-ing jet are also shown in the tables. Without the jetveto, the signal events slightly increases as S (cid:39)
27 (12),but the background events increase more as B (cid:39)
27 (14)in Case A (B) for the ¯ tZ (cid:48) process. This illustrates the advantage of imposing the veto on the subleading jet.To estimate the signal significance, we use [43] Z = (cid:112) S + B ) ln (1 + S/B ) − S ] . (17)This becomes the well-known Z (cid:39) S/ √ B form for S (cid:28) B , but it does not hold in the current case. We require Z ≥ σ discovery. In Case A (B), therefore, the Z (cid:48) can be discovered at 5 σ in the ¯ tZ (cid:48) process with integratedluminosity L = 290 (730) fb − . Discovery in the tZ (cid:48) process would require more data: L = 410 (1060) fb − in Case A (B). Combining the tZ (cid:48) and ¯ tZ (cid:48) processes, onecould discover the Z (cid:48) with lower integrated luminosities: L = 180 (450) fb − in Case A (B). Therefore, betterdiscovery potential is attained with the combined tZ (cid:48) and¯ tZ (cid:48) processes. In the following, we will give results forthis combined case and also call it tZ (cid:48) process collectivelyif there is no confusion.Before closing this subsection, we briefly discuss theuse of some existing LHC data to search for the tcZ (cid:48) coupling. CMS [29] has studied the SM process pp → tZq in the three lepton (electron or muon) final statewith 8 TeV data, measuring the cross section of σ ( pp → tZq → (cid:96)νb(cid:96) + (cid:96) − q ) = 10 +8 − fb, which is consistent with SM Cuts Signal (Case A) ¯ tZj t ¯ tZ t ¯ tW − W − Z +light jets W − Z +h.f. jets Total BG Pre-selection cuts
Selection cuts (No jet veto)Selection cuts tZ (cid:48) and SM background processes in Case A ( m Z (cid:48) = 150GeV). The effect of the selection cuts without the subleading jet veto is also shown. (See text for details.) The second columngives the signal process, while the effects on individual backgrounds are tabulated in third to seventh columns. Cross sectionsfor backgrounds of the conjugate process tZ (cid:48) are given in parentheses, if they differ from the case of the ¯ tZ (cid:48) process: tZj (thirdcolumn), t ¯ tW + (fifth column) and W + Z +light jets (sixth column), where similar sets of cuts as the ¯ tZ (cid:48) process are applied.The last column shows the sum of all background cross sections.Cuts Signal (Case B) ¯ tZj t ¯ tZ t ¯ tW − W − Z +light jets W − Z +h.f. jets Total BG Pre-selection cuts
Selection cuts (No jet veto)Selection cuts m Z (cid:48) = 200 GeV). prediction of 8.2 fb. Taking this as background, CMS hasalso searched for the BSM process pp → tZ induced by tqZ ( q = u, c ) couplings; no evidence was found, resultingin the 95% CL upper limits of B ( t → uZ ) < . B ( t → cZ ) < . tZq production has beensearched for with the invariant mass cut of 76 GeV < m (cid:96)(cid:96) <
106 GeV on two oppositely-charged same-flavor leptons. Hence, the search is sensitive to the tZ (cid:48) process if the Z (cid:48) mass falls into this window. Themeasured cross section for the three muon channel is σ ( pp → tZq → µνbµ + µ − q ) = 5 +9 − fb, while the SMprediction is around 2.1 fb with an uncertainty of lessthan 10%. Following the same event selection cuts as theCMS analysis, we calculate the Z (cid:48) contribution to be 17.4fb ×| g Rct / . | for m Z (cid:48) = 95 GeV by MadGraph followedby showering and incorporating CMS based detector ef-fects. Symmetrizing the experimental uncertainties bynaive average and allowing the Z (cid:48) effect to enhance thecross section up to 2 σ of the measured value, we obtainan upper limit of | g Rct | (cid:46) .
05 for m Z (cid:48) ∼ m Z . B. Dimuon process: pp → Z (cid:48) + X → µ + µ − + X The flavor conserving ccZ (cid:48) coupling g Rcc in Eq. (10)gives rise to the parton-level process c ¯ c → Z (cid:48) . Thus, the Z (cid:48) can also be searched for via pp → Z (cid:48) + X → µ + µ − + X (dimuon process), where existing dimuon resonancesearch results at the LHC can already constrain | g Rcc | .The experimental searches do not veto extra activities X ;hence, we also include subdominant contributions from cg → cZ (cid:48) and gg → c ¯ cZ (cid:48) processes, induced by the RH ccZ (cid:48) coupling. In the following analysis, we adopt the 13TeV results by ATLAS [44] and CMS [45] (both basedon ∼
13 fb − data). The ATLAS analysis puts 95% CLupper limits on Z (cid:48) production cross section times Z (cid:48) → µ + µ − branching ratio for 150 GeV (cid:46) m Z (cid:48) (cid:46) R σ , which is defined as the ratio of dimuonproduction cross section via Z (cid:48) to the one via Z or γ ∗ (in the dimuon-invariant mass window of 60–120 GeV),for 400 GeV (cid:46) m Z (cid:48) (cid:46) R σ = σ ( pp → Z (cid:48) + X ) B ( Z (cid:48) → µ + µ − ) σ ( pp → Z + X ) B ( Z → µ + µ − ) , (18) N o r m a li z ed d i s t r i bu t i on Invariant mass m µµ in GeV signal (m Z' = 150 GeV)signal (m Z' = 200 GeV)Z/ γ * backgroundtt ‾ backgroundWt backgroundWW backgroundWZ backgroundZZ background FIG. 6. Normalized distributions of dimuon invariant massfor the dimuon process pp → Z (cid:48) + X → µ + µ − + X in CaseI ( m Z (cid:48) = 150 GeV), II ( m Z (cid:48) = 200 GeV) and for the back-grounds, with close to default cuts in MadGraph. N o r m a li z ed d i s t r i bu t i on p T of leading muon ( µ ) in GeV signal (m Z' = 150 GeV)signal (m Z' = 200 GeV)Z/ γ * backgroundtt ‾ backgroundWt backgroundWW backgroundWZ backgroundZZ background 0 0.05 0.1 0.15 0.2 0.25 0 50 100 150 200 250 N o r m a li z ed d i s t r i bu t i on p T of subleading muon ( µ ) in GeV signal (m Z' = 150 GeV)signal (m Z' = 200 GeV)Z/ γ * backgroundtt ‾ backgroundWt backgroundWW backgroundWZ backgroundZZ background FIG. 7. Normalized p T distributions for leading [left] and subleading [right] muons, for the dimuon process and its backgroundsas in Fig. 6. and convert them into the limits on σ ( pp → Z (cid:48) + X ) B ( Z (cid:48) → µ + µ − ) by multiplying the SM prediction of σ ( pp → Z + X ) B ( Z → µ + µ − ) = 1928 . • Case I: (cid:12)(cid:12) g Rcc (cid:12)(cid:12) = 0 . m Z (cid:48) = 150 GeV; • Case II: (cid:12)(cid:12) g Rcc (cid:12)(cid:12) = 0 . m Z (cid:48) = 200 GeV.We assume narrow Z (cid:48) width (Γ Z (cid:48) (cid:46) B ( Z (cid:48) → µ + µ − ) = 1 / Z / γ ∗ .Other nonnegligible contributions arise from t ¯ t , W t and
W W production, while contributions from
W Z and ZZ production are less significant. As in the tZ (cid:48) case, wedo not include backgrounds associated with nonpromptleptons.The signal and background samples for the dimuonprocess are generated in a similar way as in the previ-ous subsection, except the treatment of additional jets.In this case, we generate matrix elements of signal andbackgrounds with up to two additional jets, followed byshowering. The LO Z/γ ∗ (DY) cross section is normal-ized to the NNLO QCD+NLO EW one with LO photon-induced channel by the correction factor 1.27. The latteris obtained by FEWZ 3.1 [47] in the dimuon-invariantmass range of m µµ >
106 GeV. The LO t ¯ t and W t crosssections are normalized to the NNLO+NNLL ones by thefactors 1 .
84 [48] and 1 .
35 [49], respectively. As for
W W , W Z and ZZ , the LO cross sections are normalized to theNNLO QCD ones by the factors 1 .
98 [50], 2 .
07 [42] and1 .
74 [51], respectively.Normalized distributions of the dimuon invariant mass m µµ are given in Fig. 6 for the dimuon process in Case I, II and the backgrounds, obtained by close-to-defaultcuts in MadGraph. The p T distributions of the leadingand subleading muons are given in Fig. 7. We apply twosets of cuts on signal and background events as in theprevious subsection. Pre-selection cuts : The two muons in an event are re-quired to have transverse momenta p µT >
50 GeV, maxi-mum pseudo-rapidity | η | µ < .
5, with minimum separa-tion ∆
R > . Selection cuts : Events are selected such that eachevent contains two oppositely-charged muons with lead-ing muon transverse momentum p µ T >
60 (75) GeV, andsubleading muon p µ T >
55 (60) GeV in Case I (II). Weimpose an invariant-mass cut of | m µµ − m Z (cid:48) | <
15 GeVon the two muons in both Case I and II.The effects of the two sets of cuts on the signal andbackgrounds are tabulated in Table III for Case I, andin Table IV for Case II. From these tables, we see thatthe number of background events B is significantly largerthan signal events S in both Case I and II, even afterthe selection cuts. In this case, the signal significance ofEq. (17) becomes Z (cid:39) S/ √ B , which we use to estimatethe discovery potential of the dimuon process. We findthat the Z (cid:48) in benchmark Case I (II) can be discoveredin the dimuon process at 5 σ with integrated luminosityof L = 110 (170) fb − . We remark that in actual ex-perimental searches the Z (cid:48) mass would be scanned overa certain range and the look-elsewhere effect would beincluded. The latter effect will reduce the signal signifi-cance we estimated, pushing the integrated luminositiesrequired for discovery to higher values. IV. DISCOVERY POTENTIAL
In this section, we first extend the results of the previ-ous section to higher Z (cid:48) masses within the effective theoryframework of the RH tcZ (cid:48) and ccZ (cid:48) couplings, then givethe discovery potential of the Z (cid:48) in the tZ (cid:48) and dimuonprocesses at the 14 TeV LHC. We then reinterpret these Cuts Signal (Case I)
Z/γ ∗ t ¯ t W t W W W Z ZZ Total BG
Pre-selection cuts
Selection cuts m Z (cid:48) = 150 GeV).Cuts Signal (Case II) Z/γ ∗ t ¯ t W t W W W Z ZZ Total BG
Pre-selection cuts
Selection cuts m Z (cid:48) = 200 GeV).
200 300 400 500 600 70000.010.020.030.040.05 m Z ' ( GeV ) | g c t R |
200 300 400 500 600 70000.010.020.03 m Z ' ( GeV ) | g cc R | ℒ =
300 fb - ( σ ) ℒ =
300 fb - ( σ ) ℒ = - ( σ ) ℒ = - ( σ ) ATLAS limit ( % CL ) CMS limit ( % CL ) FIG. 8. [Left] 5 σ discovery reach in | g Rct | strength vs m Z (cid:48) for the combination of the pp → tZ (cid:48) and ¯ tZ (cid:48) processes at the 14TeV LHC with 300 fb − (upper red solid line) or 3000 fb − (lower blue solid line) data, and corresponding 3 σ reach shown bydashed lines. [Right] Same as left panel, but for | g Rcc | vs m Z (cid:48) for the dimuon process pp → Z (cid:48) + X → µ + µ − + X . The gray(semi-transparent blue) shaded region is excluded at 95% CL by the dimuon resonance search of ATLAS [44] (CMS [45]) with ∼
13 fb − data at the 13 TeV LHC. B ( Z (cid:48) → µ + µ − ) = 1 / Z (cid:48) /m Z (cid:48) (cid:46)
1% are assumed in both panels. model-independent results based on the gauged L µ − L τ model [17]. We also discuss the sensitivity on the LH tcZ (cid:48) coupling, directly linked to the P (cid:48) and R K anomalies. A. Model-independent results
In the previous section, we studied the tZ (cid:48) and dimuonprocesses for m Z (cid:48) = 150 and 200 GeV with benchmarkvalues of the effective couplings g Rct and g Rcc . In this sub-section, we extend the analysis to higher Z (cid:48) masses upto 700 GeV and to arbitrary values of g Rct and g Rcc , andillustrate the Z (cid:48) discovery potential at the 14 TeV LHCwith 300 and 3000 fb − integrated luminosities.For m Z (cid:48) = 150 and 200 GeV, we simply rescale the re-sults of the previous section by | g Rct | and | g Rcc | . For higher Z (cid:48) masses from 300 to 700 GeV, in steps of 100 GeV,we follow the same ways as the 200 GeV case for thegeneration of events and the application of cuts. In par-ticular, we adopt the same dimuon-invariant mass cut of | m µµ − m Z (cid:48) | <
15 GeV. We choose a Z (cid:48) width such thatΓ Z (cid:48) /m Z (cid:48) (cid:46)
1% is satisfied for each mass. We assume B ( Z (cid:48) → µ + µ − ) = 1 / Z (cid:48) masses, as control of SM backgrounds becomes more difficult toward m Z (cid:48) ∼ m Z .We leave this case for future analysis. We restrict theanalysis for the Z (cid:48) mass up to 700 GeV, as the S and B for the tZ (cid:48) process, obtained from Eq. (17) with 5 σ , getsmaller than O (1) beyond this mass. On the other hand,for the dimuon process, the S/B ratios become very lowfor masses beyond 700 GeV, and proper understandingof systematic uncertainties would be needed.The discovery reach for the effective couplings g Rct and g Rcc are shown in the left and right panels of Fig. 8, respec-tively, for 150 GeV ≤ m Z (cid:48) ≤
700 GeV. In the left panel,the upper red (lower blue) solid line represents the 5 σ dis-covery reach for the tZ (cid:48) process with 300 (3000) fb − inte-grated luminosity, while the corresponding dashed linesrepresent the 3 σ reach. In the right panel, the discov-ery reaches for the dimuon process are similarly shown;in this case, existing LHC results for dimuon resonancesearches already constrain g Rcc , as discussed in Sec. III B,and the 95% CL exclusion set by ATLAS [44] (CMS [45])with around 13 fb − of 13 TeV data is shown by the gray(semi-transparent blue) shaded region.We see that, at the 14 TeV LHC with 300 (3000) fb − data, the tZ (cid:48) process can be discovered for | g Rct | = 0 . m Z (cid:48) (cid:39)
490 (700) GeV; the dimuon process can0 - - Y Ut Y U c m Z ' =
150 GeV, v Φ =
600 GeV, m U = Y Ut Y U c m Z ' =
500 GeV, v Φ =
600 GeV, m U = δ Uc = λ , δ Ut = λ , t Z' + t Z' ( σ ) ,dimuon ( σ ) , ℬ ( t → c Z' ) ATLAS limit ( % CL ) CMS limit ( % CL ) FIG. 9. [Left] 5 σ discovery reach in Y Ut – Y Uc plane for m Z (cid:48) = 150 GeV with v Φ = 600 GeV (Γ Z (cid:48) (cid:39) .
74 GeV) and m U = 3 TeVwith 3000 fb − data: red solid line for the tZ (cid:48) process, and horizontal blue solid line for the dimuon process. Green dash-dot lines are contours for B ( t → cZ (cid:48) ) = 10 − and 10 − . The gray shaded region is the 95% CL exclusion by the ATLASdimuon resonance search [44]. The mixing parameter δ Ut ( δ Uc ) exceeds λ (cid:39) .
23 beyond the vertical dotted (horizontal dashed)line. [Right] Same as left panel, but for m Z (cid:48) = 500 GeV (Γ Z (cid:48) (cid:39)
27 GeV). The CMS [45] 95% CL exclusion, shown by thesemi-transparent blue shaded region, is overlaid on the gray shaded ATLAS exclusion and gives stronger constraint. be discovered for | g Rcc | = 0 .
01 up to m Z (cid:48) (cid:39)
460 (650)GeV. We also read the discovery reach for representa-tive Z (cid:48) mass values: | g Rct | (cid:38) . . | g Rcc | (cid:38) . . m Z (cid:48) = 150 GeV; | g Rct | (cid:38) .
026 (0 . | g Rcc | (cid:38) .
011 (0 . m Z (cid:48) = 500 GeV, with 300(3000) fb − data. The dimuon process can probe smaller Z (cid:48) couplings than the tZ (cid:48) process, but these two cou-plings are independent in general.The results in Fig. 8 are model independent, exceptfor the assumptions of narrow Z (cid:48) width and B ( Z (cid:48) → µ + µ − ) = 1 /
3, which are motivated by the gauged L µ − L τ model. For arbitrary B ( Z (cid:48) → µ + µ − ), the discovery reachcan be obtained from Fig. 8 by simply replacing | g Rct | → | g Rct | (cid:112) × B ( Z (cid:48) → µ + µ − ) , (19)with similar replacement for | g Rcc | . We remark that thesame results apply to the LH coupling g Lct ( g Lcc ) if the RHcoupling g Rct ( g Rcc ) is set to zero.
B. Interpretation in the gauged L µ − L τ model Both the tZ (cid:48) and dimuon processes can probe theeffective Z (cid:48) couplings implied by the gauged L µ − L τ model [17]. In this subsection, we reinterpret the model-independent results of the previous subsection within the gauged L µ − L τ model through the expressions for g Rct and g Rcc in Eqs. (8) and (9), and discuss the discoverypotential at the 14 TeV LHC with 3000 fb − data.From Eq. (14), one can observe that a smaller v Φ is better probed for fixed m Z (cid:48) and mixing parame-ters δ Ut and δ Uc . Applying the 5 σ discovery reach ofFig. 8, we find that the tZ (cid:48) process can be discoveredfor m Z (cid:48) = 150 (500) GeV with δ Ut = δ Uc = λ (cid:39) .
23 if v Φ (cid:46) . .
0) TeV; the dimuon process can be discoveredfor the same parameters if v Φ (cid:46) . .
2) TeV. In gen-eral, if the two Yukawa couplings have a same value, i.e. δ Uc /δ Ut = Y Uc /Y Ut = 1, we find the dimuon process tohave better discovery potential. If the Yukawa couplingsare hierarchical such that Y Uc /Y Ut = λ , the discoveryreach of the tZ (cid:48) process becomes v Φ (cid:46)
390 (470) GeV,which is better than the dimuon process v Φ (cid:46)
190 (220)GeV for m Z (cid:48) = 150 (500) GeV with δ Ut = λ . These v Φ values are, however, already excluded by the neu-trino trident production [See Eq. (12)]. Taking a milderhierarchy such that Y Uc /Y Ut (cid:39) .
47 (0 . v Φ (cid:46)
790 (990) GeV for m Z (cid:48) = 150 (500) GeV with δ Ut = λ . In this case, the two processes can probe theparameter region allowed by the neutrino trident produc-tion. For a slightly smaller Y Uc /Y Ut , the tZ (cid:48) process can In the gauged L µ − L τ model, a nonzero g Rct is accompaniedwith a nonzero g Rtt , leading to the gg → t ¯ tZ (cid:48) process. The lattercould contribute to the signal region of the tZ (cid:48) process despite theveto on extra jets. We, however, found that such a contributionis smaller than 1% for | g Rct | ∼ | g Rtt | . We ignore the effects fromthe t ¯ tZ (cid:48) production in the following analysis. m U ( TeV ) ℒ ( f b - ) m Z ' =
150 GeV, Y Uc = Y Ut = v Φ =
600 GeV m U ( TeV ) ℒ ( f b - ) m Z ' =
500 GeV, Y Uc = Y Ut = v Φ =
600 GeV t Z' + t Z' ( σ ) t Z' + t Z' ( σ ) δ Ut = λ FIG. 10. Integrated luminosities needed for 5 σ discovery (red solid lines) of the tZ (cid:48) process at the 14 TeV LHC as a functionof vector-like quark mass m U with Y Ut = 1 . Y Uc = 0 .
75 and v Φ = 600 GeV, for m Z (cid:48) = 150 GeV [left] and 500 GeV [right].The 3 σ reach is given by red dashed lines, while vertical dotted lines indicate the m U value below which the mixing parameter δ Ut exceeds λ (cid:39) . have better discovery potential than the dimuon processwith neutrino trident production constraint satisfied.The mixing parameters δ Ut and δ Uc , defined inEq. (13), depend on Y Ut , Y Uc , m U as well as v Φ (= m Z (cid:48) /g (cid:48) ). In Fig. 9, we show the impact of the Yukawacouplings on the discovery of the Z (cid:48) by taking v Φ = 600GeV, close to the lower end of Eq. (12), to maximize thediscovery reach. We also fix m U = 3 TeV, but differentchoices of m U will just give rescaled figures.In the left panel of Fig. 9, the discovery reach is given inthe Y Ut – Y Uc plane for m Z (cid:48) = 150 GeV. The red and hor-izontal blue solid lines represent the discovery reach forthe tZ (cid:48) and dimuon processes, respectively. We only con-sider the parameter region where the mixing parameterssatisfy | δ Ut | , | δ Uc | ≤ λ , shown by the vertical dotted andhorizontal dashed lines, respectively. The gray shadedregion represents the 95% CL exclusion by the dimuonresonance search of ATLAS [44]. The latter can alreadyprobe the parameter region that satisfies | δ Uc | ≤ λ . Thedimuon process can be discovered for Y Uc (cid:38) .
7, andgenerally has a larger discovery zone than the tZ (cid:48) pro-cess, in particular for small Y Ut . Interestingly, there isan overlap of discovery zones of the two processes for Y Ut (cid:38) . Y Uc (cid:38) .
7, and discovery might be possi-ble for both processes. This might be useful to probe theflavor structure of the model. As the Z (cid:48) is lighter thanthe top quark, t → cZ (cid:48) may happen. The green dash-dotcontours are plotted for B ( t → cZ (cid:48) ) = 10 − and 10 − .One can see that the tZ (cid:48) process can probe the regionwhere B ( t → cZ (cid:48) ) < − .In the right panel of Fig. 9, a similar plot is shown for m Z (cid:48) = 500 GeV. We again take v Φ = 600 GeV, whichgives the Z (cid:48) width of Γ Z (cid:48) (cid:39)
27 GeV. This is rather largeand the dimuon-invariant mass distribution would spread outside the invariant mass cut | m µµ − m Z (cid:48) | <
15 GeV, ap-plied in our collider study of the last subsection with thenarrow width assumption. Hence, the discovery reachesshown in the last subsection do not apply. In order toevaluate the discovery potential in this case, we regen-erated the signal events for the case of m Z (cid:48) = 500 GeVwith Γ Z (cid:48) (cid:39)
27 GeV and redid the cut-based analysis withthe same cuts as the narrow width case, but relaxing theinvariant mass cut to | m µµ − m Z (cid:48) | <
55 GeV. We thenobtain the model-independent discovery reach: | g Rct | (cid:38) . , | g Rcc | (cid:38) . , (Γ Z (cid:48) = 27 GeV) (20)at m Z (cid:48) = 500 GeV for 3000 fb − data. The result getsslightly worse due to increased number of SM backgroundevents. With these results, we plot in the right panel ofFig. 9 the discovery reach for m Z (cid:48) = 500 GeV. The qual-itative feature is similar to the m Z (cid:48) = 150 GeV case, butthe ATLAS constraint is now weaker than the CMS [45]95% CL limit on dimuon resonance search, as illustratedby the gray shaded region being overlaid by the semi-transparent blue shaded region.Fixing the Yukawa couplings, we can see the indi-rect discovery reach for the vector-like quark mass scale m U . For illustration, we take a hierarchical pattern ofthe Yukawa couplings Y Ut = 1 . Y Uc = 0 .
75 with v Φ = 600 GeV. In Fig. 10, integrated luminosities re-quired for the discovery of the tZ (cid:48) process are shown byred solid lines as a function of m U for m Z (cid:48) = 150 GeV[left] and 500 GeV [right]. The red dashed lines are forthe 3 σ reaches. The vertical dotted lines mark the min-imum value of m U satisfying the small mixing condition | δ Ut | ≤ λ . With 3000 fb − data, discovery of m U (cid:39) m Z (cid:48) cases.Similar plots for the dimuon process are given in Fig. 112 m U ( TeV ) ℒ ( f b - ) m Z ' =
150 GeV, Y Uc = v Φ =
600 GeV m U ( TeV ) ℒ ( f b - ) m Z ' =
500 GeV, Y Uc = v Φ =
600 GeV dimuon ( σ ) dimuon ( σ ) δ Uc = λ ATLAS limit ( % CL ) CMS limit ( % CL ) FIG. 11. Same as Fig. 10, but for the dimuon process with gray (semi-transparent blue) shaded region showing the 95% CLexclusion by the dimuon resonance search of ATLAS [44] (CMS [45]). for m Z (cid:48) = 150 GeV [left] and 500 GeV [right]. The gray(semi-transparent blue) shaded region shows the 95% CLexclusion by the dimuon resonance search of ATLAS [44](CMS [45]), as in Fig. 9. With 3000 fb − data, discov-ery is possible for m U (cid:38) m Z (cid:48) cases. Thedimuon resonance search limits push up m U , such thatdiscovery is possible for the m Z (cid:48) = 150 (500) GeV caseafter ∼
80 (110) fb − data is accumulated at the 14 TeVLHC, while 3 σ evidence can be made with ∼
30 (50) fb − data. This means discovery could be made with LHCRun 2 data, where experiments can easily change be-tween 13 and 14 TeV collision energies.Note that the ATLAS and CMS 95% CL limits as-sume narrow Z (cid:48) width, while our discovery reach for m Z (cid:48) = 500 GeV is estimated with rather large width(Γ Z (cid:48) (cid:39)
27 GeV). Note also that CMS gives stronger limitfor m Z (cid:48) = 500 GeV, in part due to the observed limitbeing better than expected by ∼ σ [45], while our dis-covery reach was estimated by inclusion of ATLAS-baseddetector effects. We have not taken into account system-atic uncertainties and backgrounds associated with non-prompt leptons. These would lead to uncertainties in theintegrated luminosity for discovery quoted above. C. Sensitivity for LH tcZ (cid:48) coupling motivated by P (cid:48) and R K anomalies So far we concentrated on the RH tcZ (cid:48) coupling, whichis inspired by, but not directly linked with, the P (cid:48) and R K anomalies. Let us now discuss the LH tcZ (cid:48) couplingthat is directly linked to these anomalies.The LH tcZ (cid:48) and bsZ (cid:48) couplings are related by theSU(2) L relation of Eq. (4): g Lct (cid:39) V cs V ∗ tb g Lsb + V cb V ∗ tb g Lbb ∼ g Lsb + λ g Lbb , where CKM suppressed terms are neglectedexcept the g Lbb term. Using Eq. (7), one can express the first term as g Lsb = m Z (cid:48) v Φ ∆ C µ . The upper and lowerlimits for v Φ in Eq. (12) then leads to0 . × − (cid:18) m Z (cid:48)
150 GeV (cid:19) (cid:18) | ∆ C µ | (34 TeV) − (cid:19) (cid:46) | g Lsb | (cid:46) . × − (cid:18) m Z (cid:48)
150 GeV (cid:19) . (21)Here, the best-fit value of ∆ C µ (cid:39) − (34 TeV) − froma recent global analysis [52] is used in the lower limit,while its dependence is canceled out in the upper limit.The latter is set by the B s mixing constraint with the Z (cid:48) effect allowed within 15%. The g Lbb term can be as largeas the g Lsb term if the Yukawa couplings are hierarchical,such that | g Lbb /g Lsb | = | Y Qb /Y Qs | ∼ λ − , which is indeedadvocated in Ref. [17] as a viable solution for the P (cid:48) anomaly. However, the relative sign of the two terms areopposite because ∆ C µ < g Lsb while g Lbb is positive by definition [See Eq. (6)]. Hence a large g Lbb tends to suppress g Lct .We thus conclude that | g Lct | can not be larger than | g Lsb | .The latter is constrained by Eq. (21). We then obtain theupper limits on the LH tcZ (cid:48) coupling: (cid:12)(cid:12) g Lct (cid:12)(cid:12) max ∼ × − ( m Z (cid:48) = 150 GeV) , × − ( m Z (cid:48) = 500 GeV) , × − ( m Z (cid:48) = 700 GeV) . (22)If we set g Rct = 0, we can directly apply the discoveryreach of Fig. 8 [left] to the LH coupling g Lct . We findthat, for the P (cid:48) and R K motivated case, the maximallyallowed values of | g Lct | are beyond (i.e. smaller than) thediscovery reach with 3000 fb − data, by a factor of 5–10.One cannot even attain 3 σ evidence for the | g Lct | valuesgiven in Eq. (22).3We remark that we have estimated the signal tZ (cid:48) events at LO and have not taken into account QCD cor-rections, which may enhance the number of signal events.Moreover, the discovery reach might be improved by com-bining ATLAS and CMS data.We note in passing that the LH ccZ (cid:48) coupling is alsorelated to the LH bsZ (cid:48) coupling, but in a more compli-cated way: g Lcc (cid:39) V cs V ∗ cb g Lsb ) + | V cs | g Lss + | V cb | g Lbb ,where terms containing the d quark are neglected withthe choice of Y Qd (cid:39) K and B d meson mixingconstraints. Choosing different Yukawa coupling hierar-chies with m Z (cid:48) = 150 GeV, we find the following upperlimits on | g Lcc | from the B s mixing constraint on v Φ andthe small mixing conditions | δ Qq | ≤ λ [ q = s, c, b, t , de-fined as in Eq. (13)]: | g Lcc | (cid:46) × − for Y Qb = 1, Y Qs = − m Q = 24 TeV; | g Lcc | (cid:46) × − for Y Qb = 1, Y Qs = − λ and m Q = 5 . | g Lcc | (cid:46) × − for Y Qb = λ , Y Qs = − m Q = 5 . m Q are chosen such that the best-fit value of∆ C µ (cid:39) − (34 TeV) − is realized. From the right panel ofFig. 8, we read the discovery reach of the dimuon processas | g Lcc | (cid:38) . × − for m Z (cid:48) = 150 GeV with 3000 fb − data. Interestingly, the third case with a skewed Yukawahierarchy | Y Qb /Y Qs | = λ could be discovered, as long as v Φ (cid:38) V. SUMMARY AND DISCUSSION
The P (cid:48) and R K anomalies in B → K ( ∗ ) transitionsmay indicate the existence of a new Z (cid:48) boson with FCNCcouplings. In this paper, we studied the LHC signaturesof the RH tcZ (cid:48) coupling ( g Rct ) that is inspired by, but notdirectly linked to, the B → K ( ∗ ) anomalies. We first ex-amined the tcZ (cid:48) -induced process cg → tZ (cid:48) → bν (cid:96) (cid:96) + µ + µ − ( tZ (cid:48) process) and its conjugate process (¯ tZ (cid:48) process)at the 14 TeV LHC within the effective theory frame-work. We then discussed the implications in a specific Z (cid:48) model, namely the gauged L µ − L τ model of Ref. [17].In this model, the RH tcZ (cid:48) coupling is induced by mix-ings of the SU(2) L -singlet vector-like quark U with thetop and charm quarks, which also induce the flavor-conserving ccZ (cid:48) coupling. We thus also considered the c ¯ c → Z (cid:48) → µ + µ − (dimuon process) at the LHC. Weperformed a collider study taking into account detectoreffects and major SM background processes.We find that the ¯ tZ (cid:48) process has a better chance fordiscovery than the tZ (cid:48) process because of smaller back-grounds, and the combination of the two processes, whichwe also call the tZ (cid:48) process collectively, can further en-hance discovery potential. The tZ (cid:48) process can be discov-ered with 3000 fb − data for the Z (cid:48) masses in 150–700GeV, with | g Rct | = O (0 .
01) and B ( Z (cid:48) → µ + µ − ) = 1 / | g Rct | (cid:38) m Z (cid:48) = 150 (500) GeV.Reinterpreted within the gauged L µ − L τ model, theseresults imply that one can discover the Z (cid:48) if the mixingparameters of the vector-like quark U with the top andcharm quarks, δ Ut and δ Uc , are O (0 .
1) and the VEV of the exotic Higgs is not too large, i.e. v Φ (cid:46) tZ (cid:48) and dimuon processes are correlated, withthe dimuon process having better discovery potential if | δ Ut | ∼ | δ Uc | , starting with LHC Run 2 data. But if themixings are hierarchical, such that | δ Uc /δ Ut | (cid:46) .
4, the tZ (cid:48) process would have better discovery potential. How-ever, g Rct tends to be suppressed in this case, and discoveryis not possible at the HL-LHC if | δ Uc /δ Ut | (cid:46) λ (cid:39) . | δ Ut | ≤ λ for v Φ values allowed by the neutrinotrident production. We illustrated the discovery zonesin the model imposing the existing ATLAS and CMSdimuon resonance search constraints, and showed thatthere exist interesting parameter regions where both the tZ (cid:48) and dimuon processes can be discovered. If this is thecase, the simultaneous measurement of the two processescan uncover the flavor structure of the model.We also discussed the sensitivity for the LH tcZ (cid:48) cou-pling g Lct that is directly linked to the B → K ( ∗ ) anoma-lies. We first identified the range of the LH bsZ (cid:48) cou-pling g Lsb favored by the b → s(cid:96) + (cid:96) − transition data, andthen obtained the upper limits on | g Lct | using SU(2) L symmetry. We find that the | g Lct | values implied by the B → K ( ∗ ) anomalies are beyond the discovery reach ofthe tZ (cid:48) process at the HL-LHC. However, the sensitiv-ity might be improved by inclusion of QCD correctionsto the signal cross section, and/or by combining ATLASand CMS data.The gauged L µ − L τ model further implies flavor-conserving ttZ (cid:48) couplings, which lead to the pp → t ¯ tZ (cid:48) production process at the LHC. This process may providenot only another discovery channel of the Z (cid:48) , but alsouseful information on the flavor structure of the model.In particular, the three production modes, namely tZ (cid:48) ,dimuon and t ¯ tZ (cid:48) processes can be correlated by the de-pendence on the two Yukawa couplings Y Ut and Y Uc . Wenote that the ccZ (cid:48) couplings can be also probed throughthe cg → cZ (cid:48) process, if one has efficient charm tagging.These will be studied elsewhere.In this paper, we focused on collider signatures of the Z (cid:48) couplings to the top and charm quarks, but discoveryof the Z (cid:48) may also come from the couplings to the down-type quark sector. In particular, the gauged L µ − L τ model predicts a nonzero LH bbZ (cid:48) coupling g Lbb if the LH bsZ (cid:48) coupling exists. The bbZ (cid:48) coupling induces the pro-cess b ¯ b → Z (cid:48) → µ + µ − and can be searched in the similarway as the ccZ (cid:48) coupling at the LHC. Taking for illustra-tion m Z (cid:48) = 200 GeV, v Φ = 1 . Y Qb = 1, Y Qs = − λ and m Q = 24 TeV, giving ∆ C µ = − (34 TeV) − for the B → K ( ∗ ) anomalies, we find g Lbb (cid:39) × − and theinduced Z (cid:48) production cross section of σ ( pp → Z (cid:48) ) (cid:39) B ( Z (cid:48) → µ + µ − ) (cid:39) / ccZ (cid:48) -induced dimuon process,we obtain the cross section of σ ( pp → Z (cid:48) → µ + µ − ) (cid:39) Z (cid:48) can be discovered with ∼ − integrated luminosity. The b ¯ b → Z (cid:48) production process4has also been studied in other Z (cid:48) models constructed forthe B → K ( ∗ ) anomalies [53, 54].We emphasize that the RH tcZ (cid:48) coupling cannot beconstrained well by B and K physics, but is on similarfooting as the current B → K ( ∗ ) anomalies. In par-ticular, the coupling may exist even if the P (cid:48) and R K anomalies evaporate in the future. Hence, it is impor-tant to explore the RH tcZ (cid:48) coupling regardless of thefate of the B → K ( ∗ ) anomalies, with potential of discov-ering a new Z (cid:48) gauge boson as a dimuon resonance withweaker and FCNC quark couplings. Our study thereforeillustrates a unique role of top physics in the flavor pro-gram. If discovery is made at the LHC, one would then need to probe the handedness of the coupling via angu-lar distributions, while c ¯ c → Z (cid:48) discovery (and maybealso cg → cZ (cid:48) and t ¯ tZ (cid:48) ) would provide complementaryinformation, opening up a rich program. ACKNOWLEDGMENTS
We thank Y. Chao for discussions. WSH is supportedby grants MOST 104-2112-M-002-017-MY2, MOST 105-2112-M-002-018 and NTU 105R8965, MK is supportedby NTU-105R104022 and NTU-G029927, and TM is sup-ported by MOST-104-2112-M-002-017-MY2. [1] R. Aaij et al. [LHCb Collaboration], Phys. Rev. Lett. , 191801 (2013) [arXiv:1308.1707 [hep-ex]].[2] R. Aaij et al. [LHCb Collaboration], JHEP , 104(2016) [arXiv:1512.04442 [hep-ex]].[3] R. Aaij et al. [LHCb Collaboration], Phys. Rev. Lett. , 151601 (2014) [arXiv:1406.6482 [hep-ex]].[4] S. Wehle et al. [Belle Collaboration], Phys.Rev. Lett. , no. 11, 111801 (2017)doi:10.1103/PhysRevLett.118.111801 [arXiv:1612.05014[hep-ex]].[5] S. Descotes-Genon, J. Matias and J. Virto, Phys. Rev. D , 074002 (2013) [arXiv:1307.5683 [hep-ph]].[6] W. Altmannshofer and D.M. Straub, Eur. Phys. J. C ,2646 (2013) [arXiv:1308.1501 [hep-ph]].[7] F. Beaujean, C. Bobeth and D. van Dyk, Eur. Phys. J.C , 2897 (2014) Erratum: [Eur. Phys. J. C , 3179(2014)] [arXiv:1310.2478 [hep-ph]].[8] R.R. Horgan, Z. Liu, S. Meinel and M. Wingate, Phys.Rev. Lett. , 212003 (2014) [arXiv:1310.3887 [hep-ph]].[9] T. Hurth and F. Mahmoudi, JHEP , 097 (2014)[arXiv:1312.5267 [hep-ph]].[10] R. Alonso, B. Grinstein and J. Martin Camalich, Phys.Rev. Lett. , 241802 (2014) [arXiv:1407.7044 [hep-ph]].[11] G. Hiller and M. Schmaltz, Phys. Rev. D , 054014(2014) [arXiv:1408.1627 [hep-ph]].[12] D. Ghosh, M. Nardecchia and S.A. Renner, JHEP ,131 (2014) [arXiv:1408.4097 [hep-ph]].[13] T. Hurth, F. Mahmoudi and S. Neshatpour, JHEP ,053 (2014) [arXiv:1410.4545 [hep-ph]].[14] W. Altmannshofer and D.M. Straub, Eur. Phys. J. C ,382 (2015) [arXiv:1411.3161 [hep-ph]].[15] X.G. He, G.C. Joshi, H. Lew and R.R. Volkas, Phys. Rev.D , R22 (1991).[16] R. Foot, Mod. Phys. Lett. A , 527 (1991).[17] W. Altmannshofer, S. Gori, M. Pospelov and I. Yavin,Phys. Rev. D , 095033 (2014) [arXiv:1403.1269 [hep-ph]].[18] K. Harigaya, T. Igari, M.M. Nojiri, M. Takeuchi andK. Tobe, JHEP , 105 (2014) [arXiv:1311.0870 [hep-ph]].[19] W. Altmannshofer, S. Gori, M. Pospelov and I. Yavin,Phys. Rev. Lett. , 091801 (2014) [arXiv:1406.2332[hep-ph]]. [20] F. del Aguila, M. Chala, J. Santiago and Y. Yamamoto,JHEP , 059 (2015) [arXiv:1411.7394 [hep-ph]].[21] F. Elahi and A. Martin, Phys. Rev. D , 015022 (2016)[arXiv:1511.04107 [hep-ph]].[22] K. Fuyuto, W.-S. Hou and M. Kohda, Phys. Rev. D ,054021 (2016) [arXiv:1512.09026 [hep-ph]].[23] A. Arhrib, K. Cheung, C.-W. Chiang and T.-C. Yuan,Phys. Rev. D , 075015 (2006) [hep-ph/0602175].[24] O. Cakir, I. T. Cakir, A. Senol and A.T. Tasci, Eur. Phys.J. C , 295 (2010) [arXiv:1003.3156 [hep-ph]].[25] J.I. Aranda, F. Ramirez-Zavaleta, J.J. Toscanoand E.S. Tututi, J. Phys. G , 045006 (2011)[arXiv:1007.3326 [hep-ph]].[26] S.K. Gupta and G. Valencia, Phys. Rev. D , 035017(2010) [arXiv:1005.4578 [hep-ph]].[27] M.I. Gresham, I.W. Kim and K.M. Zurek, Phys. Rev. D , 034025 (2011) [arXiv:1102.0018 [hep-ph]].[28] J.N. Ng and P.T. Winslow, JHEP , 140 (2012)[arXiv:1110.5630 [hep-ph]].[29] A.M. Sirunyan et al. [CMS Collaboration],arXiv:1702.01404 [hep-ex].[30] S.R. Mishra et al. [CCFR Collaboration], Phys. Rev.Lett. , 3117 (1991).[31] A. Crivellin, G. D’Ambrosio and J. Heeck, Phys. Rev.Lett. , 151801 (2015) [arXiv:1501.00993 [hep-ph]].[32] S. Schael et al. [ALEPH, DELPHI, L3, OPAL, SLD, LEPElectroweak Working Group, SLD Electroweak Group,and SLD Heavy Flavour Group Collaboration], Phys.Rept. , 257 (2006) [hep-ex/0509008].[33] J. Campbell, R.K. Ellis and R. R¨ontsch, Phys. Rev. D , 114006 (2013) [arXiv:1302.3856 [hep-ph]].[34] J.M. Campbell and R.K. Ellis, JHEP , 052 (2012)[arXiv:1204.5678 [hep-ph]].[35] ATLAS collaboration, ATLAS-CONF-2014-058.[36] J. Alwall et al. , JHEP , 079 (2014) [arXiv:1405.0301[hep-ph]].[37] T. Sj¨ostrand, L. L¨onnblad, S. Mrenna and P. Z. Skands,hep-ph/0308153.[38] J. Alwall et al. , Eur. Phys. J. C , 473 (2008)[arXiv:0706.2569 [hep-ph]].[39] J. de Favereau et al. [DELPHES 3 Collaboration], JHEP , 057 (2014) [arXiv:1307.6346 [hep-ex]].[40] A. Alloul, N.D. Christensen, C. Degrande, C. Duhr andB. Fuks, Comput. Phys. Commun. , 2250 (2014)[arXiv:1310.1921 [hep-ph]]. [41] J. Pumplin, D.R. Stump, J. Huston, H.-L. Lai,P.M. Nadolsky and W.-K. Tung, JHEP , 012 (2002)[hep-ph/0201195].[42] M. Grazzini, S. Kallweit, D. Rathlev and M. Wiesemann,Phys. Lett. B , 179 (2016) [arXiv:1604.08576 [hep-ph]].[43] G. Cowan, K. Cranmer, E. Gross and O. Vitells, Eur.Phys. J. C , 1 (2011) Erratum: [Eur. Phys. J. C ,2501 (2013)] [arXiv:1007.1727 [physics.data-an]].[44] ATLAS Collaboration, ATLAS-CONF-2016-045.[45] CMS Collaboration, CMS-PAS-EXO-16-031.[46] CMS Collaboration, CMS-PAS-EXO-15-005.[47] Y. Li and F. Petriello, Phys. Rev. D , 094034 (2012)[arXiv:1208.5967 [hep-ph]].[48] ATLAS-CMS recommended predictions for top-quark-pair cross sections: https://twiki.cern.ch/twiki/ bin/view/LHCPhysics/TtbarNNLO [49] N. Kidonakis, Phys. Rev. D , 054018 (2010)[arXiv:1005.4451 [hep-ph]].[50] T. Gehrmann et al. , Phys. Rev. Lett. , 212001 (2014)[arXiv:1408.5243 [hep-ph]].[51] F. Cascioli et al. , Phys. Lett. B , 311 (2014)[arXiv:1405.2219 [hep-ph]].[52] S. Descotes-Genon, L. Hofer, J. Matias and J. Virto,JHEP , 092 (2016) [arXiv:1510.04239 [hep-ph]].[53] S.M. Boucenna, A. Celis, J. Fuentes-Martin, A. Vicenteand J. Virto, JHEP1612