G221 Interpretations of the Diboson and Wh Excesses
UUTTG-11-15, MI-TH-1522, CETUP2015-007
G221 Interpretations of the Diboson and
W h
Excesses
Yu Gao, Tathagata Ghosh, Kuver Sinha, and Jiang-Hao Yu Mitchell Institute for Fundamental Physics and Astronomy,Department of Physics and Astronomy,Texas A&M University, College Station, TX 77843-4242, USA Department of Physics, Syracuse University, Syracuse, NY 13244, USA Theory Group, Department of Physics and Texas Cosmology Center,The University of Texas at Austin, Austin, TX 78712, USA (Dated: July 24, 2018)
Abstract
Based on an SU (2) × SU (2) × U (1) effective theory framework (aka G
221 models), we investigatea leptophobic SU (2) L × SU (2) R × U (1) B − L model, in which the right-handed W (cid:48) boson has themass of around 2 TeV, and predominantly couples to the standard model quarks and the gauge-Higgs sector. This model could explain the resonant excesses near 2 TeV reported by the ATLAScollaboration in the W Z production decaying into hadronic final states, and by the CMS collabo-ration in the
W h channel decaying into b ¯ b(cid:96)ν and dijet final state. After imposing the constraintsfrom the electroweak precision and current LHC data, we find that to explain the three excesses in W Z , W h and dijet channels, the SU (2) R coupling strength g R favors the range of 0 . ∼ .
68. Inthis model, given a benchmark 2 TeV W (cid:48) mass, the Z (cid:48) mass is predicted to be around 2 . e + e − event recently observed at CMS. A 3 ∼ a r X i v : . [ h e p - ph ] N ov . INTRODUCTION The ATLAS collaboration has recently reported excesses in searches for massive reso-nances decaying into a pair of weak gauge bosons [1]. The anomalies have been observed inall hadronic final states in the
W Z , W W , and ZZ channels at around 2 TeV invariant massof the boson pair. The analysis has been done with 20.3 fb − of data at 8 TeV, with localsignificances of 3.4 σ , 2.6 σ , and 2.9 σ in the W Z , W W , and ZZ channels, respectively.Several groups [2] have studied this excess. Similar moderate diboson excesses have alsobeen reported from the CMS [3, 4] experiment. Intriguingly, the CMS experiment reportedaround 2 σ excesses slightly below 2 TeV in the dijet resonance channel [5] and eνb ¯ b [6]channel which may arise from a W (cid:48) → W h process.A natural question to ask is whether a single resonance whose peak is around 2 TeVand width less than 100 GeV can nicely fit all the excesses. The tagging selections used inthe analysis do not give a completely clear answer - around 20% of the events are sharedamong the three channels [1], leading to the possibility of cross contamination. While asingle resonance is definitely the simplest option, a more realistic possibility is that severalresonances are present at the 2 TeV mass scale, where new physics presumably kicks in.The most natural scenario is then that these resonances are associated with the spontaneousbreaking of extra gauge groups at that scale. Scalars in the extra sectors, for example, wouldneed significant mixing with the Standard Model Higgs to be reproduced at the LHC andgive the observed excesses. The other option is that the resonances are gauge bosons of thenew gauge groups, which acquire mass through a Higgs mechanism in the extra sector. Thisis the avenue we pursue in this paper.There are several immediate caveats when one considers this possibility. Firstly, extragauge bosons will decay to the diboson channels through their mixing with the SM W and Z . Such mixing is constrained by electroweak (EW) precision tests, necessitating thebalance between obtaining the correct cross-section to fit the excesses and accommodatingEW constraints. The second caveat is that the SM fermions can be charged under the extragauge group and let the exotic gauge bosons decay into SM fermionic states. One then hasto be careful about dilepton and dijet constraints for such a resonance, with the possibilitythat the former is evaded by working in the context of a leptophobic model. Thirdly, theexcess in the ZZ channel cannot be accounted for only with exotic gauge bosons. Thismakes such scenarios falsifiable in the near future; the persistence of the excess in the ZZ channel would indicate extra physics at the 2 TeV scale, apart from the exotic gauge bosonsconsidered here.The purpose of this paper is to investigate exotic gauge bosons W (cid:48) as a candidate forthe 2 TeV resonance in the light of the caveats mentioned above. In extended gauge groupmodels, usually both the W (cid:48) boson and the Z (cid:48) bosons exists. We would like to focus on thelow energy effective theory of extended gauge group models , in which all the heavy particlesother than the W (cid:48) and Z (cid:48) bosons decouple. This has been studied in the SU (2) × SU (2) × U (1)framework, as the so-called G221 models [7, 8]. The G
221 models are the minimal extensionof the SM gauge group to incorporate both the W (cid:48) and Z (cid:48) bosons. Various models havebeen considered under this broad umbrella: left-right (LR) [15–17], lepto-phobic (LP), hadro-2hobic (HP), fermio-phobic (FP) [7, 8, 18–20], un-unified (UU) [21, 22], and non-universal(NU) [23–27].As an explicit model, we will focus on the leptophobic (LP) G221 model with two stagesymmetry breaking. In the first stage breaking, a doublet Higgs (LPD) or a triplet Higgs(LPT) could be introduced. In this model, the W (cid:48) boson couplings to the SM leptons arehighly suppressed. Therefore, this leptophoic model could escape the tight constraints fromlepton plus missing energy searches. At the same time, the W (cid:48) boson couplings to the SMquarks and gauge bosons are similar to the typical left-right model. Therefore, the W (cid:48) canbe produced at the LHC with potentially large production rate, and mainly decay to thedijet, t ¯ b , W Z and
W h final states, instead of the (cid:96)ν final states. We will explain the resonantexcesses near 2 TeV reported by the ATLAS collaboration in the
W Z production decayinginto hadronic final states, and by the CMS collaboration in the
W h channel decaying into b ¯ b(cid:96)ν and dijet final state. Given the W (cid:48) mass at 2 TeV and expected signal rate on the W Z final state, the model parameters are fixed. Therefore, we predict the Z (cid:48) mass and couplingsto the SM particles. For the LPD model, the Z (cid:48) mass is predicted to favor 2 ∼ ∼ W (cid:48) boson which is totally leptophobic,the Z (cid:48) will couple to the SM leptons due to the extra U (1) charge. The CMS experimenthas recently reported a 2.9 e + e − event [28] that can be well explained by the Z (cid:48) resonancein both LPD and LPT models. Even if only previous no-signal data in dilepton searchesare considered as a constraint m Z (cid:48) < . ∼ . Z (cid:48) mass prediction. We also include the electroweak precision constraints inthe parameter space. Although some parameter region of the LPD model might be highlyconstrainted due to the dilepton final states, the LPT model could satisfy all the constraintsand explain the W Z , W h and dijet excesses.The rest of the paper is structured as follows. In Section II, we describe the model indetail. In Section III, we describe the constraints on our model coming from electroweakprecision tests. In Section IV, we describe our main results and predictions. We end withour conclusions.
II. THE SU (2) × SU (2) × U (1) MODEL
As mentioned in the introduction, we will be explicitly working in the context of the G G
221 models are the minimal extension of theSM gauge group to incorporate both the W (cid:48) and Z (cid:48) bosons. This model can be treated as thelow energy effective theory of extended gauge group models with all the heavy particles otherthan the W (cid:48) and Z (cid:48) bosons decouple. The gauge structure is SU (2) × SU (2) × U (1). There aretwo kinds of breaking patterns: the SU (2) ⊗ U (1) breaking down to U (1) Y (breaking patternI, where the W (cid:48) mass is smaller than the Z (cid:48) mass), and the SU (2) ⊗ SU (2) breaking downto SU (2) L (breaking pattern II, where the W (cid:48) and Z (cid:48) bosons have the same mass). In thebreaking pattern I, the model structure is the left-right symmetry SU (2) L × SU (2) R × U (1) X with different charge assignments in fermion sector, while in the breaking pattern II, themodel includes two left-handed SU (2) with SU (2) L × SU (2) L × U (1) Y gauge structureand different charge assignments in fermion sector. We will mainly be interested in the3epto-phobic (LP) model. In this model, the following symmetry breaking pattern (breakingpattern I) is applied with gauge structure SU (2) L × SU (2) R × U (1) X . In the first stage, thebreaking SU (2) R × U (1) X → U (1) Y occurs at the ∼ SU (2) L × U (1) Y → U (1) em takes place at the EW scale.The gauge couplings for SU (2) L , SU (2) R , and U (1) X are denoted by g L , g R and g X ,respectively. In the above notation, the gauge couplings are given by g L = e sin θ , g R = e cos θ sin φ , g X = e cos θ cos φ . (1)where the couplings are correlated by the SM weak mixing angle θ a new mixing angle φ . In this model, the SM left-handed fermion doublets are charged under the SU (2) L , theright-handed quark doublet are charged under the SU (2) R . We identify the U (1) X as the U (1) B − L gauge symmetry in the following. The charge assignments of the SM fermions areshown in Table I.TABLE I: The charge assignments of the SM fermions under the leptophobic G
221 model.
Model SU (2) L SU (2) R U (1) B − L Lepto-phobic (cid:32) u L d L (cid:33) , (cid:32) ν L e L (cid:33) (cid:32) u R d R (cid:33) for quarks, Y SM for leptons. At the TeV scale, the SU (2) R × U (1) B − L → U (1) Y breaking can be induced by ascalar doublet Φ ∼ (1 , / (LPD) or a scalar triplet (1 , (LPT) with a vacuumexpectation value (VEV) u . Another bi-doublet scalar is introduced for the subsequent SU (2) L × U (1) Y → U (1) Q at the EW scale. This is denoted by H ∼ (2 , ¯2) with two VEVs v and v . We will prefer to change variables and work with a single VEV v = (cid:112) v + v anda mixing angle β = arctan( v /v ). We define a quantity x , which is the ratio of the VEVs x = u v , (2)with x (cid:29)
1. Usually the physical observables are not sensitive to the parameter β as itcontributes to physical observables only at the order of 1 /x . So in the following discussion,we will fix sin 2 β to be one to maximize the W (cid:48) couplings to the gauge bosons and the Higgsboson.The gauge bosons of the G
221 model are denoted by SU (2) L : W ± ,µ , W ,µ ,SU (2) R : W ± ,µ , W ,µ ,U (1) B − L : X µ . (3) the quantum number assignment is under ( SU (2) L , SU (2) R ) U (1) B − L W (cid:48) and Z (cid:48) bosons obtain masses and mix with the SM gaugebosons. To order 1 /x the eigenstates of the charged gauge bosons are W ± µ = W ± µ + sin φ sin 2 βx tan θ W ± µ , (4) W (cid:48)± µ = − sin φ sin 2 βx tan θ W ± µ + W ± µ . (5)While for the neutral gauge bosons Z µ = W Z µ + sin φ cos φx sin θ W H µ , (6) Z (cid:48) µ = − sin φ cos φx sin θ W Z µ + W H µ , (7)where W H and W Z are defined as W H µ = cos φW µ − sin φX µ , (8) W Z µ = cos θW µ − sin θ (sin φW µ + cos φX µ ) , (9) A µ = sin θW µ + cos θ (sin φW µ + cos φX µ ) . (10)Correspondingly, the masses of the W (cid:48) and Z (cid:48) are given by M W (cid:48)± = e v θ sin φ ( x + 1) , M Z (cid:48) = e v θ sin φ cos φ (cid:0) x + cos φ (cid:1) , (11)for the LPD model, and M W (cid:48)± = e v θ sin φ (2 x + 1) , M Z (cid:48) = e v θ sin φ cos φ (cid:0) x + cos φ (cid:1) , (12)for the LPT model.For the LPD, the relevant Feynman rules on the fermion couplings are written as W (cid:48)± f f (cid:48) : e √ θ ( f W (cid:48) L P L + f W (cid:48) R P R ) , (13)with f W (cid:48) L = − sin φ sin(2 β ) x tan θ , f W (cid:48) R = tan θ sin φ , (14)and Z (cid:48) f f : e sin θ cos θ ( f Z (cid:48) L P L + f Z (cid:48) R P R ) , (15)with f Z (cid:48) L = ( T − Q ) sin θ tan φ − ( T − Q sin θ ) sin φ cos φx sin θ (16) f Z (cid:48) R = ( T − Q sin φ ) sin θ sin φ cos φ + Q sin θ sin φ cos φx . (17)5or the LPD, the gauge boson self-couplings are given as follows, with all momentaout-going. The three-point couplings take the form: V µ ( k ) V ν ( k ) V ρ ( k ) : − if V V V [ g µν ( k − k ) ρ + g νρ ( k − k ) µ + g ρµ ( k − k ) ν ] , (18)where the coupling strength f V V V for the W W Z (cid:48) and W (cid:48) W Z are f W W Z (cid:48) = e sin φ cos φ cot θx sin θ , f W (cid:48) W Z = e sin φ sin(2 β ) x sin θ . (19)Similarly, the HW W (cid:48) and
HZZ (cid:48) couplings in the LPD are
HW W (cid:48) : g µν e v θ f HW W (cid:48) , HZZ (cid:48) : g µν e v θ cos θ f HZZ (cid:48) , (20)with the coupling strengths are f HW W (cid:48) = − sin(2 β ) tan θ sin φ + sin(2 β )(tan θ − cot θ sin φ ) x sin φ , (21) f HZZ (cid:48) = − sin θ tan φ + cos φ (sin θ cos φ − sin φ ) x sin θ sin φ . (22)For the LPT Feynman rules, the only change on the couplings to the fermion, gauge andHiggs bosons is that replacing x to 2 x for the W (cid:48) couplings, and replacing x to 4 x for the Z (cid:48) couplings.According to the above Equations 11 and 12, the W (cid:48) mass and the Z (cid:48) mass are stronglycorrelated through the mixing angle cos φ . Given the W (cid:48) mass and the mixing angle cos φ ,the Z (cid:48) mass is fully determined. The Figure 1 shows when the W (cid:48) mass is at 2 TeV the Z (cid:48) masses in LPD and LPT models as a function of the mixing angle cos φ . As a benchmarkpoint, we will pick up the mixing angle cos φ = 0 . M W (cid:48) = 2 TeV. Using the aboveFeynman rules, one can calculate the decay width and branching ratios of W (cid:48) and Z (cid:48) tovarious SM states. The details are shown in the Appendix. For future reference, we displaybelow the branchings for W (cid:48) and Z (cid:48) at the point M W (cid:48) = 2 TeV and M Z (cid:48) = 2 . φ = 0 .
8, in the LPD G
221 model. Fromthe Figure 2, we also see that the branching ratio Br( W (cid:48) → W Z ) is almost equal to thebranching ratio Br( W (cid:48) → W h ). This is because when the W (cid:48) is heavy, the decay product W and Z are highly boosted with the longitudinal polarization (cid:15) µL ( k ) ∼ k µ . According tothe equivalence theorem, we know σ ( W (cid:48) → W Z ) ∼ σ ( W (cid:48) → W h ). Similarly we see that σ ( Z (cid:48) → W W ) ∼ σ ( Z (cid:48) → Zh ). III. ELECTROWEAK PRECISION CONSTRAINTS
In this Section, we describe the constraints coming from EW precision tests (EWPTs)[29, 30].In [7, 8], a global-fit analysis of 37 EWPTs was performed to derive the allowed modelparameter space in the LP G (221 G . From Eq. 11, it is clear that M W (cid:48) and Since there is tree-level mixing between the extra gauge bosons and the SM gauge bosons, all the EWPTdata cannot be described by the conventional oblique parameters (
S, T, U ). A global fit is thus performed. PDLPT Φ M Z ' (cid:64) G e V (cid:68) FIG. 1: Given the W (cid:48) mass at 2 TeV, the Z (cid:48) masses in the lepto-phobic doublet (LPD)model and the lepto-phobic triplet (LPT) as a function of the mixing angle cos φ . q (cid:45) q't (cid:45) bWZWH M W' (cid:61) Φ B r a n c h i ng R a ti o (cid:72) W ' (cid:76) ll ΝΝ (cid:45) qq (cid:45) tt (cid:45) (cid:43) bb (cid:45) WWZH M W' (cid:61) (cid:72) LPD (cid:76) Φ B r a n c h i ng R a ti o (cid:72) Z ' (cid:76) M Z ' (cid:64) TeV (cid:68)
FIG. 2: The branchings of W (cid:48) (left column) and Z (cid:48) (right column) to various SM states inthe lepto-phobic doublet (LPD) G
221 model at the point M W (cid:48) = 2 TeV, as a function ofthe mixing angle cos φ . M Z (cid:48) are not independent parameters. Therefore, M W (cid:48) was chosen as the input mass. Theother independent parameters are the gauge mixing angle φ and the mixing angle β . Sincethe parameter scan is not very sensitive to the angle β , which becomes important only at O (1 /x ), it can be ignored. Thus, the scans will be presented in the ( M W (cid:48) , c φ ) plane or the( M W (cid:48) , M Z (cid:48) ) plane.In Fig. 3 and Fig. 4, we show the allowed parameter space (colored region) of thelepto-phobic doublet (LPD) G
221 model and the lepto-phobic triplet (LPT) G
221 model,7 M W ' (cid:64) TeV (cid:68) c o s Φ M W ' (cid:64) TeV (cid:68) M Z ' (cid:64) T e V (cid:68) FIG. 3: Allowed parameter space (blue colored region) of the lepto-phobic doublet (LPD) G
221 model at 95% CL in the cos φ − M W (cid:48) and M Z (cid:48) − M W (cid:48) planes after including EWPTconstraints. M W ' (cid:64) TeV (cid:68) c o s Φ M W ' (cid:64) TeV (cid:68) M Z ' (cid:64) T e V (cid:68) FIG. 4: Allowed parameter space (blue colored region) of the lepto-phobic triplet (LPT) G
221 model at 95% CL in the cos φ − M W (cid:48) and M Z (cid:48) − M W (cid:48) planes after including EWPTconstraints.respectively, at 95% CL in the cos φ − M W (cid:48) and M Z (cid:48) − M W (cid:48) planes after including EWPTconstraints.For both the LPD and LPT models, the allowed region in the cos φ − M W (cid:48) plane showsthat direct search constraints favor small cos φ , which is expected because the W (cid:48) coupling isproportional to 1 / sin φ , leading to small W (cid:48) production rate in these regions. However, cos φ can not be too small due to the perturbativity of the g and g X coupling strength. Conversely,in the cos φ − M Z (cid:48) plane, small cos φ is disfavored by direct LHC search constraints because8 Z (cid:48) (cid:39) M W (cid:48) / cos φ .In the M Z (cid:48) − M W (cid:48) plane of the Fig. 3 and Fig. 4, we can see that the LPD model, with M W (cid:48) ∼ M Z (cid:48) ≥ . M W (cid:48) ∼ M Z (cid:48) ≥ . IV. RESULTS AND PREDICTIONS
In this Section, we present our main results for explaining the
W Z , W h and dijet excesseswith our model. We discuss in turn the results for the W (cid:48) and the Z (cid:48) bosons. A. Results for W (cid:48) Before proceeding to the W (cid:48) predictions in our model, we note from Fig. 2 that thereis appreciable branching of W (cid:48) into SM fermions. When resonantly produced in Drell-Yanprocesses, W (cid:48) → lν and Z (cid:48) → ll decays lead to tight constraints on the mass of W (cid:48) [12] and Z (cid:48) [13] bosons if their couplings to leptons resemble those between the SM W, Z bosons toSM leptons. In our leptophobic scenario, the leptons are not charged under SU (2) R and the W (cid:48) → lν decays are forbidden. Thus the current W (cid:48) mass constraint does not apply to ourmodel. We will see later, however, the Z (cid:48) → ll constraint is significant.First let us focus on the W Z excess. The signal rate in the
W Z channel is evaluatedas σ W (cid:48) Br ( W (cid:48) → W Z ) A eff , and A eff is taken to be around 13%, which is the dibosonevent selection efficiency [1]. Including the event selection efficiency and luminosity, thesignal cross section σ W (cid:48) Br ( W (cid:48) → W Z ) should be around 3 ∼
15 fb. Theoretically, the W (cid:48) production cross-section σ W (cid:48) in our G221 model can be obtained via the scaling from aNNLO ‘sequential SM’ cross-section: σ W (cid:48) = σ NNLO (cid:18) g W (cid:48) L g SM (cid:19) , (23)where g W (cid:48) L and g SM denote for the W (cid:48) and SM W coupling to the quarks. We adoptthe NNLO W (cid:48) production cross-section from Ref. [12], which is taken to be 292 fb for a‘sequential SM’ 2 TeV W (cid:48) .Our results for W (cid:48) are presented in Fig. 5, where we show the cross section times branchingfor W (cid:48) in our model as a function of the mixing angle cos φ for various channels. From topto bottom, the blue solid, purple solid, green solid, and red dashed lines show the model’sprediction signal cross-section in the qq (cid:48) , tb , W Z , and
W h channels, respectively. Thehorizontal shaded yellow band denotes the parameter space compatible with the ATLAS
W Z excess with a cross section of 3 ∼
15 fb. Thus a large range of the mixing angle value,0 . < cos φ < .
92, can explain the
W Z excess.Given the
W Z signal, the equivalence theorem requires the W (cid:48) → W h decay happen ata comparable rate to that of the longitudinal polarization of Z in the W (cid:48) → W Z process.Since W (cid:48) is heavy, the daughter Z boson is boosted and dominated by its longitudinal mode.Hence BR( W (cid:48) → W Z ) ≈ BR( W (cid:48) → W h ) and an equally large signal in the
W h channel ispredicted. 9 W' (cid:61) q (cid:45) q 't (cid:45) bWZWH cos Φ Σ (cid:180) B r (cid:64) f b (cid:68) FIG. 5: The cross section times branching to different channels for a 2 TeV W (cid:48) , as afunction of cos φ . The coincident green and red lines denote the branching times crosssection to W Z and
W h channels. The shaded yellow (blue) band denotes the region thatis compatible with the ATLAS
W Z (dijet) excess. The
W Z and
W h contours overlap dueto the Goldstone equivalence theorem.Interestingly, CMS has reported a 2 σ up-fluctuation in the eνb ¯ b search [6] that could arisefrom a 1.8-2.0 TeV W (cid:48) that decays into W h . Since the 95% confidence level uncertainty at M W (cid:48) = 2 TeV is given [6] at 8 fb, a 2 σ up-fluctuation approximately suggests an 8 fb W (cid:48) signal. Thus, approximately the same range of cos φ that fits the W Z excess would also fitthis putative excess. We note that a similar excess in the µνb ¯ b channel was not seen [6] in thesame analysis. More data will settle the question of whether this excess will be statisticallyestablished in the future.As a benchmark point for these two channels, we choose cos φ = 0 .
8. At this point, thecross section times branching of the W (cid:48) boson to various channels are as follows: σ ( pp → W (cid:48) ) BR ( W (cid:48) → qq (cid:48) ) = 150 fb ,σ ( pp → W (cid:48) ) BR ( W (cid:48) → tb ) = 71 fb ,σ ( pp → W (cid:48) ) BR ( W (cid:48) → W Z ) = 6 . ,σ ( pp → W (cid:48) ) BR ( W (cid:48) → W h ) = 6 . . (24)10e now turn to the dijet channel. CMS also reported a ∼ σ up-fluctuation [5] in quark-quark invariant mass at 1.8 TeV. By including the cut efficiency and luminosity, we obtainthe dijet excess σ ( pp → W (cid:48) → jj ) around 100 ∼
200 fb. If considered as an excess, it isconsistent with a ‘sequential SM” W (cid:48) → qq signal [5]. Our benchmark point yields 30% of the σ BR( W (cid:48) → qq ) in comparison to the Sequential SM case, and fits in excess well. In Fig. 5,the horizontal blue band shows the region with a dijet cross section around 100 ∼
200 fbthat explains the dijet excess. Alternatively, even if the dijet data is interpreted as a boundthat marginally excludes a Sequential SM W (cid:48) at 2 TeV, our 2 TeV W (cid:48) at the benchmarkpoint can still be allowed due to its smaller couplings to the quarks.It is also interesting to note an associated single top tb final state is also expected at 71fb, as listed in Eq. 24. While still below current LHC limits [31], it can be searched at futurehigh statistics runs.In conclusion, we see that after imposing the constraints from EWPT and current LHCdata, we can explain the W Z , W h and dijet excesses together for a range of values of the SU (2) R coupling strength g R in the range 0 . ∼ .
68, which coresspondings to the range0 . < cos φ < . B. Results for Z (cid:48) We now turn to constraints on the Z (cid:48) boson in our model, and comment on the possibilityof explaining the W W excess. Since we know the favored region of the W (cid:48) mass and themixing angle cos φ , the favored Z (cid:48) mass and couplings could be fully predicted. Using ourbenchmark point with cos φ = 0 .
7, the Z (cid:48) mass is predicted to be 2.9 TeV for LPD modeland 3.5 TeV for LPT model. Our main results for the Z (cid:48) boson in the benchmark pointare summarized in Fig. 6. In the left panel, we show the results for the LPD model as thefunction of the mixing angle, and the right panel shows the LPT model s the function ofthe mixing angle.Firstly, we consider the dilepton constraint in the two charged lepton channel, relevantfor Z (cid:48) → ll . The leptons in our model are charged under U (1) and thus Z (cid:48) → ll processescan occur via the Z (cid:48) mixing with Z . In ATLAS’s recent dilepton analysis [13, 14], the Z (cid:48) mass with ‘Sequential SM’ couplings is constrained to 2.7 ∼ Z (cid:48) mass is around 2 ∼ φ region from the W (cid:48) : 0 . < cos φ < .
85 . Fig. 6 shows the EWPT constraints allow a Z (cid:48) mass as low as 2.1 TeV for M W (cid:48) ∼ Z (cid:48) mass to be consistent withthe dilepton search bound, Z (cid:48) must either have a small production cross section, i.e. smallercouplings to quarks, and/or a lower decay branching ratio into leptons than a sequential SM Z (cid:48) does. The combination of these two factors can be optimized by varying the cos φ value.At the benchmark point cos φ = 0 .
7, which corresponds to M Z (cid:48) = 2 . l ΝΝ (cid:45) qq (cid:45) tt (cid:45) (cid:43) bb (cid:45) WWZH M W' (cid:61) (cid:72) LPD (cid:76) (cid:45) (cid:45) (cid:45) (cid:45) Φ Σ(cid:180) B r (cid:64) f b (cid:68) M Z ' (cid:64) TeV (cid:68) ll ΝΝ (cid:45) qq (cid:45) tt (cid:45) (cid:43) bb (cid:45) WWZH M W' (cid:61) (cid:72) LPT (cid:76) (cid:45) (cid:45) (cid:45) (cid:45) Φ Σ(cid:180) B r (cid:64) f b (cid:68) M Z ' (cid:64) TeV (cid:68)
FIG. 6: The cross section times branching to different channels for different mixing angle(or Z (cid:48) mass) in the doublet model (left panel) and in the triplet model (right panel), as afunction of cos φ .times branching for the various channels are given below: σ ( pp → Z (cid:48) ) BR ( Z (cid:48) → qq (cid:48) ) = 0 .
40 fb ,σ ( pp → Z (cid:48) ) BR ( Z (cid:48) → tt ( bb )) = 0 .
20 fb ,σ ( pp → Z (cid:48) ) BR ( Z (cid:48) → ll ) = 0 .
48 fb ,σ ( pp → Z (cid:48) ) BR ( Z (cid:48) → νν ) = 0 .
10 fb ,σ ( pp → Z (cid:48) ) BR ( Z (cid:48) → Zh ) = 0 .
01 fb ,σ ( pp → Z (cid:48) ) BR ( Z (cid:48) → W W ) = 0 .
01 fb . (25)We found a minimal Z (cid:48) production at 21% of the Sequential SM cross-section and a Z (cid:48) → ll at 2.9 TeV that explains the recent dielectron event at the CMS [28] and predict a similarresonance in di-muon channel. On the other hand, if we consider previous non-signal dileptondata, the LPD model has a lowest BR( Z (cid:48) → ll )=12% within EWPT constraints, which aretoo large to evade Z (cid:48) → ll constraints and a Z (cid:48) mass greater than 2.8 TeV is needed, whichis possible with a smaller cos φ : 0 . < cos φ < .
72. From Figure 5, the smaller cos φ , thesmaller the cross section times branching ratio for a 2 TeV W (cid:48) . Therefore, to explain thethe W Z , W h and dijet excesses and escape the dilepton constraint in the LPD model, oneneeds to take the mixing angle to be around 0 . < cos φ < . Z (cid:48) mass is around 3 ∼ φ region. This Z (cid:48) is beyond the search limits of the current dilepton bound. As shownin Fig. 4, the EWPT constraints in the LPT scenario allow M Z (cid:48) ≥ . M W (cid:48) ∼ e + e − event at 2.9 TeV. However, such a large Z (cid:48) masswould be unsuitable to explain the diboson W W excess.In conclusion, we find that, the LPD scenario predicts a Z (cid:48) boson with mass around 2 ∼ . < cos φ < .
72, which corresponds to M Z (cid:48) > . Z (cid:48) boson with mass around 3 ∼ W W diboson excess.
V. CONCLUSIONS
We investigated the prospects of the leptophobic SU (2) L × SU (2) R × U (1) B − L model asa potential explanation to the diboson and W h excesses. In our discussion, we fixed the W (cid:48) mass to be 2 TeV. Within the electroweak precision data limits, we found that to explain the W Z , W h and dijet excesses together, the SU (2) R coupling strength g R favors the range of0 . ∼ .
68 and a range for mixing angle 0 . < cos φ < .
85. We noticed that the Z (cid:48) massand couplings are determined by the two parameters appeared in the W (cid:48) sector. Therefore,given the favored region to explain the excesses, the Z (cid:48) masses are determined to be around2 ∼ ∼ Z (cid:48) decay widths to the dilepton,dijet, and gauge bosons are predicted. We found the ATLAS W W and ZZ excesses areunlikely to arise from the heavy Z (cid:48) from this model due to a much heavier Z (cid:48) mass in theLPT model. Within electroweak precision limits, the benchmark LPD point can explain theCMS’s recent dielectron event at 2.9 TeV, while the heavier LPT Z (cid:48) could also be consistentwith 2.9 TeV mass, or evade dilepton bounds even in case if future data do not establish the2.9 TeV excess.As a model independent check, the leptonic decay of the W (cid:48) → W Z bosons would leadto a 3 l + E/ T final state with the same invariant mass around 2 TeV. No significant excesshas been reported in this channel, and the current CMS [9] data place a constraint of σ × BR( W (cid:48) → lν ) below 0.1 fb for M W (cid:48) = 2 TeV. Given the SM W Z leptonic decaybranching fractions, the relative size to the four jet final state is 0.03. If the four jet
W Z excess persists, an associated σ W (cid:48) BR( W (cid:48) → lν ) excess at 0.2 fb is expected. Also, nosignificant deviation from the SM was observed from ATLAS’s recent analysis [10] of thesemileptonic W Z/W W → lνjj channel. It is noted that many of the aforementioned up-fluctuations are statistically limited in the current data and LHC run 2 updates will greatlyhelp confirm or clarify the excesses.In summary, the recent tantalizing excesses in the W Z , W h , and dijet channels can beaccommodated with the LPT model and a limit range of parameter space of the LPD model,in a manner consistent with both EWPT and LHC constraints.
Note after published : With a 2.9 TeV Z (cid:48) event observed in Ref. [28], we updated ourpaper by discussing the possible 2.9 TeV Z (cid:48) signature together with the 2 TeV W (cid:48) excess.13 cknowledgements We would like to thank the CETUP 2015 Dark Matter Workshop in South Dakota forproviding a stimulating atmosphere where this work was conceived and concluded. Y.G.thanks the Mitchell Institute for Fundamental Physics and Astronomy for support. T.G. issupported by DOE Grant DE-FG02-13ER42020. K.S. is supported by NASA AstrophysicsTheory Grant NNH12ZDA001N. The research of JHY is supported by the National ScienceFoundation under Grant Numbers PHY-1315983 and PHY-1316033.
Appendix A: Heavy Gauge Boson Decay Width
The partial decay width of V (cid:48) → ¯ f f isΓ V (cid:48) → ¯ f f = M V (cid:48) π β (cid:20) ( g L + g R ) β + 6 g L g R m f m f M V (cid:48) (cid:21) Θ( M V (cid:48) − m f − m f ) , (A1)where β = (cid:115) − m f + m f M V (cid:48) + ( m f − m f ) M V (cid:48) ,β = 1 − m f + m f M V (cid:48) − ( m f − m f ) M V (cid:48) . (A2)The color factor N c is not included and the top quark decay channel only open when the Z (cid:48) and W (cid:48) masses are heavy.The partial decay width of V (cid:48) → V V isΓ V (cid:48) → V V = M V (cid:48) πM V M V g V (cid:48) V V β β Θ( M V (cid:48) − M V − M V ) , (A3)where β = (cid:115) − M V + M V M V (cid:48) + ( M V − M V ) M V (cid:48) ,β = 1 + 10 M V + M V M V (cid:48) + M V + 10 M V M V + M V M V (cid:48) . (A4)The partial decay width of V (cid:48) → V H (where V = W or Z boson and H is the lightestHiggs boson) is Γ V (cid:48) → V H = M V (cid:48) π g V (cid:48) V H M V β β Θ( M V (cid:48) − M V − M V ) , (A5)where β = (cid:115) − M V + m H M V (cid:48) + ( M V − m H ) M V (cid:48) ,β = 1 + 10 M V − m H M V (cid:48) + ( M V − m H ) M V (cid:48) . (A6)14
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