UUCI-TR-2011-06 A Z (cid:48) Model for the CDF Dijet Anomaly
Felix Yu ∗ Department of Physics and Astronomy,University of California, Irvine, CA 92697-4575, USA (Dated: April 1, 2011)
Abstract
We adopt a bottom-up approach to constructing a new physics model to explain the CDF excessseen in dijets with an associated lepton and missing transverse energy. We find that the 145GeV broad feature seen by CDF in the dijet invariant mass distribution can be explained by a Z (cid:48) boson with a mass of 145 GeV that couples only to first generation quarks. After dijet resonanceconstraints are considered, a sizeable region of the parameter space favored by the CDF anomalyremains viable. PACS numbers: 13.85.-t ∗ [email protected] a r X i v : . [ h e p - ph ] A p r . INTRODUCTION Recently, using 4.3 fb − , the CDF collaboration reported a 3.3 sigma excess over StandardModel (SM) background in dijet events with an associated lepton (electron or muon) andmissing energy [1]. This excess is present in the dijet invariant mass range of 120–160GeV, and a Gaussian fit to the background-subtracted histogram in this mass range givesa Gaussian peak at 144 ± Z (cid:48) model with a Z (cid:48) mass of about 150 GeV. In Sec. III, webriefly discuss the collider constraints on Z (cid:48) masses and couplings and conclude that flavor-universal Z (cid:48) models that could explain the CDF anomaly are excluded. We therefore discardflavor-universality and consider the Z (cid:48) ud model, a Z (cid:48) that couples equally to and only to thefirst generation quarks, which we present in Sec. IV. We conclude in Sec. V with a summaryand a brief discussion of possible cross-channels to check at the Tevatron or the LHC.2 I. APPROACH
New physics parameter space is large, and many different models can be made to fit theexcess. In our bottom-up approach, we seek minimal extensions of the SM, keeping in mindboth theoretical and experimental constraints on such extensions.The CDF event selection calls for events with one electron (muon) with E T ( p T ) >
20 GeVand no other leptons with p T >
10 GeV; in addition, a Z mass window (from 76 − − R = (cid:112) (∆ η ) + (∆ φ ) = 0 . E T >
30 GeV and | η | < .
4: the dijet system must have p T ≥
40 GeV. Inaddition, events are required to have missing transverse energy (MET) /E T >
25 GeV. Thetransverse mass of the single hard lepton and the MET is required to be compatible witha W -candidate, m WT = (cid:113) p (cid:96)T /E T (1 − cos(∆ φ (cid:96)ν )) ≥
30 GeV. Additional details regarding jetenergy corrections and isolation requirements are given in [1] (cf. Table 4.2 and Section 8.1of the Cavaliere thesis).The event excess is present in both electrons and muons. For electrons, the excess numberof events is 156 ±
42, and for muons, the excess is 97 ±
38. Naively summing the system-atic errors in quadrature, we find the total excess is 256 ± . × acceptance) of about 60fb for the Tevatron collider. If we presume the lepton arises from a W boson, the requiredeffective cross section for NP production including a hard W boson is about 270 fb, and ifwe estimate the acceptance factor for our signal to be about 10%, then we are looking fora total signal cross section of about 2.7 pb. For comparison, the measured W W/W Z crosssection is 18.1 ± ± ± O (1 pb) production cross section, including W emission.There are two main issues from a bottom-up perspective. First, considering the excessin the dijet invariant mass distribution from 120–160 GeV, we can interpret it as a coloredresonance, an uncolored resonance, or a kinematic feature from a cascade decay. Second,concerning the presence of the hard lepton, we can consider, in turn, scenarios that arelepton number violating, lepton number conserving but flavor violating, or lepton number3nd flavor conserving with the separate possibility of kinematic suppression of additionalleptons. Separately, the observed MET could arise from SM neutrinos, or it could arisefrom a NP source of missing energy: in the first case, we could again consider possible NPscenarios of lepton flavor and/or number violation, but this is redundant and unnecessarygiven the hard lepton. We will first discuss the dijet invariant mass excess as a possiblekinematic feature from a cascade decay chain. A. Cascade decay chain explanation for the m jj excess Invariant mass distributions from cascade decay chains can appear to have broad reso-nance features when the underlying particle masses are tuned appropriately and the correctparticle combinations are isolated [2, 3]. A simple example of such a cascade decay chain iswhen a massive color octet decays via a on- or off-shell massive color triplet to a color sin-glet that subsequently escapes the detector: in supersymmetry (SUSY), this is the familiargluino cascade decay, ˜ g → q ˜ q → qq ˜ χ , which can have a large rate if the m ˜ χ < m ˜ g . Forexample, if m ˜ g = 420 GeV, m ˜ q = 380 GeV, and m ˜ χ = 150 GeV, the exact dijet invariantmass edge would be 164 GeV and the dijet invariant mass distribution would exhibit theusual triangular shape, assuming the emitted quarks are massless. Since the quarks showerand hadronize, however, we expect the triangular feature to be smoothed out and the dis-tribution to have a tail from jet-parton momenta mismatch as well as pollution by wrongdijet combinations.There are several difficulties with making such a possibility work. First, generating alepton together with this dijet invariant mass feature requires additional ingredients. If weassume the lepton arose from the same decay chain, we can consider an illustrative SUSYexample: ˜ g → q ˜ q → qq ˜ χ ± → qq(cid:96) ± ˜ ν . (1)In this SUSY example, we would need to have large R -parity violation in order to singlyproduce the ˜ g , but we would also need to minimize R -parity violation in order to forcethe prescribed decay chain. If we retain R -parity and still assume the ˜ ν is the lightestsupersymmetric particle (LSP), we can assume the gluino is either produced in pairs orin association with a squark. In either case, the searches for SUSY in final states of onelepton, jets, and MET [4] or opposite-sign dilepton events, jets, and MET [5] have put strict4onstraints on gluinos and squarks with masses below about 500 GeV (and even up to 700GeV).If we make ˜ χ the LSP, then the lepton could minimally arise from the leptonic decay ofa W boson: such a W could be produced from a heavy squark to light squark decay or in achargino to neutralino decay (or vice-versa). An example SUSY process for the CDF excessin this case is ˜ q ˜ g → ( q ˜ χ ± )( q ˜ q ) → ( q W ˜ χ )( q q ˜ χ ) , (2)where the W → (cid:96)ν , q is soft, and q and q are hard jets that give the invariant massexcess. Here, in contrast with the above gluino decay in Eq. (1), the necessary addition ofa weak gauge coupling is a model-independent penalty in order to incorporate the W in acascade decay chain, and the ≈
22% leptonic branching ratio of the W boson is an additionalpenalty. An alternative to Eq. (2) is if a slepton were part of the cascade process, but suchdecay chains typically give rise to large multilepton signals, which are disfavored from [4]and [5]. Moreover, cascade processes such as Eq. (2) can be easily checked in the jets+METcross-channel, and recent results [6–8] on these final states indicate that such spectra wouldneed fine-tuning in order to evade constraints. Other choices for the stable LSP besides aneutralino or sneutrino are ruled out or disfavored from the recent searches for long-livedmassive charged particles [9–11].To summarize, a SUSY decay chain explanation for the dijet excess suffers from twocompeting considerations. In order to have an appreciable SUSY colored cross section atthe Tevatron, we must make the gluinos and squarks relatively light. Yet, the requirement tohave a lepton emitted in a cascade requires a slepton, a sneutrino, or a W insertion, makingthe resulting effective cross section for a 2 jets + lepton + MET final state disfavored givenATLAS and CMS searches. Since there is a great deal of freedom in arranging the SUSYspectrum, however, we do not rule out a SUSY explanation for the CDF anomaly but insteadleave such a construction for future work.We can also consider a non-SUSY decay chain explanation. The simplest would be anon-SUSY version of Eq. (1), which minimally requires the introduction of a new heavycolor octet X and triplet Q , X → qQ → qqW → qq(cid:96)ν . (3)We note that other color representations for the initial particle are also obviously possible:5he only assumption is that the W at the end of the decay arises from a weak coupling vertexinvolving a SM quark and some new physics particle, which must necessarily be in the tripletrepresentation of SU (3). For example, the new Q can be considered as a fourth generationquark, though no such assumption is truly motivated from the bottom-up approach. Wenote that although this decay chain readily produces all of the final state particles of theCDF anomaly, the decay chain arises from a resonance, and so must couple directly toquarks and/or gluons. This implies the constraints and phenomenology are similar to thedijet resonance considerations, and so we will incorporate this discussion with the nextsubsection. B. Resonance decaying to two jets
A more straightforward bottom-up construction is to hypothesize the two jets arise from aresonance, not a cascade decay chain. Given the lack of b -tagging information about the jets,we note the resonance, if colored, could be one of many different color representations under SU (3). In addition, the emission of the hard lepton and the MET requirement allows one ofseveral possibilities: NP could be lepton number violating (LNV), lepton flavor violationg(LFV), or lepton number and flavor conserving. Because the MET requirement is small,we can naturally associate the MET to be a neutrino emission and confine our discussionto NP scenarios that conserve lepton number and lepton flavor. We leave the possibleconstruction of a viable LNV or LFV model for future work. Therefore, we consider a newphysics resonance that decays to two jets where the decay chain includes a W boson, or theresonance is produced in association with a W boson. The Tevatron production cross sectionthen necessarily includes weak coupling and the W leptonic branching fraction penalty: toavoid this, we could instead consider a W (cid:48) boson that decays favorably to leptons. Recentconstraints on a new W (cid:48) boson with leptonic couplings, however, completely exclude anysuch W (cid:48) boson with a mass below about 1.5 TeV [12–16].The main difficulty with the resonance + SM W model is that, by construction, the newresonance can always be produced in an s -channel process without an associated W bosonand hence is subject to direct searches for dijet resonances. Correspondingly, the dijet reso-nance cannot be strongly coupled (the dijet search constraints are discussed in Sec. III), buteven so, we are left with many possibilities for the couplings and character of the new reso-6ance. The resonance can be colored or uncolored, can couple exclusively to gluons, quarks,or both, and can conserve or violate quark flavor. We will not consider a resonance couplingexclusively to gluons, because we require the resonance to be produced in association witha W boson. Similarly, we will not consider a fractionally-charged resonance with a gluon-(anti-)quark coupling because the coupling would be non-diagonal if the resonance were inthe same SU (3) representation as the (anti-) quark, and for higher SU (3) representations,the gluon-quark resonance would require a careful consideration of constraints to ensure itremains viable. We reserve a study of phenomenology and constraints of this interestingquark–gluon resonance model for future work.If the resonance has quark-(anti-)quark couplings, we could expect the dominant processfor associated W boson production to come from the 2–2 t -channel scattering process qq → W X qq → ( (cid:96)ν )( qq ) , (4)where the t -channel exchanged SU (3) fundamental could also be a fourth generation quark.We see that this process is reminiscent of Eq. (3): in fact these production processes canbe considered as differing cases of the same underlying new physics model that introduces anew SU (3) octet X qq and a new SU (3) triplet Q . We remark that if the t -channel exchangeparticle is a SM quark, then the only two free parameters are the resonance-quark-quarkcoupling and the width of the resonance, since the mass of the resonance is fixed from theGaussian fit to the dijet excess performed by CDF. On one hand, these two free parametersare constrained by direct dijet searches, and on the other hand, these are the only parametersavailable to ensure the cross section for resonance + W production matches the observednumber of events at CDF. If the t -channel also included a fourth generation quark, however,then we have additional freedom to modify separately the direct dijet cross section and theresonance + W production cross section.Alternatively, for the resonance with quark-(anti-)quark couplings, the dominant processfor W emission could be from s -channel production, as in qq → W (cid:48) → W Z (cid:48) → ( (cid:96)ν )( qq ) . (5)Here, we have changed the resonance notation to the traditional Z (cid:48) to emphasize that it isa color singlet. Again, the advantage of this s -channel construction is there are separatecouplings that control the CDF event excess and the direct dijet production of Z (cid:48) : this model7reedom can clearly be used to evade constraints from direct searches while also ensuringthe correct production cross section for the excess. A similar process to Eq. (5) would beproduction of a techni-rho decaying to a techni-pion: qq → ρ T C → W π
T C → ( (cid:96)ν )( qq ).The s -channel explanation is disfavored, however, from both the CDF data (cf. Fig. 9.13of [1]) and the bounds on new dijet resonances (discussed in detail in Sec. III). In the CDFanalysis, they do not find a resonance feature in the jj(cid:96)ν invariant mass; instead, the totalinvariant mass is consistent with the background hypothesis. We note that we can avoid gen-erating a feature in m jj(cid:96)ν by postulating additional decay products that are invisible, soft,or otherwise missed by the detector. Such constructions and their corresponding experimen-tal constraints are very model dependent, however, so following our bottom-up approach,we consider t -channel production of a Z (cid:48) resonance + SM W boson with only SM quarksexchanged. We will find that we can successfully fit the CDF dijet excess with such a Z (cid:48) model.In summary, from a bottom-up perspective, we discussed the possibility of a dijet cascadedecay invariant mass feature and a dijet resonance. We also considered the origin of theobserved lepton: if the lepton comes from a W boson, then the full cross section wouldrequire a weak coupling and pay a price in the W leptonic branching ratio. On the otherhand, if the lepton is from a cascade decay, then model-dependent tuning is needed toensure a large branching fraction for a single lepton. Given these considerations, we findthe simplest new physics model for explaining the CDF anomaly is a Z (cid:48) dijet resonanceproduced in association with a W that decays leptonically, as shown in Fig. 1. FIG. 1. W + Z (cid:48) ud associated production with a t -channel SM d quark. II. BOUNDS ON A NEW Z (cid:48) BOSON
From our bottom-up approach, the simplest model to explain the CDF anomaly is a Z (cid:48) dijet resonance produced in association with a leptonically decaying W boson. Constraintson such a light Z (cid:48) , however, are very stringent.For instance, a Z (cid:48) boson with SM Z couplings to leptons is ruled out below a mass of1071 GeV [17]. From a bottom-up approach, however, we do not require the Z (cid:48) to couple toleptons, and hence we can postulate that the Z (cid:48) is leptophobic, i.e. only couples to quarks.Even so, searches for dijet resonances place strong constraints on this type of Z (cid:48) boson.The most recent results from ATLAS [18] and CMS [19], however, look for dijet invariantmasses above 200 GeV and 220 GeV, respectively, in order to avoid, presumably, the QCDbackground contamination in the low dijet mass region. These hard cuts will clearly discardour light Z (cid:48) events. Similarly, CDF and D0 searches applicable to leptophobic Z (cid:48) bosonshave dijet mass thresholds of at least 180 GeV [20–24] or look for tt resonances [25]. All ofthese constraints apply to Z (cid:48) masses outside our range of interest, given the Gaussian fit ofCDF’s dijet excess has a mean 144 GeV.We find the relevant experimental constraint on dijet resonances in this mass range comesfrom the UA2 collaboration [26]. In this analysis, they assumed a Z (cid:48) with exactly SMcouplings and a width that scaled with the mass ratio of the Z (cid:48) to the Z . In addition, thecross section was also corrected with a K-factor of about 1.30 [27], based on the K-factorcalculated for SM Drell-Yan Z production. Their results concluded that a SM-like Z (cid:48) isexcluded at 150 GeV.Although our naive leptophobic Z (cid:48) model with SM Z couplings to quarks is ruled outfrom UA2 data, we can choose to abandon flavor universality. In this case, we expect theUA2 bound implies our Z (cid:48) coupling needs to be about 1 / √ Z couplingto quarks. If we retain flavor universality, we can satisfy the UA2 constraint and producethe desired CDF excess with a g universal = 0 . − .
25, but we would also need to considerconstraints from Higgs searches in the (cid:96)νbb final state [28]. We will therefore consider a Z (cid:48) that only couples to up and down quarks with equal couplings, avoiding flavor constraints.This is our minimal model motivated from a bottom-up approach to the CDF dijet, lepton,and MET events excess. Taking into account the Z (cid:48) mass will be fixed by the CDF dijetGaussian fit, this model has two free parameters: g ud and the Z (cid:48) ud width.9 V. THE Z (cid:48) ud MODEL AND SIMULATION
Faced with the severe constraint from UA2 on light Z (cid:48) bosons in the 150 GeV mass range,we construct the Z (cid:48) ud model with the Lagrangian L ⊃ − g ud Z (cid:48) udµ uγ µ u − g ud Z (cid:48) udµ dγ µ d , (6)where Z (cid:48) ud is a new U (1) (cid:48) gauge boson, and g ud is the new coupling, same for both up anddown quarks. The Z (cid:48) ud is a singlet under the Standard Model gauge group and we turn offits mixing with the SM Z boson. (For a recent review on Z (cid:48) models and phenomenology,see [29] by P. Langacker.)For our purposes, we can consider the Z (cid:48) ud as a particular leptophobic Z (cid:48) model basedon gauging the SM baryon number symmetry. While additional field content is needed tocancel anomalies, such a full model description would follow the earlier work along the linesof [30–32].We simulate the Z (cid:48) ud production for masses between 125 GeV to 175 GeV, couplings g ud at leading order (LO) from 0.20 to 0.40, and a Z (cid:48) ud width of 8 GeV or 12 GeV, usingMadGraph 5 v.0.5.1 [33] and MadEvent v.4.4.56 [34–36] interfaced with Pythia 6.4.20 [37]and PGS 4 [38]. For testing the match to the CDF excess, we generate Tevatron pp collisionsat √ s = 1 .
96 TeV, pp → W ± Z (cid:48) ud , use the Pythia interface to decay, shower, and hadronize,and then perform rough clustering and detector simulation using PGS. We apply identicalcuts as the CDF analysis [1]. At each point of mass, coupling, and width, we count thenumber of events within the signal region of 120 GeV < m jj <
160 GeV. Based on thisevent count and the Gaussian fit performed by CDF, we find the best fit point is at abouta Z (cid:48) mass of 144 GeV and a coupling g ud ∼ .
33, irrespective of the Z (cid:48) width, see Fig. 2and Fig. 3.We also need to calculate the UA2 constraint [26] for this g ud coupling v. Z (cid:48) ud mass plane.To do so, we simulate each model point for S pp S collisions of pp at √ s = 630 GeV to get a(LO) Z (cid:48) ud s -channel production cross section estimate. We also calculate the Z (cid:48) cross sectionlimit from Fig. 5 of [26]. Based on the g ud scaling of the cross section, we can get a (LO)constraint on the g ud coupling allowed by the UA2 search. Our results are displayed in Fig. 2for a Z (cid:48) ud with an 8 GeV width and Fig. 3 for a 12 GeV width. We used BRIDGE v.2.21 [39]to calculate the Z (cid:48) width for each point to ensure the partial width of Z (cid:48) → uu, dd stayed10 .200.22
125 130 135 140 145 150 155 160 165 170 175 g ud Z' ud Mass (GeV)CDF Favored Region and UA2 Constraints, Z' ud Width = 8 GeV
FIG. 2. (color online). The blue (orange) curves are the 1 (2) σ bounds on g ud coupling for given Z (cid:48) mass and obtained from matching the observed number of excess events seen at CDF (see text).The purple (green) vertical lines indicate the 1 (2) σ limits of the Z (cid:48) mass from the Gaussian fit of m jj performed by CDF. The red curve indicates the extracted limit (at LO) on the coupling g ud from the UA2 search for SM-like Z (cid:48) s decaying to two jets [26] (see text). The Z (cid:48) width is fixed tobe 8 GeV for entire mass range. below 8 GeV. As a point of comparison, for a Z (cid:48) mass of 145 GeV, g ud = 0 .
35, the calculated Z (cid:48) width to quarks is 2 .
824 GeV. Additional invisible decay modes would need to added ina full model to account for the remaining Z (cid:48) width.Our results demonstrate that the CDF anomaly can be favorably fit with a Z (cid:48) ud of massbetween about 140 GeV and 150 GeV and a coupling of 0 . (cid:46) g ud (cid:46) .
36. For a Z (cid:48) ud widthof 8 GeV, however, slightly more than half of this favored region is excluded by UA2. If we11 .200.22
125 130 135 140 145 150 155 160 165 170 175 g ud Z' ud Mass (GeV)CDF Favored Region and UA2 Constraints, Z' ud Width = 12 GeV
FIG. 3. (color online). Same as Fig. 2, except for a Z (cid:48) with a width of 12 GeV. increase the Z (cid:48) ud width to 12 GeV, though, the UA2 constraint eliminates only a small partof this favored region.We note that we did not include K-factors for the Tevatron and UA2 production crosssections used in Fig. 2 and Fig. 3, while the UA2 collaboration did include NLO K-factorsin their SM-like Z (cid:48) exclusion limit contour. Clearly, a full calculation of the NLO K-factorsfor Z (cid:48) ud s -channel and W ± Z (cid:48) ud associated production is beyond the scope of this work. Wenaively expect, however, the NLO K-factor for s -channel Z (cid:48) ud production to be about 1.30,given the work of [27], which should rescale the UA2 exclusion curve down by about 6.5%.In this case, even if no K-factor enhancement to W ± Z (cid:48) ud production at Tevatron is assumed,our conclusions remain the same and much of our favored region is left intact.12 . CONCLUSIONS AND FUTURE SEARCHES We have performed a bottom-up analysis of the excess events in the dijet, lepton, METfinal state seen by CDF. After discussing possible new physics constructions that couldexplain the excess, we found a minimal model that satisfied all present collider constraintsand had a minimal number of free parameters. The Z (cid:48) ud model introduces a new Z (cid:48) gaugeboson that only couples to first generation quarks. We calculated the exclusion curves forthis model for two different Z (cid:48) ud widths and found that a significant portion of the CDFfavored region was not excluded from the UA2 dijet constraint.It remains to identify possible cross-channels for checking the validity of this model. Whilethe CDF author acknowledges the entire anomaly may be an underestimated background(see Chapter 9 of the Cavaliere thesis [1]), a search in the same exclusive dijets, lepton,MET channel by D0 would certainly corroborate or refute the excess. A dijet signal fromDrell-Yan production of the Z (cid:48) ud boson may be lost in the QCD background at Tevatronand the LHC, but a signal may be recoverable if the backgrounds are very well understood.Separately, because the lepton here arises from associated W production, a smaller penaltyin cross section would be achieved by looking for a photon + dijet signal . At the LHC,since exclusive dijet searches are expected to be difficult because of the QCD background,one possible search channel is in the exclusive four jets final state. Using MadEvent 4.4.56,we estimate the LO cross section for di- Z (cid:48) ud production at the 7 TeV LHC with g ud = 0 . O (1 fb − ). Since we have an estimate for the Z (cid:48) ud mass, the QCD background can readilybe subtracted out from a sideband subtraction method, and wrong combinatorics can beremoved from a mass window cut and a dijet p T requirement [1, 3]. Additional searchchannels may also be available, but their presence would be motivated from the particularfull model completion of the Z (cid:48) ud minimal model presented here. In a future work, we willconsider possible full model completions and differentiate their phenomenology.Recent work that also discussed light dijet resonances include [40–42]. In particular, wenote a very similar model was considered in [42]. We thank Tao Han for bringing up this point. CKNOWLEDGEMENTS
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