ATLAS on-Z Excess Through Vector-Like Quarks

We investigate the possibility that the excess observed in the leptonic-$Z +$jets $+\slashed{E}_T$ ATLAS SUSY search is due to pair productions of a vector-like quark $U$ decaying to the first-generation quarks and $Z$ boson. We find that the excess can be explained within the 2$\sigma$ (up to 1.4$\sigma$) level while evading the constraints from the other LHC searches. The preferred range of the mass and branching ratio are $6100.3$-$0.45$, respectively.

Introduction After the LHC 8 TeV run, an excess has been reported in the leptonic-Z + jets + / E T ("on-Z") channel by the ATLAS collaboration [1]. The observed number of the signal events are 16 and 13 for the final-state electrons and muons, respectively, whereas the standard model (SM) predicts 4.2 ± 1.6 and 6.4 ± 2.2. The discrepancy corresponds to the 3σ level, which stimulates many theoretical studies [2][3][4][5][6][7][8][9][10][11][12][13][14]. #1 The on-Z signal was investigated originally to search for the supersymmetry (SUSY) [1], and most of the theoretical works have been performed within the framework of SUSY. In this letter, we instead consider models with vector-like (VL) quarks as an alternative scenario. The VL particles are predicted in new physics models, e.g., the little Higgs models [18][19][20][21][22] and the composite Higgs models [23][24][25][26][27][28][29]. We assume that the VL quarks are pair-produced directly at the LHC by the QCD interactions. #2 Then, they decay into SM quarks and bosons through their mixings with the SM quarks, since otherwise they become stable and conflict with the cosmology and experiments [30][31][32][33][34][35][36][37][38]. The decay modes involve productions of the on-shell Z bosons, which contribute to the ATLAS signal. Since the branching ratios of the VL quark depend on details of the models, they are supposed to be free parameters in this letter, and we examine whether this scenario works as a candidate of the on-Z excess.
The models with the VL quarks may be distinguished from the SUSY ones if signal event distributions are precisely measured. In particular, the SUSY models tend to predict events with larger jet multiplicity, e.g., through the gluino pair production, pp →gg,g → qqχ 0 1 → qqZG [1,2,5], whereχ 0 1 is the lightest neutralino, andG is the gravitino. #3 In contrast, the VL quark U decays into less-multiple jets through, e.g., U → qZ. Although the current integrated luminosity at the LHC is not large enough to determine the distributions, the data may prefer a lower jet multiplicity. Thus, we also study the event distributions in the VL quark models.
Model We extend the SM by introducing a VL quark which has the electric charge of 2/3 and only decays to the first-generation quarks. Discussions for VL quarks carrying the electric charge of −1/3 or decaying also to the second-generation quarks go along the same lines. #4 The interactions of the VL quark with gluons and photons are governed by the gauge symmetries. On the other hand, the interactions to the weak gauge and Higgs bosons are model dependent, and we employ an effective-model approach. The interaction of the VL quark with the weak gauge and Higgs bosons are parameterized as [42] #1 Although no excess has been observed by the CMS collaboration [15,16], the ATLAS collaboration has reported a new result based on the 13 TeV data recently [17], which shows the deviation at the 2.2σ level.
#4 On the other hand, decays to the third-generation quarks are severely constrained by the LHC Run-I searches. For example, VL quarks of the mass less than 800 GeV have been already excluded [39][40][41].
where g is the SU(2) L gauge coupling constant, c W cosine of the Weinberg angle, v ≃ 246 GeV the vacuum expectation value of the Higgs field, M U the mass of the VL quark, and with Γ U being the total width of the VL quark. The VL couplings with the first-generation quarks are constrained to be less than O(0.01) [43]. In order to avoid this constraint, η is taken to be small. The following discussion does not depend on its detail as long as the VL quark decays promptly. For simplicity, we only consider the case that the VL quark couples to the left-handed light quarks. #5 In the following discussion, we take the branching ratio of the VL quark, Br(U → V q), as free parameters by expressing the κ V (V = W, Z, h) as where q = u, d and Note that the branching ratios are independent of η.

Analysis
We consider pair-production processes of the VL quark U, decaying to the first-generation quarks along with Z, W or Higgs bosons at the 8 TeV LHC: Those processes are generated at the tree level using MadGraph5 aMC@NLO v2.3 [44]. The model file of the VL quark [42,45] is implemented via FeynRules v2.3 [46]. The generated events are passed to PYTHIA v6.428 [47] for decaying the Z, W and Higgs bosons as well as showering and hadronization, and then interfaced to the Delphes3-based detector simulator in CheckMATE v1.2.1 [48,49], which is tuned to reproduce the performance of the ATLAS detector. The cross sections of the VL-quark pair productions are estimated at the next-tonext-to-leading order (NNLO) accuracy with Hathor v2.0 [50]. MSTW 2008 NNLO (68%CL) PDF [51] is used with the factorization and renormalization scales set at the mass of the VL quark.
We then analyze the generated events following the LHC analyses below [7,48]. #5 The following study does not depend on this assumption. The chirality structure may be identified by investigating angular correlations of the final-state particles. In the dark-red (light-red) region, the ATLAS on-Z excess [1] is explained within the 1σ (2σ) level, while the gray-and blue-shaded regions are excluded at 95% C.L. by the CMS leptonic-Z +jets + / E T search [15] and ATLAS 2-6 jet + / E T search [52], respectively. The vector-like quark is assumed to decay with Z or W boson emission (left panel) and Z or Higgs boson emission (right panel).
The first ATLAS analysis is used to search for parameter regions where the ATLAS excess is reproduced, and the other analyses are used to constrain the parameter space. We also checked that the other LHC searches implemented in CheckMATE v1.2.1 do not give severer constraints.

Results
In Fig. 1 we show the parameter regions where the ATLAS excess in the leptonic-Z + jets + / E T channel [1] is reproduced within 1σ (dark-red shaded region) and 2σ (lightred shaded region), corresponding to the signal event number of 12.1 ≤ N sig ≤ 24.7 and 5.8 ≤ N sig ≤ 31 [7], respectively. The model parameter space is spanned by the mass of the VL quark and the branching ratio Br(U → Zu). In the figure we assume that the VL quark decays via Z or W boson emission (Z-W decay in the left panel) or via Z or Higgs boson emission (Z-Higgs decay in the right panel). The excluded regions from the other LHC analyses, i.e., the CMS search in the leptonic-Z + jets + / E T final states [15] and ATLAS search in the 2-6 jets + / E T final states [52] are also shown as the gray-and blue-shaded regions, respectively. We see that the VL quark model with a mass of 610 M U 760 GeV can explain the ATLAS excess within 2σ (up to 1.4σ) in both the Z-W and Z-Higgs decay cases.  [11] are also shown (black dots with error bars). The highest bins contain overflow events.
The CMS search in the leptonic-Z +jets + / E T final states excludes the parameter space of m U 710 GeV and Br(U → Zu) 0.4-0.5. Since the same final states as the ATLAS on-Z excess are investigated, the 95% C.L. exclusion lines are roughly parallel to the 1σ and 2σ ATLAS signal-region contours. The CMS exclusion region covers the whole 1σ ATLAS signal region (dark-red shaded region) for M U > 550 GeV, but still allowing the 2σ signal region (light-red shaded region) for wide range of the VL quark mass due to the large uncertainty on the signal event number of the ATLAS on-Z excess.
On the other hand, the 2-6 jets + / E T search is sensitive to a smaller Z-branching region and excludes the whole 1σ ATLAS signal region as well as a part of the 2σ signal region for M U 680 GeV. In the Z-W decay case, the model parameter space of M U < 550 GeV is almost excluded, while there remains an allowed region for Br(U → Zu) 0.2 in the Z-Higgs decay case. This is because the 2-6 jets + / E T search is not so sensitive to the parameter space dominated by the Higgs-involving U decays, which basically do not leave large / E T . The CMS constraint is stronger than the ATLAS 2-6 jets + / E T search for Br(U → Zu) 0.8. Next we show the / E T , H T and jet-multiplicity distributions predicted by the VL quark model with M U = 680 GeV and Br(U → Zu) = 0.8 for the Z-W decay case (red boxes) in Fig. 2. This model point gives 8.3 signal events, which agrees with the ATLAS on-Z excess at 1.6σ. The black dots show the ATLAS data with the expected SM backgrounds being subtracted (taken from Ref. [11]). In the figure, all the model distributions show marginal agreements with the ATLAS ones. For the / E T , H T and jet-multiplicity distributions, χ 2 /d.o.f. = 7.7/9, 5.4/7 and 7.0/5, respectively. It is mentioned that the jetmultiplicity distribution of the VL quark model peaks around 2-3 number of jets, which may be a distinguishable feature of the model. Future LHC Run-II data is expected to reveal the detailed nature of the excess.
Conclusion In this letter we have investigated the possibility that the excess observed in the ATLAS SUSY search in the leptonic-Z + jets + / E T final states is due to pair productions of the VL quark U, which only decays to the first-generation quarks. We find that the excess can be explained within the 2σ (up to 1.4σ) level while evading the constraints from the other LHC searches such as the CMS leptonic-Z +jets+ / E T and ATLAS 2-6 jets + / E T searches. The 2σ preferred range of the VL-quark mass and branching ratio of the Z-boson involving decay are 610 M U 760 GeV and Br(U → Zu) 0.3-4.5 (depending on the decay modes of the VL quark), respectively. The / E T , H T and jet-multiplicity distributions predicted by the VL-quark model show marginal agreements with those of the ATLAS excess. In conclusion, there is room for VL quark models to explain the ATLAS on-Z excess, and upcoming results from the 13 TeV LHC would confirm or refute the VL quark interpretation of the excess.