Probing triple-W production and anomalous WWWW coupling at the CERN LHC and future \( \mathcal{O}(100) \) TeV proton-proton collider

Journal of High Energy Physics, Mar 2015

Triple gauge boson production at the LHC can be used to test the robustness of the Standard Model and provide useful information for VBF di-boson scattering measurement. Especially, any derivations from SM prediction will indicate possible new physics. In this paper we present a detailed Monte Carlo study on measuring W ± W ± W ∓ production in pure leptonic and semileptonic decays, and probing anomalous quartic gauge WWWW couplings at the CERN LHC and future hadron collider, with parton shower and detector simulation effects taken into account. Apart from cut-based method, multivariate boosted decision tree method has been exploited for possible improvement. For the leptonic decay channel, our results show that at the \( \sqrt{s}=8(14)\left[100\right] \) TeV pp collider with integrated luminosity of 20(100)[3000] fb−1, one can reach a significance of 0.4(1.2)[10]σ to observe the SM W ± W ± W ∓ production. For the semileptonic decay channel, one can have 0.5(2)[14]σ to observe the SM W ± W ± W ∓ production. We also give constraints on relevant Dim-8 anomalous WWWW coupling parameters.

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Probing triple-W production and anomalous WWWW coupling at the CERN LHC and future \( \mathcal{O}(100) \) TeV proton-proton collider

Received: July Probing triple-W production and anomalous WWWW coupling at the CERN LHC and future proton-proton collider Yiwen Wen 0 1 2 5 Huilin Qu 0 1 2 5 Daneng Yang 0 1 2 5 Qi-shu Yan 0 1 2 3 4 Qiang Li 0 1 2 5 Yajun Mao 0 1 2 5 Open Access 0 1 2 c The Authors. 0 1 2 0 No. 5, Road Yiheyuan, Beijing, 100871 China 1 No. 19(A) , YuQuan Road, Shijingshan District, Beijing, 100049 China 2 Peking University , No. 5, Road Yiheyuan, Beijing, 100871 China 3 College of Physics Sciences, University of Chinese Academy of Sciences 4 Center for High Energy Physics, Peking University 5 Department of Physics and State Key Laboratory of Nuclear Physics and Technology Triple gauge boson production at the LHC can be used to test the robustness of the Standard Model and provide useful information for VBF di-boson scattering measurement. Especially, any derivations from SM prediction will indicate possible new physics. In this paper we present a detailed Monte Carlo study on measuring W W W production in pure leptonic and semileptonic decays, and probing anomalous quartic gauge W W W W couplings at the CERN LHC and future hadron collider, with parton shower and detector simulation effects taken into account. Apart from cut-based method, multivariate boosted decision tree method has been exploited for possible improvement. For the leptonic decay channel, our results show that at the integrated luminosity of 20(100)[3000] fb1, one can reach a significance of 0.4(1.2)[10] to observe the SM W W W production. For the semileptonic decay channel, one can have 0.5(2)[14] to observe the SM W W W production. We also give constraints on relevant Dim-8 anomalous W W W W coupling parameters. proton-proton; collider; Monte Carlo Simulations; Hadronic Colliders 1 Introduction 2 Effective interactions for aQGCs 3.1 3.2 4.1 Cut-based method Multivariate analysis BDT method 3.3 Numerical results Cut-based method Multivariate analysis BDT method 4.3 Numerical results 5 Anomalous W W W W couplings 5.1 aQGC in pure leptonic decay channel 5.2 aQGC in semileptonic decay channel 4 Standard model W W W production in semileptonic decay channel 6 W W W production and aQGC at 100 TeV future pp collider 6.1 Pure leptonic decay channel Semileptonic decay channel 6.3 Anomalous quartic couplings 7 Unitarity safety discussion 8 Conclusion Introduction Since the beginning of the LHC era, no significant deviation from the Standard Model (SM) of particle physics has been observed. Instead, the SM has achieved great success, especially after the recent discovery of a 125126 GeV Higgs boson in both CMS and ATLAS experiments at the LHC [14]. Nevertheless, we still look forward to Beyond Standard Model physics to explain some mysterious facts, such as the existence of dark matter and the electroweak-Plank scales hierarchy problem. Hence, further test on SM and searching for new physics beyond the SM become urgent quests for both theorists and experimentalists. On the other hand, the upgrade of LHC to higher collision energy and luminosity, and the promising plan for future O(100) TeV proton-proton collider, make it possible to measure various rare SM processes, including, e.g. multi-boson productions. To study anomalous bosonic couplings is one possible way to explore new physics. In U(1)Y gauge symmetry. Any presences of anomalous couplings may result in observable deviation from SM. To study vector boson interactions, therefore, can either further confirm the SM and the spontaneously symmetry breaking mechanism, or shed a light on new Extra contributions other than the SM predictions can be induced by possible new physics, which can be expressed in a model independent way by introducing high-dimensional operators which lead to anomalous triple or quartic gauge couplings (aTGCs or aQGCs). The explorations of aTGCs have already been done at the LEP [5, 6], Tevatron [7, 8], and later at the LHC [9, 10] through the dibosons production. Compared with TGCs measurement, triple gauge boson production [1114], though suffered from lower cross sections and complicated final state topology, is essential for testing QGCs. As discussed in refs. [15, 16], it is possible that the QGCs deviate from SM prediction while the TGCs do not. For instance, the exchange of extra heavy boson between vector boson can generate tree-level contributions to four gauge boson couplings while the effect on the triple gauge vertex appears only at 1-loop and is accordingly suppressed [15, 16]. decay at the As to aQGCs, previous Monte-Carlo (MC) and experimental studies have been carried W W W W aQGC via the same sign W W channel [32]. In the next few years, the LHC at CERN will be upgraded with higher center-ofmass energy and luminosity and it is expected that it will set more strict constraints W W W W vertices, Eboli et al. [35] studied on the vector boson fusion (VBF) WW channel This paper will present detailed study on triple gauge boson production via exploring the W W W W anomalous coupling. Our work extends Eboli et al. and Snowmass study as an independent test on triple electroweak gauge boson physics. We begin by introducing the aQGC related effective theory and specifying the effective Lagrangian in section 2, and then present our MC simulation on SM W W W production with pure leptonic decay channel in section 3 and semileptonic channel in section 4. In section 5, we demonstrate the result on the W W W W aQGC study. The W W W production and aQGC at 100 TeV hadron collider analysis will be given in section 6. Unitarity safety on the aQGC limits is discussed in section 7. Finally, we draw our conclusion in section 8. Effective interactions for aQGCs An effective Lagrangian can be constructed in a model independent way for the anomalous gauge invariance. The Lagrangian can be expressed in non-linear or linear representation [15, 20]. Since a higgs boson has been discovered in LHC, it is more preferable to work in the linear context. The lowest order genuine aQGC operators in linear representation are dimension-8 (dim-8). There are three classes of such operators: operators containing only covariant containing only the field strength [35]. In our research, we choose to study the below three dim-8 operators: LS0 = LS1 = LT 0 = parameter associated with the energy scale of the new degrees of freedom. One should note that the effective Lagrangian leads to tree-level unitarity violation at corresponding high energy. Usually, one can adjust the rising cross section by introducing an appropriate form factor. However, the choice of form factor is arbitrary and can be disputable [38, 39]. In this paper, we just present our results with some typical form factor, following the commonly used formalism [16]. represents the form factor cutoff scale. Figures 1 shows the energy scale at which tree-level unitarity would be violated without up to the given energy. The region below the red line is unitarity safe. These bounds are estimated by using the form factor tool available with VBFNLO [37]. The form factor is determined by calculating on-shell vector bosons scattering and computing the zeroth partial wave of the amplitude. As unitarity criterion the absolute value of the real part of the zeroth partial wave has to be below 0.5. The MC simulations are carried out within MadGraph/MadEvent v5 [40]. The effective Lagrangian of W W W W aQGCs are incorporated in MadGraph based on the FeynRules-UFO-ALOHA [4244] framework. The signal and background processes are first generated at parton level by MadGraph [40] and MadEvent [41], and then passed through the interface to Pythia 6 [45] for parton shower and hadronization. The detector simulations are done by using Delphes 3.0 package [46], where we focus on CMS detector 1014 1013 1012 1011 1010 109 108 1014 1013 1012 1011 1010 109 108 (a) Unitarity bounds up to 14 TeV. (b) Unitarity bounds up to 100 TeV. at the 8 and 14 TeV LHC and a combined ATLAS-CMS detector [47] at the future 100 TeV proton-proton collider. Finally, all events are delivered to ExRootAnalysis [48] and analyzed with ROOT [49]. In the analysis step, we use both traditional cut-based method and Multivariate Analysis (MVA) boosted decision tree (BDT) method [50]. The MVA BDT method is carried out under the TMVA package [51] included in ROOT. The characteristic signal of this channel contains three well-defined leptons with total electric charge 1, in association with large missing transverse energy E/ T . Some example the ratio of about 35% and is handled by TAUOLA [52]. Figure 2a involves TGCs and figure 2c involves higgs coupling, both are not sensitive to aQGC. Five main backgrounds are taken into account: W Z (including virtual photon contributions), ttW , ZZ, ttZ and W W Z, where W Z and ttW are dominant. Notice that the 4 leptons final state can be possible backgrounds with one lepton unidentified. In order to improve event generating efficiency, we choose the following pre-selection cuts to generate unweighted events at parton level with MadGraph/MadEvent. (1) PT l,j 10 GeV, (2) E/ T 20 GeV, (4) Rjj > 0.4, Rll > 0.3, Rjl > 0.3, (a) With TGC. (b) With (anomalous) QGC. (c) With higgs coupling. (d) W emission. where R of a particle. For those backgrounds containing unidentified leptons, we do not apply any of the above cuts on leptons in order not to make bias. Meanwhile, in the hard process generation with MadGraph/MadEvent we adopt the CTEQ6L1 parton distribution functions (PDFs) [53] and set the renormalization and factorization scales as default dynamic scales. In Delphes, we consider no pileup and mean 20 pileup scenarios at 8 TeV LHC, no pileup, pileup 50 and 140 at 14 TeV LHC, and 50 and 140 pileup at future 100 TeV protonproton collider. As mentioned before, we present both cut-based method and BDT method to evaluate the feasibility of observing W W W production. Cut-based method In the cut-based analysis step, we apply the following high level cuts: (1) In order to select signal-like events, we require 3 and only 3 leptons in one event, 35 GeV, the rest two leptons PT l > 20 GeV, (3) In order to suppress top quark related backgrounds, we exclude events with b(4) To reject virtual photon production and leptons from hadron decay, we require the invariant mass of lepton pair mll > 12 GeV, (5) The transverse mass of 3 lepton system mT > 300 GeV, (6) Rll > 0.5. We present our analysis in two schemes. scheme 1 (s1): we require at least one pair of opposite-sign same-flavor (OSSF) boson production related samples. Scheme 2 is to further suppress the backgrounds with Z boson leptonic decay. Multivariate analysis BDT method duction. A typical MVA classification analysis consists of two independent phases: the training phase, where the MVA methods are trained, tested and evaluated, and application phase, where the methods are applied to the concrete classification problem they have been trained for. Before going into training phase, we preselect the events with the preselection cuts: (1) 3 and only 3 leptons in one event, the sum of electric charge of 3 leptons should be 1 or 1, (2) E/ T > 25 GeV, (3) Exclude events with b-tagged jet, (4) the mass of arbitrary two leptons mll > 12 GeV, (5) Rll is larger than 0.5. After preselection, we input the following discriminating variables to the TMVA package: Mlll, PTlll , and the mll of the lepton pair with mll closest to MZ . These variables would be used for MVA training. (A) 8TeV LHC with 20 fb1 integrated luminosity (B) 14TeV LHC with 100 fb1 integrated luminosity 0 jet above threshold(Scheme1 0 PileUp) 0 jet above threshold(Scheme2 0 PileUp) 0 jet above threshold(Scheme1 20 PileUp) 0 jet above threshold(Scheme2 20 PileUp) 0 jet above threshold(Scheme1 0 PileUp) 0 jet above threshold(Scheme2 0 PileUp) 0 jet above threshold(Scheme1 50 PileUp) 0 jet above threshold(Scheme2 50 PileUp) 0 jet above threshold(Scheme1 140 PileUp) 0 jet above threshold(Scheme2 140 PileUp) 20 40 60 80 100 120 140 160 180 20 40 60 80 100 120 140 160 180 Numerical results What we are interested in is evaluating the feasibility of observing triple gauge boson PTcujt is the jet reconstructing cut and nj is reconstructed jet number. The purpose of setting this special cut is to suppress more top-quark related background and keeping high signal efficiency at the same time. Compared with the signal process, ttW and ttZ tend to radiate more jets. Furthermore, the hard physics scale is higher and thus one or more jets can be harder than the jets in signal. The significances are shown in figure 3, calculated with eq. (3.1). It is interesting to note that when PTcujt is getting larger, the significance goes higher. This means the cases of no requirement of jet PT have the largest significances (which comes from the statistic increasing). Thus we are not going to apply any jet veto in the following. We list the 8 TeV event numbers for the signal and backgrounds and significances in 14 TeV LHC. We note that Scheme 2 tends to have larger significance than Scheme 1, due to further suppression on WZ background. The results of the two scheme can be combined in future experimental studies. Moreover, the BDT method can gives us some gain but Signif = p2 ln(Q), Q = (1 + Ns/Nb)Nobs exp(Ns). Cross section [fb] Cross section [fb] the LHC with s = 8 TeV and integrated luminosity of 20 fb1. the LHC with s = 14 TeV and integrated luminosity of 100 fb1. In semileptonic decay channel analysis, we use exactly the same simulation framework as in pure leptonic decay channel in section 3. We only consider the most significant case decay. The other opposite charge W boson decays hadronically into two jets. Here three main categories of background processes contribute to this channel: boson. Both electroweak process and QCD process are included, process and QCD process are included, ttW , all decay modes are included. When generating events at MadGraph , we apply the following preselection cuts. (1) PT,j 20 GeV, PT,l 10 GeV. (2) E/ T 10 GeV. (4) Rjj > 0.4, Rll > 0.4, Rjl > 0.4. Cut-based method Note that Backgrounds containing unidentified leptons dont have cuts related to leptons In the cut-based analysis step, the optimized event selection is shown in table 3, where Multivariate analysis BDT method The event preselections before going into training phase of BDT are shown as below: (1) The event contains two and only two reconstructed leptons with PT > 20 GeV and (2) E/ T > 30 GeV, leading lepton PT , E/ T , the invariant mass of two leading jets mjj, distance between the Numerical results Table 4 shows the 8 TeV event numbers for the signal and backgrounds and significances As shown in the table 5, with the pileup increasing, the significance drops rapidly when using cut-based method. It mainly dues to the pileup jets which result in worse jet energy = 2 Cross section [fb] = 2 = 2 (+, +) or (, ) 30 GeV = 2 2, 3 20 GeV 2 30 GeV |mjj mW | 15 GeV 15 GeV the LHC with resolution. Figure 4a shows the jet number distribution from different pileup scenarios. Jet number increases with pileup. Especially, in 140 pileup scenario, most of events contain at least 4 jets, this would make the Njet cut has less efficiency to separate signal from backgrounds. Similarly, in figure 4b, the invariant mass of two leading jets mjj distribution has a broader peak near W boson mass and harder tail in 140 pileup case. This would also reduce the discrimination between signal and backgrounds. In general, unlike the pure leptonic decay channel case, the significance of observing the W W W production in semileptonic channel suffers more contamination from pileup event because it is difficult to identify the jets original source, whether it come from signal or pileup. Anomalous W W W W couplings aQGC in pure leptonic decay channel via MadGraph/MadEvent after preselection cuts mentioned in section 3, can grow quickly with the increase of the absolute values of aQGCs, as demonstrated in figure 5. Furthermore, as shown in figure 6, the aQGCs lead to excesses on the hard tails in various (a) Number of jet. (b) The invariant mass of the two leading jet. Cross section [fb] the LHC with kinematic region. Thus we refine the cuts in both schemes in section 3 to enhance the sensitivity of QGCs without form factor as following, e.g.: (1) E/ T > 350 GeV, (2) The transverse mass of 3 leptons mT > 1 TeV, (3) leading lepton PT > 200 GeV. (1) E/ T > 80 GeV, (2) The transverse mass of 3 leptons mT > 250 GeV, (3) leading lepton PT > 50 GeV. For the form factor case, E/ T and leptons would be softer, thus we refine our cuts as: No form factor, or n = 0 in ff No form factor, or n = 0 in ff 14 TeV LHC with different form factors applied. After all these selection cuts, the significances are calculated and displayed as following as functions of the QGCs fS0, fS1 and fT 0, at the 8 TeV LHC with an integrated luminosity shown in ref. [36], pileup would not affect aQGC measurement at hard kinematic region, thus we produce aQGC samples without pileup mixing. As mentioned in section 3, we category 2 different analysis schemes, but only the more stringent results (Scheme 2) are presented here. The results of 8 TeV LHC and 14 TeV LHC are shown in table 6 and table 7, both with/without form factor results are shown. Compared with the figure 1, for 8 TeV results, even with form factors applied, the aQGC limits are unitarity unsafe. But for 14 TeV results, they are close to unitarity safe region. o r 5 C No form factor, or n = 0 in ff leading lepton PT LHC, with or without aQGCs and form factor. No form factor 1.32 109 2.00 109 5.56 1012 upper limit 1.30 109 2.03 109 5.44 1012 8.74 109 1.08 108 1.30 1010 upper limit 8.87 109 1.17 108 1.21 1010 at 8 TeV LHC via W W W production pure leptonic decay channel with integrated luminosity of 20 fb1. Units are in GeV4. aQGC in semileptonic decay channel After generating event and applying preselection cuts mentioned in section 4, some distrishown in figure 7. The aQGC has more excess at hard tail. Based on this characteristic, to further improve the sensitivity on aQGC, we refine the cuts in addition (2) E/ T > 150 GeV. (2) E/ T > 50 GeV. For the form factor case, E/ T and jets would be softer, thus we refine our cuts as: The aQGC limits for 14 TeV LHC are given in table 8, via W W W production semilep0 100 200 300 400 500 600 700 800ml9ljj0(0GeV) No form factor 1.78 1010 1.79 1010 2.66 1010 2.78 1010 5.80 1013 5.87 1013 2.80 109 3.47 109 3.08 109 4.44 109 1.21 108 1.29 108 1.29 108 1.81 108 4.48 1011 3.46 1011 2.46 1010 1.76 1010 at 14 TeV LHC via W W W production pure leptonic decay channel with integrated luminosity of 100 fb1. Units are in GeV4. One can also compare our results with the previous MC simulation given by Snowmass Collaboration [36] and O. Eboli et al. based on vector boson fusion (VBF) [35], respectively, as shown in table 9. The semileptonic channel results still suffer from bad jet energy resolution. But in pure leptonic channel, due to the optimized selection, we set a more looser limits on QGCs. However, triple W production channel has simpler event topology and populates at different kinematic phase space, thus can present us more information other than VBF channel. production and aQGC at 100 TeV future pp collider We also studied W W W production and aQGCs at 100 TeV future proton-proton collider. The simulation framework is basically the same as in 8 TeV and 14 TeV LHC study. However, at the level of detetor fast simulation, we use the Snowmass combined LHC detector which is a hybrid of CMS and ATLAS detectors [47], using the tracker components from 4.56 1010 4.58 1010 9.46 1010 9.85 1010 2.80 1012 2.70 1012 3.08 109 4.00 109 3.39 109 5.26 109 1.20 108 1.28 108 1.40 108 1.77 108 7.60 1011 6.00 1011 4.03 1010 2.88 1010 at 14 TeV LHC via W W W production semileptonic decay channel with integrated luminosity of 100 fb1. Units are in GeV4. W W W in p.l decay 95% CL with 100 fb1 W W W in s.l decay 95% CL with 100 fb1 99% CL with 100 fb1 Snowmass W W W upper limit lower limit upper limit 1.8 1010 1.8 1010 2.7 1010 2.8 1010 4.6 1010 4.6 1010 2.2 1011 2.4 1011 9.5 1010 9.9 1010 2.5 1011 2.5 1011 1.2 1012 CMS and calorimeter from ATLAS, etc. Effects of average 50 and 140 pileup scenarios will be considered here. Pure leptonic decay channel with 3000 fb1integrated luminosity. the same as the studies of LHC in section 3 and 5. The event numbers for the signal, backgrounds and significances are listed in table 10. One can see that it reaches a significance of Semileptonic decay channel Unlike the LHC, in 100 TeV proton proton collider, the pileup contamination in semileptonic channel is more severe. Therefore, we optimise the event selection cuts again (most of them are related to jets) (see table 11). We only consider those jet in the tracker re Anomalous quartic couplings We also wish to explore the potential of probing aQGC at 100 TeV collider. The event selections of aQGC is basically the same as in section 5. We list the results of both pure leptonic and semileptonic channel in table 13 and table 14. Cross section [fb] 92185 1670 82060 1696 15240 4408 18180 5034 24226 1283 at future proton-proton collider with = 2 (+, +) or (, ) 30 GeV 2 2, 4 |mjj mW | 25 GeV 40 GeV Cross section [fb] at future proton-proton collider with 2.93 1012 3.04 1012 1.30 1012 1.16 1012 3.69 1015 2.97 1015 1.65 109 1.87 109 1.50 109 2.37 109 2.06 108 2.75 108 2.15 108 2.84 108 9.18 1012 6.76 1012 9.90 1011 7.30 1011 at 100 TeV future proton proton collider via W W W production pure leptonic decay channel with No form factor 1.03 1010 1.00 1010 1.93 1010 2.21 1010 2.00 1013 2.00 1013 8.79 1010 1.08 109 1.17 109 2.27 109 2.99 109 3.26 109 5.18 109 7.59 109 3.10 1011 1.60 1011 1.84 1010 6.80 1011 100 TeV proton proton collider via W W W production semileptonic decay channel with integrated luminosity of 3000 fb1. Units are in GeV4. Required Luminosity (f b1) Unitarity safety discussion tables 7, 8, 13, 14 with figure 1, one can see that applying those form factors will not yet lead to unitarity safe, due to lack of luminosity. We provide the needed luminosity estimated based on our analysis in section 6.3 to reach unitarity safety in tables 15 and 16. In general, it needs very high luminosity to reach safe unitarity. Same situation appears be satisfied with a dipole form factor, however, unitarity conserving new physics with a structure more complex than that represented by a dipole form factor is possible [30]. The future upgrade of LHC and the next generation 100 TeV proton-proton collider with higher center of mass energy and luminosity enable measurement of triple gauge boson potential process that can be exploited to test the SM predictions and probe W W W W anomalous coupling exclusively with lower background contamination. In summary, our study shows that at 8 TeV LHC with an integrated luminosity of gain in pure leptonic channel is bigger than semileptonic channel, which may be due to that the QCD backgrounds increase much faster than the pure leptonic background. although less tighter than the previous results from VBF process, however, triple W production channel populates at different kinematic phase space, thus can present us more than Snowmass due to optimized selection cuts. Moreover, it is the first time to study the Acknowledgments This work is supported in part by the National Natural Science Foundation of China, under Grants No. 11475180, No. 10721063, No. 10975004, No. 10635030 and No. 11205008, and National Fund for Fostering Talents in Basic Science, under Grant No. J1103206. Open Access. 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Yiwen Wen, Huilin Qu, Daneng Yang, Qi-shu Yan, Qiang Li, Yajun Mao. Probing triple-W production and anomalous WWWW coupling at the CERN LHC and future \( \mathcal{O}(100) \) TeV proton-proton collider, Journal of High Energy Physics, 2015, 25, DOI: 10.1007/JHEP03(2015)025