Sgluons in the same-sign lepton searches

In this work I present the interpretation of the ATLAS search of same-sign lepton production in association with $b$-jets in the context of the 4-top quark signal from sgluon decays. I show that using just 3.2/fb data sample from Run 2 the exclusion limit is already competitive with the Run 1 one. Public data allow to exclude sgluons with masses up to 0.95 TeV. Prospects for the total Run 2 integrated luminosity of 100/fb are briefly discussed.


Introduction
With the Large Hadron Collider (LHC) delivering data at an unprecedented energy of 13 TeV a lot of work has been devoted to their interpretation in the context of BSM physics. For the time being, the main focus is on the Minimal Supersymmetric Standard Model (MSSM) or the so-called exotics. This of course leaves a lot of interesting models out. From the viewpoint of supersymmetry, this is a serious limitation. Recent years brought a lot of attention to the extended SUSY models, from simple extensions, like the NMSSM, to models with an extended QCD sector like, for example, various models with Dirac gluinos. Studies proved that MSSM bounds are in many cases not applicable to these models [1]. On the other hand, 13 TeV data might be already more constraining than the 7 and 8 TeV one, even though the collected integrated luminosity is smaller. This then raises an important question about the validity of such models in light of new data.
Especially interesting are the multi top-quark processes which, while characterized by a high mass scale, enjoy a big boost when going from 7 or 8 to 13 TeV. The 4-top quark final state was already searched for by ATLAS [2][3][4][5] and CMS [6][7][8] at Run 2. In the MSSM this kind of final state may appear as decay products of 3rd generation stops (produced either directly or as decay products of intermediate gluinos). In general SUSY models the resonance structure might be quite different, though. One might for example expect a two body decay of a new color resonance directly to a tt pair. This is a general feature of models containing color octet (EW-singlet) scalars, commonly dubbed sgluons. Their LHC phenomenology was previously investigated in the context of R-symmetric/N = 2/Dirac gaugino SUSY models, hyper-pions in vector-like confinement gauge theories and universal extra dimensions [9][10][11][12][13][14][15][16][17][18][19][20].
Within the framework of the MRSSM [21] sgluons are expected to decay, depending on theirs mass, mainly into gluons or top quarks. This kind of signatures, in both channels, were searched for by the experimental collaborations in 7 and 8 TeV data. ATLAS excludes at 95% CL pair produced, complex sgluons decaying (with branching ration 1) to gluon pair in mass range from 100 to 287 GeV [29]. For tt decay mode, sgluons are excluded at 95% CL up to 1.06 TeV [30]. It should be noted though, that these exclusions are based on the simplified model with a complex sgluon from Ref. [31] while in the MRSSM the cross section is roughly 2 times smaller. 1 At the time of writing there are no 13 TeV analyses addressing directly sgluon pair production. Therefore, all mentioned exclusions come from Run 1. This makes any projections for the target Run 2 integrated luminosity very difficult. To fill this gap, this work recasts current ATLAS limits from search of SUSY in the 4-top quark final state in Ref. [2] to sgluon pair production.
The paper is structured as follows. The next section describes and motives the effective sgluon model used in this work. Section 3 presents NLO cross sections for the sgluon pair production. In section 4 the setup for the Monte Carlo simulation is described. Section 5 then describes the parametrization of the detector response and the encoded ATLAS analysis. The reproduced analysis is then validated on the associated production of top quark pair and a gauge boson, comparing predicted numbers of background events with the ones quoted by the ATLAS work. The analysis is then applied to the signal events. The work finishes with the derivation of the limit on the sgluon mass and prospects for this limit for the predicted 100 fb −1 data sample of Run 2.
2 Description of the model I work in the framework of a simplified model inspired by the MRSSM scenario in which all the superpartners but the CP -odd sgluon are heavy. The Standard Model (SM) gets extended by a real color-octet (EW-singlet) scalar O. It couples exclusively to gluons and top quarks as given by the Lagrangian where D µ is the SU (3) C covariant derivative and sum over the color index a is understood. This is motivated by the MRSSM particle spectrum in which a complex sgluon field gets split into CP -even and odd components through a D-term SUSY breaking contribution [24]. Since physical gluino mass, which at the tree-level is exclusively controlled by the M D O , must be 1 TeV this implies that either pseudoscalar sgluon is very light and scalar one is in a TeV range or, if pseudoscalars mass is around 1 TeV, a scalar one will be in the multi-TeV range. Here I focus on the latter scenario extending the SM with a pseudoscalar sgluon which for simplicity I denote just by O (without the A subscript).
Since in the MRSSM sgluon carries an R-charge 0, once produced it can decay to SM particles. The lowest order coupling to quarks is loop-induced as show in Fig. 1. The coupling to gluons vanishes for pseudoscalar sgluons while the coupling to quarks is proportional to quark mass due to chirality. Pseudoscalar sgluons with mass m O A 2 m t and smaller than other color-charged SUSY particles will therefore decay almost exclusively to top quarks with the coupling of the form written in Eq. 2.1. This also motivates why I do not consider a single sgluon production through (loop-induced) coupling to partons. This occurs mainly through coupling of gluons to the CP -even one, which is significantly heavier than the CP -odd one and whose production is additionally suppressed by a small value of the loop-induced coupling.
It should be noted though that the effective model described by the Lagrangian from Eq. 2.1 is quite generic and can come from a multitude of complete, high scale theories. Different models would then by characterized by a different chiral structure of the coupling c, though.

NLO QCD corrections to sgluon pair production
For the Lagrangian of Eq. 2.1 sgluons are produced at the LO through Feynman diagrams in Fig. 2. The corresponding partonic cross sections are 3 : whereŝ ≡ (p q + pq) 2 or (p g + p g ) 2 and β is sgluon's velocity in the center of mass system of colliding partons.
The first calculation of higher order corrections to the sgluon pair production was done in Ref. [31] for a simplified model with a complex sgluon. Since Ref. [20] a general procedure for obtaining NLO capable UFO [32] models for MadGraph5_aMC@NLO [33] using conjunction of FeynRules [34], NLOCT [35], FeynArts [36] and FormCalc [37] became available. In Ref. [20] this procedure was applied to, among others, obtaining an NLO model for a real sgluon field. Since the original model, available under https://feynrules.irmp.ucl.ac. be/wiki/NLOModels, does not work for the complex coupling ıc as in Eq. 2.1, a new model (this time in 5-flavor scheme) was generated and used for the analysis below. 4 Table 1 lists values of cross sections obtained with this model for 5 selected sgluon massed: 1, 1.25, 1.5, 1.75 and 2 TeV, for 13 and 14 TeV LHC. Numbers were obtained using the MMTH2014 baseline (5-flavor) NLO fit (MMTH2014nlo68cl) [38] interfaced through LHAPDF6 [39]. The K-factors listed in the table are defined as K ≡ σ NLO /σ LO and refer to the LO calculation with MMTH2014 baseline LO fit with α s (m Z ) = 0.135 and up to 5 active flavors (MMTH2014lo68cl). For the sgluon with mass of 1 TeV one expects more than 100 events already with the publicly available data sample of 3.2 fb −1 . Figure 3 shows the plot of the cross section as a function of the sgluon mass together with uncertainty bands for the K-factor coming from the PDFs (middle subplot) and variation of renormalization/factorization scales by a factor of 2 (bottom subplot). The central values of renormalization and factorization scales are set equal to the sgluons mass while m t = 173 GeV.
Results of an automated MadGraph5_aMC@NLO calculation were cross-checked with an independent computation based on FeynArts, FormCalc and the two-cut phase space slicing (TCPS) method [40]. The details of this computation will become available in a separate publication [41]. For the full description of the TCPS method with its application to the calculation of (S)QCD corrections to squark pair production in the MRSSM I also refer to the forthcoming publication [42].   1.45 Table 1: Cross sections for the sgluon pair production for 13 and 14 TeV LHC as a function of the sgluon mass (see main text for more details). First error comes from the scale variation, second is the PDF uncertainty (evaluated over PDF eigenvectors using hessian method). Relative statistical errors are below 10 −3 and not shown here. Column K gives global K-factors.

Signal
Signal events were generated using MadGraph5_aMC@NLO v2.4.2 and an NLO capable UFO model. For the analysis sgluons masses in the range 0.9 -1.5 TeV were considered. Renormalization and factorization scales were set equal to the sgluon mass. Sgluons were then decayed into tt pairs (and further) using MadSpin [43] generating all configurations that give two same-sign muons. All spin correlations were preserved (at the LO). Total branching ratio into these channels is given by Partonic events were matched to parton shower using MC@NLO [44] prescription and Pythia8 [45] v219. Pythia8 settings needed for consistent showering of MC@NLO events are described in Appendix A. Since there are no genuine NLO underlying event tunes in Pythia8, the default LO tune was used.

Background validation
Background samples were generated using Sherpa v.2.2 [46], with virtual matrix elements provided by OpenLoops v1.3.1 [47] and evaluated using CutTools [48,49] or COLLIER [50][51][52][53]. ttµν µ (i.e. including µ −ν µ and µ + ν µ combinations) events were generated with up to 1 additional jet at NLO order and 3 jets at LO, while for ttµ + µ − up to 1 and 2 jets, respectively, were generated. Different multiplicities were merged using the MEPS@NLO technique [54,55]. In case of ttµ + µ − a generation cut on an invariant mass of the muon pair m µ + µ − > 20 GeV was applied. Top quarks were then decayed in all ways that ensure two same-sign muons with spin correlations preserved at the LO as in the case of MadSpin. The inclusive cross sections for those samples (including appropriate top-quarks decays) are 7.77 and 5.43 fb, respectively. These predictions agree within (still very large) experimental uncertainties with the LHC measurements [56, 57].
The setup of Sherpa mostly follows standard settings. Here only the most important ones are mentioned. Samples were generated with EXCLUSIVE_CLUSTER_MODE = 1 setting (meaning that only QCD splittings are considered when reconstructing parton shower history) to ensure that ttµν µ /ttµ + µ − is always identified as the core process. Since ATLAS   Table 3: Final result of analysis (last column of Table 2) after multiplying by 3.2 fb −1 of integrated luminosity and roughly a factor of 4 to account for all possible leptonic channels taken into account in the ATLAS analysis [2] compared to column SRb3 of Tab. 5 of that analysis.
analysis uses jets with p T > 20 GeV, the merging cut was set to 15 GeV. Also, a default scale definition for the core process was used.

Recasting current ATLAS 13 TeV analysis
The ATLAS analysis of Ref. [2] targeted topologies with 2 same-sign leptons or 3 leptons, looking at 4 different signal regions. In case of the production of sgluon-pair which then decays to top-quark pairs the interesting signal region is SR3b defined in Table 1 of [2]. To match experimental data as closely as possible, the detector response was parametrized using Delphes [58] v3.3.2.
The following list gives a summary of Delphes detector card settings 5 and applied cuts: 1 Muons are identified with the efficiency of 95% if they have p T > 10 GeV and |η| < 1.5 and 85% if 1.5 < |η| < 2.7. Candidate muons are required to have p T > 20 GeV and |η| < 2.5. Candidate muons must also be isolated, that is have the scalar sum of the p T of tracks within a variable-size cone around the lepton, excluding its own track, less than 6% of the muon p T . The isolation cone size is taken to be the smaller of 10 GeV/p T and 0.3 (where p T denotes the muon's transverse momentum). 6 2 At least 3 b-tagged jets reconstructed using anti-kt algorithm [59] from FastJet [60,61] with p T > 20 GeV and |η| < 2.5 are required. Jets are b-tagged if they are within ∆R jb < 0.3 of a b-quark which had p b T > 5 GeV and |η b | < 2.5 with an efficiency [62] b-tagging efficient = 24 tanh(0.003 · p T ) 1 + 0.086 · p T (5.1) Jet energy scale correction is applied according to the formula 7 3 Effective mass m eff of the event, defined as a scalar sum of p T of signal leptons, b-jets and missing E T , must satisfy m eff > 650 GeV. The m eff spectra for the signal and ttµν, ttµ + µ − backgrounds are shown in Fig. 4.

T
> 125 GeV Table 2 shows the cross sections (in fb) for different processes passing this sequence of cuts (cuts are stacked, that is a cut in the n-th column also implies that cuts in n − 1 first columns were applied). Table 3 then compares final numbers of background events, that is after multiplying last column of Tab. 2 by 3.2 fb −1 of integrated luminosity and roughly a factor of 4 to account for all possible leptonic channels taken into account in the ATLAS analysis, with the column SRb3 of Tab. 5 of Ref. [2]. The fact that the simplified analysis based on Delphes predicts roughly the same number of events for background coming from ttµν µ /ttµ + µ − production as ATLAS one is a check of its implementation. Since a significant contribution to the background comes from elements which cannot be reliably simulated by Monte Carlo, like fake/non-prompt leptons and charge flips, the cuts used in the definition of SR3b could not be adapted. To check the separating power of those cuts on the sgluon signal a plot after cuts on same-sign muon pair and number of b-jets was done. Figure 4 shows the spectrum of the effective mass for two sgluons masses: 1 and 1.25 TeV and backgrounds from ttµν µ and ttµ + µ − . It is clear that cut of m eff > 650 GeV used in the ATLAS analysis does also a good job in separating background from the sgluon signal. For completeness I also show the numbers for background and signal events after effective mass cut but before the cut on missing E T . They are compared with original ATLAS plot in Fig. 5 together with superimposed signal from 1 TeV sgluon. The 95% CL observed upper limit on the number of signal (BSM) events in the SR3b is 3.8. The predicted number of signal events for selected sgluon masses are given in Tab. 3. The ATLAS limit corresponds then to sgluons of mass in the range 0.9 < m O < 1 TeV. To facilitate reading of its precise value, predicted numbers of signal events are plotted in Fig. 6 together with the interpolation between them. From this, sgluon masses < 0.95 GeV 6 Delphes Isolation module was modified to allow for a variable isolation cone size. 7 JES is applied before the requirement of pT > 20 GeV.   Figure 6: Predicted number of observed signal events as a function of the sgluon mass (blue points). Solid line shows interpolation between these points. Red region is excluded by ATLAS for SR3b at 95% CL. Interpreted in the context of sgluon production it corresponds to a lower limit on the sgluon mass m O 0.95 TeV.
The ATLAS experiment is supposed to gather 100 fb −1 of integrated luminosity by the end of Run 2, roughly 30 times more than what is available currently. Since statistical significance scales like a square-root of integrated luminosity, numbers in Tab. 3 suggest that even without further exploiting event kinematics and adapting cuts it should be possible to exclude (or discover) sgluons with masses up to 1.25 TeV by the end of Run 2.

Conclusions
In this work I recast current ATLAS exclusion limits coming from the search of 4-top quark final state in events with same-sign leptons to the case of sgluon pair production. Although sgluons decay to a top-quark pair without (typical in SUSY theories) presence of the invisible LSP assumed in the ATLAS analysis, cuts used turn out to work well also in this case. Currently published data allow therefore to exclude sgluons with masses 0.95 TeV, a result already on par with the 8 TeV exclusions. Just from the increased statistics it should be therefore possible to push this limit up to 1.25 TeV by the end of Run 2. Of course with an increased statistics experimental collaboration will be able to adapt the selection criteria to further exploit sgluon kinematics, pushing this exclusion even further. We therefore encourage experimentalist to look into this.

A Pythia8 technical setup
By default the final state shower algorithm in Pythia8 is based on the dipole-style recoils. As stated in Pythia8 manual, for MC@NLO where a full analytic knowledge of the shower radiation pattern in needed one has to switch to global recoil approach which does not contain color coherence phenomena (and hence factorizes). A minimal set of settings needed to consistently shower MC@NLO events is then given by 8 SpaceShower:pTmaxMatch = 1 SpaceShower:pTmaxFudge = 1. SpaceShower:MEcorrections = off TimeShower:pTmaxMatch = 1 TimeShower:pTmaxFudge = 1. TimeShower:MEcorrections = off TimeShower:globalRecoil = on TimeShower:weightGluonToQuark = 1 Those settings cannot be modified. What can be chosen, though, is when to return from the global recoil mode to the dipole recoil. Since color coherence phenomena are very important (see for example [64]), it is advantageous to switch back to dipole recoils already after the first emission. This can be done in two ways, setting TimeShower:globalRecoilMode = 1 or 2. Option 2 applies global recoil only if the first branching in evolution is a timelike splitting of a parton in an event with Born-like kinematics (the so called S-events in the MC@NLO language), while for option 1 this is done both for Born-like (S) and real-emission events (H-events). With option 2 the impact of global recoil should be minimal. For options 1 and 2 a maximal number of splittings in the timelike shower with global recoil strategy should be set to 1 through TimeShower:nMaxGlobalBranch flag. Also, to distinguish between S and H events, the number of color-charged particles for Born-like configurations must be given through TimeShower:nPartonsInBorn option. The MC@NLO matching is done at the level of the hard process. To that end, Pythia8 removes decay chains generated by MadSpin by traversing the event tree and identifying intermediate particles with status code ISTUP=±2 [65] which have a single parent. TimeShower:nPartonsInBorn then counts the number of remaining color-charged particles. For the sgluon pair production I therefore set: TimeShower:globalRecoilMode = 2 TimeShower:nMaxGlobalBranch = 1 TimeShower:nPartonsInBorn = 2 TimeShower:limitPTmaxGlobal = on 8 See Pythia8 manual at http://home.thep.lu.se/~torbjorn/pythia82html/Welcome.html, section Link to Other Programs → Matching and Merging → aMC@NLO Matching. See also the discussion in Ref. [63].