Constraining Stealth SUSY with illuminated fat jets at the LHC

We investigate the discovery potential of a Stealth SUSY scenario involving squark decays by reconstructing the lightest neutralino decay products using a large-radius jet containing a high transverse momentum photon. Requirements on the event topology, such as photon and large-radius jet multiplicity result in less background than signal. We also estimated the sensitivity of our analysis and found that it has a better exclusion potential compared to the strongest existing search for the specific benchmark points considered here.


Introduction
Among the existing beyond-the-Standard-Model (BSM) scenarios, supersymmetry (SUSY) is the leading theoretical framework that explains unresolved questions in the Standard Model such as the large hierarchy between the weak scale and the Planck scale [1,2,3,4]. Hence, it is extensively being probed at the Large Hadron Collider (LHC). However, after collecting data for more than eight years, no searches in favor of SUSY has yet been found [5,6,7,8,9,19]. Even in full models, the limits on the SUSY parameter space are rather strict [10,11,12,13,14,15,16,17,18]. As a consequence, some proponents of SUSY begin to wonder if the framework should be abandoned altogether.
In order not to abandon the appealing ideas of SUSY, models known as Stealth Supersymmetry were introduced so as to evade existing standard SUSY searches [20]. These searches typically rely on a large amount of missing transverse energy ( / E T ) [5,6,7,8], an approach motivated by R-parity which when preserved means that the lightest superpartner (LSP) is stable and contributes to missing energy. Therefore, Stealth SUSY scenarios seeks to reduce this / E T as much as possible [20,21,22]. The simplest Stealth SUSY model does this by making the standard LSP take on a new role as the lightest "visible sector" SUSY particle (LVSP) which decays into a lighter hidden sector SUSY particle. The mass Email address: mflores@nip.upd.edu.ph (Marvin Flores) configuration is setup such that the boson and fermion of the hidden chiral supermultiplet are almost degenerate so that when the former decays to the latter, it leaves little phase space for the true LSP to carry energy, thereby producing signatures of low / E T . In this paper, we study the above scenario by considering a particular toy model with a specific decay chain given bỹ whereχ 0 1 , the lightest neutralino (hereafter referred to as a "bino"), plays the role of our LVSP, andS is our hidden SUSY particle, being the fermionic "singlino" superpartner of the singlet S , with the gravitinoG playing the role of our LSP. The presence of a high-p T photon is significant since it allows us to reconstruct the bino LVSP peak by searching for a pair of large-radius jets containing a high-transverse momentum photon, that is, mχ0 1 ≈ M(γgg), something that has not been used in experiments so far. This was first pointed out in Ref. [20] whereby "illuminating" a jet (i.e., having a highp T photon inside it) renders the stealthiness weaker. We improve upon it by looking at specific event topology and show that imposing additional requirements such as large-radius jet and photon multiplicity result in less background than signal and consequently even stronger exclusion potential, thereby encouraging low-/ E T searches as promising alternatives to the usual high-/ E T ones that were performed at the LHC to look for SUSY.
During the preparation of this paper, CMS released a preliminary result [34] that targets the same final state we are considering (i.e., γgg) in a large-radius jet similar to the analysis employed in this paper although they considered gluino pair production instead of squarks that we consider here. This marks the third LHC search dedicated in probing Stealth SUSY. Whereas the former two searches relied on isolated photons [35,36], the most recent one now relies on collimated photons and gluons.
This paper is arranged as follows: Section 2 introduces the theory behind Stealth SUSY models and also motivates our specific toy model. Section 3 then explains the details of the numerical simulations and analysis as well as our results involving the reconstructed bino LVSP at various benchmark points. Finally, we draw our conclusions in Section 4.

Stealth Supersymmetry
Many searches for new physics are reliant on large missing transverse energy ( / E T ) [5,6,7,8] so a promising approach to avoid strong exclusion limits from these searches is to reduce / E T as much as possible. One such approach is R-parity violation [27,29] where the LSP is unstable and its decay products may be subject to detection. However, less missing transverse momentum is produced on average [26,28].
On the other hand, we have R-parity-preserving models such as the so-called compressed SUSY models with little net / E T [30,31,32], as well as models known as Stealth SUSY which is a genuine reduction of / E T due to having light LSP that carries little energy.
In this section, we discuss simplified stealth models relevant to our phenomenological study. More indepth discussions can be found in [20,21,22]. Stealth SUSY models typically involve the introduction of a hidden/stealth sector although it was pointed out in [37,38] that such a stealth sector is not needed. One could setup the necessary mass configuration in nextto-minimal supersymmetric Standard Model (NMSSM) by making the bino NLSP decay invisibly into a singlino LSP plus a singlet.
The main and crucial point with these stealth scenarios is that the hidden SUSY is almost unbroken. Thus the singlino and its singlet partner are mass degenerate, with the latter almost filling the mass gap between the singlino and the LSP. As a consequence, very little / E T will be expected.
In order to achieve the stealth mechanism, we follow the model in [20] and imagine that the LVSP can decay to a hidden sector field via some portal. Then, a decay chain within the hidden sector can occur ending with a massive R-odd stealth particle decaying to a nearly degenerate R-even state plus a light R-odd state. The R-even state must then decay into visible SM particles. In the simplest case, the hidden sector is taken to be a gauge singlet multiplet with a fermionS and an almost degenerate scalar S while the lightest superparticle in the spectrum is a gravitino.
One appropriate portal for the LVSP (in our case taken to be the bino) going to the stealth sector to proceed is via vector-like states Y,Ȳ charged under SM and a S YȲ coupling as discussed in [21] through the superpotential where m and m Y are the supersymmetric masses and λ is the coupling between the singlet chiral superfield S and the messenger field Y. This can induce a one-loop bino-photon-S vertex allowing bino decays intoS while radiating off a photon, as well as inducing decays of a scalar S to gluons as can be seen in Fig. 1. This grants us to consider a specific stealth decay chain shown in Fig. 2 enabling us to search for resonances composed of a photon and a pair of jets arising from the gluons to reconstruct the bino LVSP.
It should be noted that initial attempts where made to reconstruct the squark itself via M(γggq) ≈ mq but then we found that we would have to define jets with extremely large radius at around R = 2.0. Unfortunately, no experiments use large jets of this radius so we settled for the bino reconstruction instead.

Numerical Analysis and Results
We generated 20, 000 events for squark pair production with Pythia 8.235 [39] at the center-of-mass energy 13 TeV using the NNPDF 2.3 QCD+QED LO parton distribution function set [40]. We used a modified decay table where we assumed a branching ratio 1 equal to 1 for each of the decay in the chain given in Eq. 1 as well as having the following masses: the gluino mass is fixed at mg = 3000 GeV while the squark mass mq is varied in steps of 50 GeV from 1450 to 2000 GeV as well as the bino mass mχ0 1 in steps of 50 GeV from 250 to 400 GeV. The singlino and singlet masses are kept at mS = 100 GeV and m S = 95 GeV respectively with δm = 5 GeV. The respective production cross sections were obtained using NNLLFast 1.1 [41], but reduced by a factor of 4/5 since we are only considering the first two generations of squarks while NNLLFast sums over all flavours of final-state squarks including both chiralities, except for stops. The cross section of our signal ranges from 0.028 pb for mq = 1450 GeV down to 0.0033 pb for mq = 2000 GeV. CheckMATE [42,43,44] then tests all model points against existing LHC searches at √ s = 13 TeV to see which benchmark scenarios evade them.
To determine whether a point is excluded by a search or not, CheckMATE compares the estimate of signal events with observed limits at 95% C. L. of the search using where s denotes the number of signal events, ∆s the uncertainty of MC events considered only to be the statistical uncertainty, ∆s = √ s. The value of r is then calculated for every signal region of every search. In order to calculate the best exclusion limit, the "best" signal region is chosen as the one with the best expected 1 The branching ratios are intentionally simplified this way rather than calculated from a complete theory because we want to focus on the phenomenology of the final state γgg and see whether we can construct resonances from this specific topology. However, typical branching ratio of bino into photons and singlino can be of the order 10 −3 [20] but we assume this to be equal to unity for our simplified SUSY model since in certain region of parameter space BR(χ 0 1 → γ +S ) ∼ O(1) is possible [38]. exclusion potential. One can then define a point as excluded when r > 1. However, due to the fact that we do not control higher-order corrections or systematic errors, this calls for a definition of a region where exclusion is inconclusive and we define this to be the case when 0.67 < r < 1.5. That is, when one of the points falls within the range of these r-values, we cannot tell whether it is excluded or allowed. Accordingly, we define a point as allowed whenever r < 0.67 and excluded when r > 1.5.
We show an exclusion plot that determines which pairs of mq and mχ0 1 are allowed, excluded or ambiguous (shown as the green, red and yellow areas respectively), which can be seen in Fig. 3.
With the chosen benchmark points in Fig. 3, we perform our analyses using the Rivet 2.6.0 analysis toolkit [45]. The jets are clustered using FastJet 3.3.1's anti-k T algorithm [46] having R = 1.0. These large-radius jets are then trimmed [47] with p T > 450 GeV and |η| < 1.5 (these will be our large-radius jets).
Before moving on to study our signal, we made sure that the photon will indeed be contained within the large-radius jet. This of course happens when the topology is boosted. We show this by plotting the ∆R separation of the nearest photon to the leading-mass largeradius jet versus that jet's momentum. As can be seen in Fig. 4, the photon is inside the large-radius jet (i.e., ∆R < 1) whenever the jet (which contains the decay products of the bino) is boosted. We then proceeded to study the various kinematic properties of our signals by looking at distributions such as the large-radius jet multiplicities, number of smallradius jets (R = 0.4) inside the large-radius jets, / E distribution, invariant mass distribution of the leading-p T and leading-mass large-radius jet, p T distribution of the leading photon, as well as the φ distribution between the two leading photons and large-radius jets.
In the end, we included a lepton veto and then selected events whenever the following requirements are satisfied: (i) the photon (with cuts p T > 200 GeV and |η| < 2.0) multiplicity is greater than 1; (ii) the leadingmass large-radius jet ( j 1 ) contains its nearest photon (γ) (i.e., when ∆R j 1 ,γ < 1). We then plot the mass distribution of the leading-mass large-radius jet whenever its large-radius jet multiplicity is greater than 3. The combination of these three criteria (summarised in Table 1) turns out to be a strong discriminator against the background (the simulation of which is discussed below) as evidenced by Fig. 5.
We also tried using jet substructure variables [48,49] on our large-radius jets to improve the signal over background. These include the LHA (Les Houches angularities) [50], Nsubjettiness [51], ECF (Energy Correlation Function) and C 2 (double ratio of ECFs) [52]. We found that these substructure variables are not very helpful in  our case mainly due to the fact that introducing cuts on these variables reduces our few remaining signals even further after our main cuts have been implemented. Standard Model background comprised of multijets were generated (5 × 10 6 events) using Pythia 8.235 with a minimum invariant p T of 300 GeV. The simulated multijets background has a cross section of 8.53 nb. We checked that the background event simulation is consistent with matched events from MadGraph 2.6.5 [53] + Pythia 8 as well as POWHEG V2 [54,55,56,57] + Pythia 8. We also tested γ+jets, W+ jets, and Z+ jets whose contribution to the background turned out to be negligible after all the relevant cuts have been implemented. These can be seen in the cutflow table shown in 2. Here, the multijets background is clearly the most significant background in the signal region we are looking at. We also investigated tt + Z, tt + W, Z + γ as well as W + γ background channels but their contributions   are negligible as well. For the fake rate, we are only concerned about a jet being misreconstructed as a photon from one of the background samples, thereby pushing an event which would not otherwise count as a real background for lack of a photon in our signal region. Now this is impossible to do at generator level, but one can try to get an estimate from already published analysis what fraction of high p T photons in data can come from fakes. For example, reference [58] say the effect is at most 10%. The mass distributions of the benchmark points as well as the background were then normalised to their respective production cross sections using a total integrated luminosity of 150 fb −1 which roughly corresponds to Run 2 of LHC. Two such distributions are shown in Fig. 6 for the specific benchmark point with mχ0 1 = 250 GeV and mq = 1650 GeV as well as mχ0 1 = 315 GeV and mq = 2000 GeV. It can be seen that our large-radius jet selection criteria reduces the background below the signal. Even with a realistic reconstruction and trigger efficiency of 50%, we would still have enough signal events left. An experimentally similar final state, requiring an electron inside a large-radius jet was probed in ATLAS boosted heavy neutrino search [23] confirming the feasibility of our method. References [24,25] also looked at jets formed exclusively from high pT photons.
For the parameter space we have scanned, it turns out that the atlas 1802 03158 2 analysis [5] is always the strongest search. It is clear from Fig. 6 that our analysis performs better than this particular search for the 2 This particular search with an integrated luminosity of 36.1 fb −1 is motivated by the gauge-mediated supersymmetric breaking (GMSB) models where the final states that contain large values of / E and photons are present. Their search is divided into two regions: (i) diphoton events with large missing transverse energy; (ii) events with missing energy and the presence of one isolated energetic photon. The search is meant to cover gluino, squark and wino/higgsino production and their subsequent decays to NLSP that could decay into a gravitino and a photon or a Z boson. For the mass distribution shown in Fig. 6, the sensitivity (scaled down to correspond to an integrated luminosity of 36.1 fb −1 ) is given by 4.85 (2.58) for the bench- . Even if we scale up our multijet contribution by 10% from the effect of the fake rate mentioned earlier, our resulting sensitivity is roughly similar. Compare this to the 1.48 (0.92) sensitivity from the ATLAS search also corresponding to an integrated luminosity of 36.1 fb −1 . In other words, these benchmark points are clearly excluded by our analysis at 36.1 fb −1 . Fig. 7 shows our sensitivity for various squark masses, including 10%, 20% and 50% systematic errors introduced on the background. Even with a systematic error of 50%, the sensitivity of our analysis is still greater than the most sensitive ATLAS search. Since the location of the bino resonance is not determined by SUSY theory, the estimate of significance for our peaks (e.g., in Fig. 6) is only the local significance.

Conclusion
To summarise, we have investigated a Stealth SUSY scenario which reduces the missing transverse energy and reconstructed the bino resonances. We looked at various distributions and kinematic properties of our signal such as the large-radius jet multiplicities, number of small-radius jets (R = 0.4) inside the large-radius jets, / E distribution, invariant mass distribution of the leading-p T and leading-mass large-radius jet, pT distribution of the leading photon, as well as the φ distribution between the two leading photons and large-radius jets. In the end, the set of selection criteria that reduces the background below the signal are few and simple. We found that by requiring a high-transverse momentum photon within our large-radius jet, as well as pho-ton and large-radius jet multiplicities to be greater than 1 and 3 respectively, we were able to reconstruct the bino mass, mχ0 1 ≈ M(γgg). We also considered the jet substructure variables of our large-radius jet in order to improve our signal even further but we found that the effects these variables have are not that helpful.
For illustration, we did a simple sensitivity calculation of our signal over background and compared against the strongest existing search and found that our analysis has a better exclusion potential for two benchmark points considered in this letter.