Studying the sensitivity of monotop probes to compressed supersymmetric scenarios at the LHC

We investigate the sensitivity of the Large Hadron Collider to supersymmetric setups using monotop probes in which the signal is a single top quark produced in association with missing transverse energy. Our prospective study relies on Monte Carlo simulations of 300 invfb of proton- proton collisions at a centre-of-mass energy of 14 TeV and considers both leptonic and hadronic monotop decays. We present analysis strategies sensitive to regions of the supersymmetric parameter space which feature small superparticle mass splittings and illustrate their strengths in the context of a particular set of benchmark scenarios. Finally, we compare the regions of parameter space expected to be accessible with monotops probes during the next run of the LHC to the reach of more traditional search strategies employed by the ATLAS and CMS collaborations, where available.


Introduction
After more than fifty years of experimental tests, the Standard Model has proven to be a successful theory of elementary particles and their interactions. While it consistently predicts most existing high-energy physics data, it additionally includes a set of conceptual problems for which it does not provide a satisfactory answer. It is therefore widely believed to be the low-energy limit of a more fundamental theory, weak scale supersymmetry [1,2] being one of the most popular and studied setups. By associating a partner of opposite statistics with each of the Standard Model degrees of freedom, supersymmetric theories feature a way to unify the Poincaré symmetry with the internal gauge symmetries and provide an elegant solution to the hierarchy problem, amongst other appealing theoretical features.
Since so far no hint for new physics has been clearly identified, the superpartners of the Standard Model particles are constrained to lie at higher and higher scales [3,4]. Most of these bounds can however be evaded for compressed supersymmetric models where the ensemble of states accessible at the Large Hadron Collider (LHC) exhibit small mass differences. In particular, both the ATLAS and CMS experiments have been found to be insensitive to scenarios with mass gaps of about 10 GeV or less between the strongly interacting superparticles and the lightest superpartner. In these cases, pair-produced squarks and gluinos decay into missing energy carried by the lightest supersymmetric particle and leptons and/or jets too soft to reach the typical trigger thresholds of the LHC experiments. Moreover, the expected amount of missing transverse energy is smaller, which implies first that the kinematic quantities traditionally employed to reduce the Standard Model background are less efficient and second that one cannot even rely solely on missing energy triggers [5,6]. Classical search strategies based on the presence of numerous jets and leptons and a large amount of missing energy thus have poor sensitivity to compressed supersymmetric scenarios. Consequently, non-standard analyses have been developed, making use for instance of monojet or monophoton signatures [7][8][9][10][11][12][13][14][15][16][17]. They focus on topologies where a superparticle pair is produced together with an extra jet or photon that originate from initial-state radiation and can further be used both for triggering and reducing the Standard Model background.
In this work, we explore a novel way to access the compressed regions of the parameter space that relies on monotop probes, i.e., systems comprised of missing transverse energy and a singly-produced top quark. Monotop states are expected to be easily observable at the LHC for a large range of new physics masses and couplings [18][19][20][21][22][23][24], although they have not been experimentally found yet [25,26]. In the framework of simplified compressed supersymmetric scenarios where the electroweak superpartners are neglected (with the exception of the lightest neutralino), events describing the production and decay of a strong superpartner pair in association with a top quark can manifest themselves via a monotop signature, as both superpartners give rise to a small amount of missing energy and soft objects. We illustrate how to benefit from the presence of the final state top quark to gain sensitivity to the initially produced supersymmetric particles, considering both leptonically 1 and hadronically decaying top quarks. We show that by adopting a typical monotop selection strategy, 10 fb −1 of LHC collisions at a centre-of-mass energy of √ s =14 TeV should be sufficient for observing hints of new physics in the context of compressed supersymmetric scenarios. The rest of this paper is organised as follows. In Section 2, we describe our technical setup for the Monte Carlo simulations of LHC collisions at √ s = 14 TeV, both for the new physics signal and the relevant sources of background. Our analysis strategy to extract a monotop signal is detailed in Section 3 and the results for specific benchmark scenarios are presented in Section 4. Our conclusions are given in Section 5.
2 Technical setup for the Monte Carlo simulations

Signal simulation
In our simplified model framework, we consider the production of the lightest top squarkt 1 and the gluinog, that further decay into the lightest neutralinoχ 0 1 . We focus on scenarios in which the stop is a maximal admixture of the left-handed and right-handed stop gaugeeigenstates and the neutralino is assumed to be purely bino. Event generation for the hard scattering signal process relies on the implementation of the Minimal Supersymmetric Standard Model [28][29][30][31] in the MadGraph 5 program [32] that has been used to convolute hard matrix elements with the CTEQ6L1 set of parton density functions (PDF) [33]. We describe in this way the production of a pair of strong superpartners in association with either a leptonically or a hadronically decaying top quark. The decays of the produced superparticles through the (dominant)t 1 → cχ 0 1 andg → qqχ 0 1 modes and matching of the parton-level hard events with a parton shower and hadronization infrastructure has been performed with Herwig++ 2.7 [34,35]. For illustrative purposes, signal cross sections for two examples of compressed spectra scenarios with (mt 1 = mg, mχ0 1 ) = (200, 190) GeV and (110, 50) GeV are given in Table 1.

Background processes
Leptonically decaying monotop states yield event topologies comprised of one hard lepton, one jet originating from the fragmentation of a b-quark and missing transverse energy. As such, the main sources of background events consist of the production of a tt pair where one of the top quarks decays leptonically and the other one hadronically, as well as from the production of a single-top quark in association with a W -boson where either the top quark or the W -boson decays leptonically. We also consider extra background processes expected to subdominantly contribute, namely the two other single-top production modes and W -boson plus jets, γ * /Z-boson plus jets and diboson production.
Turning to hadronically decaying monotops, the above signal final state is altered with the hard lepton being replaced by a pair of hard jets. In this case, background events are dominantly comprised of fully hadronic tt events, Z-boson plus jets events in which the Z-boson decays invisibly as well as W -boson plus light-jets events in which the Wboson decays leptonically but where its decay products escape identification 2 . Additionally, single-top, W -boson plus b-jets and diboson production processes are also expected to contribute, in a subdominant way, to the total number of monotop background events.
In the simulation of the Standard Model backgrounds for both the leptonic and hadronic monotop analyses, QCD multijet production processes have been neglected. We instead assume the related background contributions will be under good control after selection requirements such as those detailed in Section 3 have been applied. Finally, all possible sources of instrumental background are also ignored. Consideration of these effects goes beyond the scope of this work which does not aim to simulate any detector effect other than a b-tagging efficiency (see Section 3).
Parton-level hard events arising from the production of a top-antitop pair, including top decays, have been simulated by convoluting next-to-leading order (NLO) matrix elements with the CTEQ6M parton density set [33] in the PowhegBox framework [36][37][38][39], and events have then been matched to Herwig++ for parton showering and hadronization. Owing to the angular-ordered nature of the Herwig++ parton shower, it is in principle necessary to apply a truncated parton showering algorithm to simulate emissions that have a smaller transverse momentum than those described by the NLO matrix elements but a larger value of the angular evolution parameter. However, the corresponding effects are typically small [40] and so have been omitted. The same machinery has been used to generate single-top events [41,42], suppressing the doubly-resonant diagrams related to the tW mode following the prescription of Ref. [43], as implemented in the PowhegBox.
In order to generate events describing the production of a W -boson with light-flavour jets (u, d, s, c) and a γ * /Z-boson with both light-and heavy-flavour jets (u, d, s, c, b), the Sherpa 2.0 [44,45] package has been used. We have followed the MENLOPS prescription to match an event sample based on NLO matrix elements related to the production of a single gauge boson to leading-order (LO) samples describing the production of the same gauge boson with one and two extra jets [46,47]. In all cases, the vector bosons have been forced to decay either leptonically or invisibly, including all three flavours of leptons, and matrix elements have been convoluted with the CTEQ6M PDF set. Moreover, the invariant masses of lepton pairs produced via a γ * /Z-boson s-channel diagram have been required to exceed 10 GeV.
The production of a W -boson with heavy flavour jets has been simulated separately using MadGraph 5 and its built-in Standard Model implementation. We have generated LO matrix elements that have been further convoluted with the LO set of parton densities CTEQ6L1 [33]. Parton-level events have been simulated including the leptonic decay of the W -boson and then showered and hadronized with Herwig++ .
Finally, diboson production has been simulated at the NLO accuracy and matched to the Herwig++ parton shower using its built-in Powheg implementation [48], the matrix elements having been convoluted with the CTEQ6M PDF set.
The total cross sections for all considered background processes are shown in Table 1.

Object reconstruction
Objects used as inputs for the leptonic and hadronic monotop search strategies of the next subsections are reconstructed as in typical single-top studies performed by the ATLAS experiment (see, e.g., Ref. [49]). Electron (muon) candidates are required to have a transverse momentum p T > 10 GeV, a pseudorapidity satisfying |η | < 2.47 (2.5) and they must be isolated such that the sum of the transverse momenta of all charged particles in a cone of radius ∆R < 0.2 3 centered on the lepton is less than 10% of its transverse momentum.
Jets are reconstructed from all visible final-state particles with a pseudorapidity satisfying |η j | < 4.9 by applying an anti-k T jet algorithm [50] with a radius parameter R = 0.4, as implemented in the FastJet program [51]. We select reconstructed jet candidates that do not overlap with candidate electrons within a distance of ∆R < 0.2, and with a transverse momentum p j T > 20 GeV and a pseudorapidity |η j | < 2.5. Any lepton candidate within a distance ∆R < 0.4 to the closest of the selected jets is then discarded. We further identify jets as originating from a b-quark if their angular distance to a B-hadron satisfies ∆R < 0.3 and impose a p T -dependent b-tagging probability as described in Ref. [52]. This corresponds to an average efficiency of 70% in the case of tt events.

Leptonic monotops
The preselection of events possibly containing a leptonically decaying monotop signal has been directly designed from the expected final-state particle content. As such, we demand the presence of exactly one lepton candidate with a transverse momentum p T > 30 GeV and one b-jet with a transverse momentum p b T > 30 GeV. To reflect the expectation that the produced supersymmetric particles (and their decay products) are largely invisible, any event containing an extra jet with a transverse momentum p j T such that p j T > min(p b T , 40 GeV) is discarded. After these basic requirements, a number of additional selection steps have been implemented to increase the sensitivity s of the analysis to the signal, where s = S/ √ S + B in which S and B are the number of signal and background events passing all selection criteria, respectively. We define in this way two signal regions, SRL1 and SRL2, dedicated to the high and low mass regions of the superparticle parameter space, respectively.
Starting with the signal region SRL1 more sensitive to high mass setups, we impose that the missing transverse momentum p miss T in the event, determined from the vector sum of the transverse momenta of all visible final-state particles, has a magnitude E miss T > 150 GeV. The orientation of the missing transverse momentum with respect to the identified lepton is constrained by imposing a minimum value to the W -boson transverse mass, where ∆φ( , p miss T ) is the difference in azimuthal angle between the lepton and the missing transverse momentum. We require selected events to satisfy m W T > 120 GeV, since when the missing transverse momentum in the event originates solely from the leptonic decay of a W -boson, the m W T distribution peaks at a lower value than when it finds its source both in a W -boson decay and in a pair of invisible particles (like in the signal case). This last selection ensures that the non-simulated QCD multijet background is negligible [53,54].
The second signal region SRL2 has been optimized for lower mass scenarios where E miss T is typically very small due to a low neutralino mass. Instead of constraining the individual quantities E miss T and m W T , we select events satisfying In doing so, signal events with low values of E miss T are retained by the selection process provided they have a suitably large value of m W T . This still ensures that the QCD multijet background contributions are small [55].
In both search strategies, the following selection criteria are imposed. Firstly, in order to reduce the number of background events in which the identified lepton and b-jet do not originate from a single top quark, a restriction on the invariant mass of the lepton plus b-jet system is imposed,

Hadronic monotops
In the hadronic case, final states related to the production of a pair of strong superpartners together with a top quark are comprised of one heavy-flavour and two lighter jets associated with the top decay, as well as missing energy and extra soft objects arising from the decays of the produced superparticles. We therefore preselect events that contain no candidate leptons and exactly one b-jet with p b T > 30 GeV. We however demand exactly three light jets and not two, this requirement being found to slightly increase the analysis sensitivity.
We design two search strategies that we denote by SRH1 and SRH2. The former aims to be sensitive to scenarios with higher superparticle masses and the latter to lower mass cases, and we require the event missing energy to satisfy E miss T > 200 GeV and E miss T > 150 GeV for the SRH1 and SRH2 regions, respectively. While an even looser missing energy selection might increase the sensitivity in the SRH2 case, this would no longer ensure a sufficient control of the non-simulated QCD multijet background and furthermore not be sensible in the context of event triggers. To improve the trigger efficiency associated with the SRH2 region, we further require the hardest non b-tagged jet in each event to fulfill p j1 T > 80 GeV, such that a trigger based on the selection of a hard jet in association with missing transverse energy may be used. In contrast, no selection on the hardest jet is imposed for the SRH1 region since triggers based on the amount of missing energy only can be used. A number of selection criterion are imposed for both strategies to improve the sensitivity of the analysis. Firstly, the invariant mass of a light dijet system, m jj , must be consistent with the mass of the W -boson, 50 GeV < m jj < 150 GeV, (3.5) where the pair of light jets is chosen such that the quantity |m W − m jj | is minimized. This pair of light-jets is then combined with the b-tagged jet to fully reconstruct the hadronically decaying top quark, the resulting system being constrained to have an invariant mass in the range 100 GeV < m bjj < 200 GeV. (3.6) This eliminates a large number of background events which do not contain a hadronically decaying top quark. In particular, it leads to a significant reduction of the W -and γ * /Zboson plus jet contributions. Next, several restrictions are applied based on the kinematic configuration of the events. The azimuthal angle between the missing transverse momentum and both the b-tagged and hardest non b-tagged jet in the event are required to be suitably large, ∆φ p miss T , p j1 > 0.6 and ∆φ p miss These selection criteria are designed to rejected events in which the missing transverse energy originates from the mismeasurement of jets or semi-leptonic decays of heavy-flavour hadrons. Including these requirements is also expected to reduce background contributions originating from QCD multijet events with large instrumental missing transverse energy. Finally to reflect the topology of signal events, the reconstructed top quark must be well separated from the missing transverse momentum with the difference in azimuthal angle exceeding ∆φ p miss T , p t > 1.8 .

Leptonic monotops
The numbers of events populating both leptonic monotop signal regions defined in Section 3.2 are listed in the third and fourth columns of Table 1, separately for the different background contributions and for the two compressed spectra scenarios mentioned in Section 2.1. We recall that for the first of these, we have adopted a scenario with (mt 1 =mg, mχ0 1 ) = (200, 190) GeV as a representative high mass setup while we have chosen (mt 1 =mg, mχ0 1 ) = (110, 50) GeV as a low mass example. The SRL1 analysis strategy is illustrated in Figure 1   The m W T distribution for the background exhibits a peak in the region m W T 80 GeV, which corresponds to events in which both the lepton and all the missing transverse momentum originate from a W -boson decay. In contrast, both signal distributions feature a suppression for m W T < 120 GeV, which motivates the m W T selection criterion of the SRL1 strategy. Despite the large number of remaining background events, the sensitivity of the SRL1 analysis to the high and low mass signal scenarios reaches 6.5σ and 3σ respectively. The SRL1 search strategy having been designed to probe higher mass spectra, is by construction less sensitive to the second scenario where the smaller neutralino mass yields comparatively less E miss T , as depicted on the right panel of Figure 1. This drop in the sensitivity is alleviated through the inclusion of the SRL2 analysis strategy that exhibits an increase of the sensitivity to the second example scenario to 5σ, with a small reduction of the sensitivity to the high mass benchmark point to 5.2σ.
To study more extensively the LHC sensitivity to different supersymmetric scenarios featuring small mass gaps among the lightest superpartners, we scan in the (mt 1 , mχ0 1 ) plane, enforcing mt 1 = mg, and derive contours corresponding to different observation boundaries. The 5σ and 3σ regions are respectively shown by solid and dashed red lines in Figure 2 where we present the independent contributions of the SRL1 (left panel) and SRL2 (right panel) search strategies. As a result of their design, the SRL1 analysis is found to be more sensitive to higher mass setups whilst the SRL2 one is more sensitive to scenarios featuring smaller superpartner masses and possibly less compressed spectra.

Hadronic monotops
We again focus on the high mass and low mass example scenarios of Section 2.1 and apply the hadronic monotop selection requirements outlined in Section 3.3. The number of signal events populating the SRH1 and SRH2 regions are presented in the fifth and sixth columns of Table 1, together with the different background contributions. The results indicate that the Standard Model background is largely comprised of events originating from tt, γ * /Z-boson plus jets, tW and W -boson plus light-jet production for both search regions. Our hadronic monotop selection strategy is illustrated on Figure 3 where we show the distribution in the invariant-mass of the reconstructed top quark after applying all SRH2 requirements, except the one on m bjj , for the two considered signal scenarios and the dominant background sources. In principle, the subdominant W -boson plus lightjet results should also be represented. However, only a very small fraction of the ∼ 10 8 simulated events have passed all selection criteria, so that after normalizing to the large associated total cross section and an integrated luminosity of 10 fb −1 the resulting statistical uncertainty is important. The W -boson plus light-jets curve has therefore been omitted.
Imposing the constraint m bjj ∈ [100, 200] GeV will retain the majority of the signal events while reducing the number of background events, particularly in the case of γ * /Z plus jets production for which the distribution does not peak significantly at the top mass. As such, after applying this final selection criteria the sensitivity of the SRH2 strategy to the high and low mass signal benchmark points is found to be 7σ and 4.8σ respectively. The SRH1 strategy being in contrast dedicated to higher mass setups, its sensitivity to the high mass scenario is found to be significantly improved and reaches 8.2σ, whilst it drops to 3.4σ for the low mass example.
As in Section 4.1, we perform a scan in the (mt 1 , mχ0 1 ) plane with the equality mt 1 = mg enforced. The results are given in Figure 4 where we show the 5σ and 3σ contours found after applying the SRH1 (left panel) and SRH2 (right panel) search strategies. As expected by design, the SRH1 analysis presents an enhanced sensitivity to compressed scenarios featuring large superparticle masses, its reach exceeding that observed in the leptonic case (left panel of Figure 2). In particular, the 5σ contour extents to very compressed scenarios   with a stop mass of about 240 GeV. The SRH2 strategy is instead more tuned to situations exhibiting smaller superparticle masses, with a possibly less compressed spectrum (right panel of Figure 4). Its reach is found to improve over the SRH1 one in the low mass region of the parameter space and to fall only slightly short of the limits expected to be set by the SRL2 leptonic monotop search (right panel of Figure 2).

Combining leptonic and hadronic monotop search strategies
As indicated from the results in the previous subsections, improved observation boundaries could be obtained by combining the reaches of all leptonic and hadronic monotop searches. This is illustrated in Figure 5 where results are merged in the most naive way, making use of the most sensitive search strategy at each parameter space point. While a more sophisticated combination might further expand the observation boundaries, our simplistic approach provides a conservative estimate of the LHC sensitivity to monotop signatures in  Figure 5. Sensitivity of the LHC to (hadronically and leptonically decaying) monotop signals induced by a compressed supersymmetric scenario after combining the four SRL1, SRL2, SRH1 and SRH2 search strategies. Results are shown in the (mt 1 , mχ0 1 ) plane for scenarios featuring mt 1 = mg and for 10 fb −1 of LHC collisions at a centre-of-mass energy of √ s = 14 TeV. We superimpose an exclusion bound derived from an ATLAS search for stops decaying into a charm quark and missing energy using monojet events [56].
the context of compressed supersymmetric scenarios. In addition, more precise quantitative statements would require the inclusion of detector effects and the instrumental background. We superimpose on our results a 95% confidence level exclusion bound, indicated by the black dotted line, set by the ATLAS collaboration on the basis of 20.3 fb −1 of collision data at a centre-of-mass energy of 8 TeV [56]. These limits are derived from a monojet search for the pair production of top squarks decaying each into a charm quark and the lightest neutralino. We observe that they surpass the 5σ observation boundary set by our combined monotop search throughout the (mt 1 , mχ0 1 ) plane. However, searching for compressed spectra supersymmetry with monotop probes would both yield an independent verification of the monojet-based results and allow one to extend the existing exclusion boundaries through the combination of uncorrelated channels.

Conclusions
We have investigated the feasibility of using monotop probes to get a handle on supersymmetric scenarios featuring a compressed spectrum. We have considered the production of a pair of strongly-interacting superpartners in association with a top quark from protonproton collisions at a centre-of-mass energy of 14 TeV. The supersymmetric spectrum being compressed, both superpartners decay into missing energy carried by the lightest supersymmetric particle and a collection of objects too soft to be reconstructed. The resulting new physics signal consequently consists of a monotop signature.
Both the leptonic and hadronic decays of the top quark have been investigated and two pairs of analysis strategies, respectively dedicated to the low and high mass regions of the parameter space, have been designed. We have shown that monotop signals induced by a compressed supersymmetric setup are in principle already reachable at the future run II of the LHC with a luminosity of 10 fb −1 in the case where the supersymmetric masses are below 250 GeV.
In this work, we have demonstrated that monotops offer an alternative option to the monophoton and monojet analyses traditionally employed for probing compressed supersymmetric scenarios. Moreover, as all three search channels are statistically independent, a combination of the results could in principle improve the coverage of the parameter space.