# LHC constraints and potential on resonant monotop production

## Abstract

We discuss the phenomenology associated with a resonant monotop collider signal, i.e. a signal in which a single top quark is resonantly produced in association with missing energy through an *s*-channel scalar exchange. We study both the bounds originating from dedicated monotop searches performed by the ATLAS and CMS experiments, and the constraints associated with other processes that could be induced by a new physics context favouring monotop production at colliders. The latter class of constraints includes, in particular, the recasting of analyses from the LHC and the TeVatron. All theoretical calculations are performed at the next-to-leading order accuracy in QCD, and we finally combine all results to establish the present limits on the parameter space and test the relevance of the monotop signal at the LHC Run 2.

## 1 Introduction

Monotop production at colliders consists in the prodution of a single top quark in association with a large amount of missing transverse energy. This quite peculiar final state has been investigated at the LHC by both the ATLAS and CMS collaborations, and both at Run 1 and 2. As monotop production is heavily suppressed in the Standard Model, its observation would consist in a clear sign of physics Beyond the Standard Model. In a new physics context, there exist two main different monotop production mechanisms [1, 2, 3]. In the first of them, the monotop system is produced from a coloured scalar or vector resonance that decays into a top quark and an invisible neutral fermion, whereas in the second of them, monotops arise from the production of a single top quark in association with an invisible scalar or vector boson via the flavour-changing couplings of the latter to the top and light quarks. After imposing invariance under the full Standard Model gauge symmetry and invoking simplicity, it can be shown that only scalar resonant monotop production and vector flavour-changing monotop production are consistent [3]. Whilst several existing experimental [4, 5, 6, 7] and phenomenological [2, 3, 8, 9, 10] studies focus on the flavour-changing option, the possibility of resonant production has been less studied, at least comprehensively [2, 5, 7, 11]. On different grounds, monotop signatures have also been considered in the case of compressed supersymmetry [12, 13, 14, 15, 16] and models with vector-like fermions [17] or explaining neutrino masses [18].

In this work, we reconsider the resonant production of monotop systems via an intermediate coloured scalar, which consists in the simplest model featuring monotop production as a key new physics signal and that is allowed after imposing invariance under the Standard Model gauge symmetry group [3]. In practice, we embed the generic effective Lagrangian for resonant monotop production [1] within the full gauge symmetry requirements of the Standard Model, which severely constrains the couplings and quantum numbers of the mediator. Hence the coloured scalar mediator has an electric charge of 2 / 3 and consists in a colour triplet \(\sigma \) that couples to a pair of different-flavour right-handed down-type quarks. Single mediator production, therefore, occurs via these di-quark couplings, while the decay of the mediator into a (right-handed) top quark plus an invisible neutral fermion \(\chi \) occurs through an independent coupling parameter. In order for the model to stay monotop-motivated, it is crucial that the fermion \(\chi \) remains undetected when produced, and thus decays outside the detector. Remarkably, this model resembles a supersymmetry-inspired simplified model in which the Standard Model field content is supplemented by neutralino and a right-handed top squark featuring *R*-parity violating couplings to the down-type quark sector.

Besides the direct investigation of monotop probes, this model is also constrained by many other searches for new physics that thus already limit the available parameter space. Hence we will take into account searches from LHC Run 1 and 2 involving jets and top quarks in the final state, as well as dijet searches at the LHC and the TeVatron. Moreover, constraints on the decay length of the invisible (unstable) particle produced in association with the top quark and contributions to the top width also importantly restricts the parameter space. Another important point concerning the resonant production of a coloured spin-0 boson is that, being a QCD process, next-to-leading order (NLO) effects are expected to be important. As the tools allowing for such a calculation at the Monte Carlo level became available recently [19], we employ the full NLO machinery to study the existing bounds, as well as to establish the LHC potential at Run 2 to test the simplest phenomenologically viable monotop model.

The paper is organised as follows. In Sect. 2 we briefly recall the details of the effective Lagrangian describing resonant monotop production and of the theoretical framework allowing for numerical Monte Carlo simulations at the NLO level. In Sect. 3, we analyse the existing bounds coming from different sources. Hence, we reinterpret the results of stop pair searches, include limits from resonance searches using dijet probes and the constraints originating from direct monotop searches at the LHC Run 1. We moreover consider the constraints stemming from the modification of the top quark width and the fact that the neutral fermion \(\chi \) has to be long-lived or decay invisibly. In Sect. 4, we collect all current constraints on the parameter space and discuss the LHC Run 2 potential, which will be relevant for the ongoing experimental analyses, and hence present our conclusions.

## 2 Theoretical framework

*y*).

*y*parameters in the \(\overline{\mathrm{MS}}\) scheme,

*y*will be performed with the anomalous dimensions as \(\beta _{\lambda _{ij}}=-\frac{\alpha _s}{\pi }\) and \(\beta _{y}=-\frac{\alpha _s}{2\pi }\).

In order to handle \(2\rightarrow 2\) resonant processes at the NLO accuracy in QCD, we work in the complex-mass scheme [20, 21, 22] where the renormalisation procedure is handled with the complex masses and complex derived parameters. Complications may consequently arise with the choice of proper Riemann sheets when the derivation of the various renormalisation constants is at stake [23]. However, in our simplified model, there is no \({\mathscr {O}}(\alpha _s)\) contribution to the particle decay widths at tree level, so that such complications are avoided. To achieve the NLO QCD accuracy in the whole phase space, we nevertheless need to evaluate the unstable particle widths by including NLO QCD corrections. For simplicity, we fix in these calculations the renormalisation scale \(\mu _R\) to the respective particle masses, and include the renormalisation group running of the \(\alpha _s\), \(\lambda _{ij}\) and *y* couplings. In the context of the width calculations, the potential impact of using a different scale is a pure next-to-NLO effect, and has therefore been ignored.

## 3 Resonant monotops in the LHC era

*i.e.*two masses and four couplings,

*y*parameters that control the two branching ratios

*y*has been traded with the \(\text{ BR }_{t\chi }\) branching ratio. We have kept the \(\lambda \) parameter free (and not the

*y*one) as it directly controls the resonant production rate of a \(\sigma \) particle. As the aim of this work is to focus on monotop models, we will exclude from our investigations any parameter space region in which the \(\sigma \) particle cannot decay into a monotop system,

*i.e.*regions for which \(m_\sigma < m_\chi + m_t\).

In this section, we will consider two classes of constraints, namely those that are respectively independent and dependent on \(\lambda \). The former ones allow us to directly exclude regions in the \((m_\chi , m_\sigma )\) parameter space at fixed \(\text{ BR }_{t \chi }\), whilst the latter ones allow us to derive upper limits on the coupling \(\lambda \) for each point of the same mass plane. The first category of constraints includes typical LHC searches for the production of a pair of coloured resonances (see Sect. 3.1), as well as searches capable of targeting the doubly-resonant production of a pair of dijet systems (see Sect. 3.2). These searches are indeed sensitive to the production and decay of a pair of \(\sigma \) particles. We only consider the QCD contribution to pair production, which only depends on the mass \(m_\sigma \). Additional contribution may arise from the process \(d\bar{d} \rightarrow \sigma \sigma ^\dagger \) via a *t*-channel *s*-quark exchange. However, for the values of \(\lambda \) allowed by the constraints, this process always yields a negligible contribution to the cross section. On different lines, the second category of constraints includes bounds that could originate from dijet (see Sect. 3.3) and monotop (see Sect. 3.4) probes, as these two final states can be induced by the resonant production and decay of a single \(\sigma \) particle. In addition, for parameter space regions in which \(m_\chi < m_t\), the top quark can undergo a three-body decay in a \(\chi j j\) final state via an off-shell \(\sigma \) particle. While no direct search is currently dedicated to such a decay, measurements of the top width yield indirect constraints on the model (see Sect. 3.5). The fermion \(\chi \) is in principle allowed to decay into a \(t^{(*)} j j\) system, with the final-state top quark being potentially off-shell, and one must ensure that \(\chi \) is stable on LHC detector scales (see also in Sect. 3.5). Finally, in the same section, we comment on the usage of the narrow-width approximation for the \(\sigma \) particle.

In our phenomenological investigations, we rely on a numerical evaluation in four dimensions of all loop integrals, so that the numerical results must be complemented by rational terms related to the \(\epsilon \)-dimensional pieces of the integrals [24, 25, 26, 27]. They consist of the so-called \(R_1\) and \(R_2\) terms, the former being universal and connected to the denominators of loop integrands and the latter being model-dependent and associated with the numerators of loop integrands. In practice, we perform loop-integral computations with the MadLoop package [28] that automatically estimates the \(R_1\) contributions and makes use of a finite set of special Feynman rules derived from the bare Lagrangian [29] to estimate the \(R_2\) ones. We have computed those \(R_2\) Feynman rules by implementing the Lagrangian of Eq. 1 into the FeynRules package [30], that we have jointly used with the NLOCT [31] and FeynArts [32] programs to export the model under the form of a UFO module [33]. Such a module contains here, in addition to tree-level information, all ultraviolet counterterms and \(R_2\) Feynman rules needed for numerical loop-calculations in QCD in the context of our monotop model. In practice, this has allowed us to make use of the MadGraph5_aMC@NLO [34] (MG5_aMC) platform for the generation of the LHC signals at the NLO accuracy in QCD.

Moreover, for the resonant processes in which the complex-mass scheme must be employed, we have verified that the NLO widths computed by MG5_aMC agree with independent in-house calculations. We now present the current bounds on the parameter space of the model.

### 3.1 LHC constraints on \(\sigma \) pair-production from supersymmetry searches

As all LHC stop searches give rise to similar bounds, we reinterpret the results of a single recent search: we thus consider the CMS-SUS-17-001 analysis, which focuses on the dileptonic mode of the top-antitop system [36]. This search is based on an integrated luminosity of 35.9 fb\(^{-1}\) of LHC Run 2 proton-proton collision data at a centre-of-mass energy \(\sqrt{s}=13\) TeV. It targets a signature made of two opposite-sign leptons (electrons or muons, with a veto on the presence of a reconstructed *Z*-boson), light and *b*-tagged jets and a significant amount of missing transverse momentum. The production of the hypothetical stop-pair signal, which in our case is identified with the production of two \(\sigma \) scalars decaying as in the process of Eq. 11, is then efficiently separated from the dominant top-antitop background by a cut on the transverse mass \(m_{T2}\) [37, 38] reconstructed from the two leptons and the missing transverse momentum. In Fig. 1, we show the LHC bound for the process in Eq. 11, assuming \(\text{ BR }_{t\chi }=100\%\) and in the plane of the two masses, \((m_\sigma , m_\chi )\). We made use of the MadAnalysis 5 platform [39, 40] and its public analysis database [41, 42], which contains the corresponding validated reimplementation [43] and the necessary Delphes 3 configuration cards for handling the simulation of the response of the LHC detectors [44].

We additionally tested the limits arising from two representative ATLAS searches for dark matter and supersymmetry in the multijet plus missing energy channel [45, 46]. Both these searches target a small 3.2 fb\(^{-1}\) luminosity of proton-proton collisions at \(\sqrt{s}=13\) TeV and consider a signature featuring one very hard jet plus subleading hadronic activity. Whilst the ATLAS-EXOT-2015-03 analysis [45] only allows for a restricted subleading jet activity, the ATLAS-SUSY-2015-06 analysis [46] includes signal regions that require a much more important jet activity. Both these analyses rely on a large set of signal regions differing by the number of jets, their kinematical configuration and the amount of missing transverse energy. Whilst both these ATLAS analyses only consider a small integrated luminosity of 3.2 fb\(^{-1}\) of proton-proton collisions, they are already limited by the systematics. The resulting bounds are consequently not expected to improve with an increased LHC luminosity [47] and the subsequent predictions can be robustly used as the best current constraints originating from multijet plus missing transverse energy production at the LHC. By using the validated MadAnalysis 5 public implementations [48, 49], we have found that they only marginally improve the exclusions at the price of a larger systematic uncertainty due to the fact that the final state in our model differs from the supersymmetric benchmarks. Thus, we will conservatively only use the exclusion from the CMS stop search in the following.

### 3.2 Searches for a pair of dijet resonances at the LHC

*i.e.*, when \(\text{ BR }_{t\chi }\) is large), it can lead to important constraints for large \(\text{ BR }_{jj} = (1-\text{ BR }_{t\chi })\) values as the resulting rate is proportional to \(\text{ BR }_{jj}^2\).

A new physics signature featuring a pair of dijet systems originating from a pair of resonances has been searched for at the LHC both during Run 1 and Run 2, and by both the ATLAS and CMS collaborations. One of the investigated benchmark models consists of a simplified model where the SM is supplemented by a light stop decaying into two jets via an *R*-parity violating interaction with a branching fraction of 100%. The corresponding experimental results can thus be directly reinterpreted as a bound on the \(\text{ BR }_{t\chi }\) branching ratio, as the signal total rate consists of the stop-pair production cross section rescaled by a \((1-\text{ BR }_{t\chi })^2\) factor.

We include in our study the CMS-EXO-12-052 final Run 1 search [50] dedicated to events exhibiting the presence of at least four jets that are then paired using an algorithm based on their angular distribution. The discrimination from the leading multi-jet background is achieved by relying on a set of kinematical variables including a reduced mass asymmetry between the two pairs of jets. The search has implemented two signal regions. The first region is dedicated to resonance masses larger than 300 GeV and benefits from the full Run 1 dataset with an integrated luminosity of 19.4 fb\(^{-1}\), whereas the second region is restricted to a smaller dataset of 12.4 fb\(^{-1}\) and solely considers resonance masses lying in the [200, 300] GeV mass window. It has been made possible to access such low masses thanks to a specific trigger that has been designed especially for this purpose, with a cost in luminosity.

Our results are shown in Fig. 2, where we consider the above-mentioned ATLAS and CMS searches and theoretical estimates of the stop pair-production cross section evaluated at the NLO accuracy in QCD [19, 53]. The strongest bound arises from the Run 2 ATLAS search for most values of the \(\sigma \) mass, with the exception of two mass points for which the Run 1 CMS search does a better job and the very low mass region that benefits from the dedicated CMS Run 2 analysis. The dip at \(m_\sigma = 250\) GeV featured in the CMS Run 1 limit is connected to a small excess of events in a single bin that has however not been confirmed by ATLAS. For fixed \(\text{ BR }_{t\chi }\), therefore, a lower bound on the mass \(m_\sigma \) can be extracted.

### 3.3 Dijet searches at the TeVatron and the LHC

Fiducial cross sections for dijet production at the TeVatron, in \(p\bar{p}\) collisions at \(\sqrt{s}=1.96\) TeV, after imposing the same jet reconstruction method and signal selection as in the CDF analysis of Ref. [59]. We compare our (normalised) predictions with the CDF limits

\(m_{\sigma }\) [GeV] | \(\sigma ^\mathrm{NLO,CDF}_{\sigma \rightarrow jj}/(\lambda ^2(1- BR_{t\chi }))\) [pb] | CDF limit [pb] [59] |
---|---|---|

260 | 252 | 110 |

300 | 132 | 45 |

400 | 26.1 | 7.2 |

500 | 5.83 | 3.9 |

620 | 0.960 | 0.8 |

700 | 0.259 | 0.6 |

The low mass regime in which \(m_\sigma \) lies in the 50–300 GeV mass window has been probed by the CMS boosted search of Ref. [57]. The tight requirements of the trigger are overcome by requiring the presence of at least one broad jet with \(p_T > 500\) GeV. Then, various jet substructure techniques are employed to discriminate a signal in which the broad jet is issued from a resonance decaying into a boosted dijet system from the QCD background. The benchmark model used in the search is a \(Z'\) model. Even though our model contains a scalar resonance and not a vector one, we do not expect significant kinematical differences in the properties of the dijet system. We have therefore simply reinterpreted the search in terms of our model by a direct comparison of the predicted production cross section with the excluded one. The results are presented in the upper left panel of Fig. 3. The 300–450 GeV mass window is only covered by the CDF analysis, which implies much weaker limits on \(\lambda \), as shown in the upper right panel of the figure. In the whole parameter space region, the best upper limit is \(\lambda < 0.46\), *i.e.* one to two orders of magnitude weaker than any limit that could be derived from the LHC results. For \(\sigma \) masses larger than 450 GeV, the trigger-based low mass search from ATLAS [55] kicks in with limits much stronger than the ones derived from the CDF results, as shown in the lower left panel of the figure. Finally, for masses greater than 600 GeV, the ATLAS limits can be combined with those obtained from the trigger-based search of CMS [56], which is presented in the lower right panel of the figure. In summary, we observe that current low mass dijet searches at the LHC give bounds on the coupling \(\lambda \) of order \(10^{-2}\), except for the 300–450 GeV mass window where only much weaker CDF limits are applicable.

### 3.4 Monotop bounds after run 1

Monotop searches have been designed to get hints for new physics in a final state comprised of a single top quark and missing transverse energy. As sketched in Sect. 2, such a final state can originate from the (potentially resonant) production of a \(\sigma \) state followed by its decay into a \(t\chi \) system. The first experimental search for monotops has been carried out by the CDF collaboration at the TeVatron [4] and solely focused on the flavour-changing monotop production mode. LHC Run 1 data has been analysed during the last few years, both by the CMS [6] and ATLAS [5] collaborations. Whilst the CMS analysis again focused only on flavour-changing monotop production, the ATLAS results have been interpreted both in the flavour-changing and resonant scenarios. The way in which they are presented however makes their reinterpretation in different theoretical frameworks highly non-trivial. The ATLAS analysis indeed assumes that all model coupling parameters are equal to a common value, and a bound on this value is presented in terms of the resonance mass. It is consequently impossible to make use of the results for model configurations not satisfying this requirement. The first monotop analysis of the LHC Run 2 results has also been recently released by the CMS collaboration [7], but it targets boosted monotop systems so that it is not relevant for the mass scales probed in this work. For these reasons, we concentrate on the CMS Run 1 monotop analysis that we consider as representative for the most constraining direct LHC search on the resonant monotop model.^{1}

Comparison of results obtained with our MadAnalysis 5 reimplementation (MA5) to those provided by the CMS collaboration (CMS-B2G-12-022) in the case of a new physics scenario featuring flavor-changing monotop production. The selection and total efficiencies are defined in Eq. 15. The official CMS numbers have been derived from the same hard-scattering events entering our simulation chain. Those events have been provided to the CMS collaboration who accepted to produce an official cutflow

Selection step | CMS | \(\epsilon _i^{\mathrm{CMS}}\) | \(\epsilon _{i, \mathrm{tot}}^{\mathrm{CMS}}\) | MA5 | \(\epsilon _i^\mathrm{MA5}\) | \(\epsilon _{i, \mathrm{tot}}^\mathrm{MA5}\) | \(\delta _i^{\mathrm{rel}}\) | |
---|---|---|---|---|---|---|---|---|

0 | Nominal | 3000 | 3000 | |||||

1 | Lepton veto | 3000 | 1.000 | 1.000 | 2983 | 0.994 | 0.994 | 0.56% |

2 | \(p_T(j_1) > 60\) GeV | 2805 | 0.935 | 0.935 | 2799 | 0.938 | 0.933 | 0.35% |

3 | \(p_T(j_2) > 60\) GeV | 1719 | 0.613 | 0.573 | 1900 | 0.679 | 0.633 | 10.8% |

4 | \(p_T(j_3) > 40\) GeV | 1116 | 0.649 | 0.372 | 1358 | 0.715 | 0.453 | 10.1% |

5 | Veto on the fourth jet | 598 | 0.536 | 0.200 | 618 | 0.455 | 0.206 | 15.1% |

6 | \(M_{3j}<250\) GeV | 294 | 0.492 | 0.098 | 269 | 0.435 | 0.090 | 11.5% |

7 | 98 | 0.333 | 0.032 | 109 | 0.405 | 0.036 | 21.6% | |

8 | 27 | 0.276 | 0.009 | 36 | 0.330 | 0.012 | 19.9% | |

S0 | 0 | 6 | 0.222 | 0.002 | 12 | 0.333 | 0.004 | 50.0% |

S1 | 1 | 19 | 0.704 | 0.006 | 23 | 0.639 | 0.008 | 9.2% |

Same as in Table 2, but for a new physics scenario featuring resonant monotop production

Selection step | CMS | \(\epsilon _i^{\mathrm{CMS}}\) | \(\epsilon _{i, \mathrm{tot}}^{\mathrm{CMS}}\) | MA5 | \(\epsilon _i^\mathrm{MA5}\) | \(\epsilon _{i, \mathrm{tot}}^\mathrm{MA5}\) | \(\delta _i^{\mathrm{rel}}\) | |
---|---|---|---|---|---|---|---|---|

0 | Nominal | 4000 | 4000 | |||||

1 | Lepton veto | 4000 | 1.000 | 1.000 | 3989 | 0.997 | 0.997 | 0.28% |

2 | \(p_T(j_1) > 60\) GeV | 3932 | 0.983 | 1.000 | 3947 | 0.989 | 0.986 | 0.66% |

3 | \(p_T(j_2) > 60\) GeV | 2872 | 0.730 | 0.983 | 3044 | 0.771 | 0.761 | 5.59% |

4 | \(p_T(j_3) > 40\) GeV | 1620 | 0.564 | 0.718 | 1944 | 0.639 | 0.486 | 13.2% |

5 | Veto on the fourth jet | 996 | 0.614 | 0.405 | 1006 | 0.517 | 0.252 | 15.8% |

6 | \(M_{3j}<250\) GeV | 536 | 0.538 | 0.249 | 479 | 0.476 | 0.120 | 11.5% |

7 | 463 | 0.863 | 0.134 | 415 | 0.866 | 0.104 | 0.30% | |

8 | 315 | 0.680 | 0.116 | 284 | 0.684 | 0.071 | 0.59% | |

S0 | 0 | 104 | 0.330 | 0.023 | 90 | 0.317 | 0.023 | 4.02% |

S1 | 1 | 189 | 0.600 | 0.040 | 159 | 0.560 | 0.040 | 6.69% |

The CMS-B2G-12-022 analysis relies on a selection that vetoes the presence of isolated electrons (muons) with a transverse momentum \(p_T\) larger than 10 GeV (20 GeV) and a pseudorapidity \(|\eta |<2.4\) (2.5), where lepton isolation is imposed by constraining the sum of the transverse momenta of all objects lying in a cone of radius \(R=0.4\) centred on the lepton to be smaller than 20% of the lepton \(p_T\). The analysis next requires the presence of at most three jets with transverse momentum \(p_T(j_1) > 60\) GeV, \(p_T(j_2) > 60\) GeV and \(p_T(j_3) > 40\) GeV respectively, and it additionally forbids the presence of a fourth jet with a \(p_T\) greater than 35 GeV. The invariant mass of the three leading jets \(M_{3j}\) is then imposed to be compatible with the top mass \(M_{3j}<250\) GeV and the missing energy has to satisfy Open image in new window . Two signal regions S1 and S0 are finally defined, the difference lying in the presence of either exactly one or exactly zero *b*-tagged jet.

*p*-values associated with the background-only (\(p_B\)) and signal-plus-background (\(p_{S+B}\)) hypotheses. These estimations assume that the number of background events \(N_b\) and signal-plus-background events \(N_b+N_s\) are Poisson-distributed, and that \(N_{\mathrm{data}}\) events have been observed (the data numbers being reported in Ref. [6]). We next freely varied the signal production cross section to the smallest value for which

### 3.5 Width constraints

*y*respectively. In addition, the

*y*coupling also determines the size of the monotop production cross section. Maximising both the production rate and the branching ratio into a monotop system may thus lead to some tensions in the values of the couplings. The \(\sigma \) branching fraction into a \(t \chi \) system, in a simplified limit, only depends on the value of the \(\lambda \) and

*y*couplings. Whilst the full result for the leading order (LO) partial width, \({\varGamma }(\sigma \rightarrow t \chi )\), is given by

*y*coupling. For example if we require \(\lambda =0.1\) and \(\text{ BR }(\sigma \rightarrow t \chi )=90\%\) (in order to limit the \(\sigma \) decay to dijets, which can give rise to strong bounds on the model, and keep the number of monotop events that are expected at the LHC high), a value of \(y \simeq 0.85\) is required. This back-of-the-envelope calculation is not used in the numerical evaluations performed in this work, where we used exact NLO calculations. Nevertheless it allows to qualitatively assess the coupling values that are required and their inter-relations.

*y*may lead to parameter space where the total width of \(\sigma \) becomes large. This is however an issue for the reinterpretation of the experimental searches, as we relied on the narrow width approximation (NWA) for the simulation of the resonant signal. This therefore imposes an upper bound on the value of the couplings which may contrast with the requirement of a large monotop production rate. To quantitatively assess where the NWA breaks down, it is convenient to fix the branching ratio in the monotop channel, and study the upper bound on the other coupling \(\lambda \) (responsible for the production rate). The total width of the \(\sigma \) resonance, \({\varGamma }_{\mathrm{tot}}\), can thus be written as

- 1.
for \(m_\chi > m_{\mathrm{top}}\), the three-body decay \(\chi \rightarrow t d s\) is open, thus potentially giving very strong bounds on the couplings;

- 2.
for \(m_W< m_\chi < m_{\mathrm{top}}\), the decay is four-body, \(\chi \rightarrow W^+ b d s\) and takes place via a virtual top quark;

- 3.
for \(m_b< m_\chi < m_W\), only a five-body decay is allowed via both an off-shell top quark and

*W*-boson.

*W*-boson mass \(m_W\), decay lengths in the metre range can be obtained. For all three kinematic regimes defined above, the decay proceeds through a virtual \(\sigma \) exchange, and the width is proportional to the product of the two couplings \((\lambda \ y)^2\). By requiring that the decay length of \(\chi \) is larger than the typical scale of an LHC detector,

*i.e.*10 metres, we can obtain an upper bound on \(\lambda \ y\), as shown in Fig. 7.

## 4 Discussion and conclusions

At 13 TeV one can have an idea of the potential of the LHC to observe a monotop signal by considering the production cross section in parameter space regions still allowed by data. A detailed study is not possible at present as this would require the generation of the corresponding Standard Model background, and even this would be only a rough analysis, considered that the 13 TeV environment and background can only be accurately determined using real data. Nevertheless, the signal cross section ranges from a few picobarns for \(m_{\sigma }=300\) GeV to the femtobarn level for resonance masses lying around \(m_{\sigma }=2\) TeV, as illustrated in Fig. 8 for a specific set of new physics couplings and masses. Those large numbers could in principle motivate the experimental collaborations to attempt a monotop search aiming to discover (or bound in a less optimistic case) the corresponding signal at the LHC Run 2.

The blue regions (triangle areas on the bottom right of each subfigure) correspond to parameter space configurations in which a monotop signal cannot be produced resonantly, the \(\sigma \rightarrow \chi t\) decay being kinematically closed. We therefore omit it from our analysis. We also represent by rectangular blue areas (bottom left of the two lower subfigures) the regions that are excluded by resonance search in the dijet-pair channel and that we have studied in Fig. 2. As already found in Sect. 3.2, the most powerful searches concern CMS and ATLAS analyses of 13 TeV LHC data, and they only have some constraining power for low \(\sigma \) masses and a large branching ratio associated with the \(\sigma \rightarrow jj\) decay (*i.e.* a not too large \(\text{ BR }_{t\chi }\) value). The light violet regions are excluded by stop searches, as detailed in Sect. 3.1. Typically, the limits presented in Fig. 1 are rescaled down proportionally to the decreasing value of \(\text{ BR }_{t\chi }\) (that lowers the signal production rate). All figures then feature black horizontal lines that delimitate the green bands of the mass planes that are excluded by dijet searches (see Sect. 3.3). For \(m_\sigma \) in the 300–450 GeV mass window, dijet bounds are weak as this corresponds to a mass configuration only probed by TeVatron searches. In contrast, LHC searches are sensitive for other \(\sigma \) masses and are especially stronger for masses lying in the 200–300 GeV and 450–1000 GeV ranges. Whilst the white areas are in principle reachable by dijet searches, the chosen \(\lambda \) values are too small to yield any constraint. In the upper left panel of the figure (for which \(\mathrm{BR}_{t\chi }= 99\%\)), the monotop bounds presented in Fig. 5 are overlaid, so that the upper part of the mass plane is excluded (dark red region). Those searches however quickly lose sensitivity with smaller \(\text{ BR }_{t\chi }\) values in association with a \(\lambda \) value also five times smaller. Finally, this panel also exhibits a trapezoid pink area that corresponds to a region in which the decay length of the \(\chi \) fermion is smaller than 10 metres, so that there is actually no monotop signal in there. There is no bound for any of the the three other \((\lambda , \text{ BR }_{t\chi })\) configurations, as the smaller \(\lambda \) value ensures a larger decay length.

To summarise, current limits severely restrict the model parameter space for light new physics states. Only small specific subregions are still allowed by data, and it is clear that future results will allow one to draw conclusive statements. In contrast, the heavier cases are still viable.

## Footnotes

- 1.
Due to the lack of publicly available material, we were unable to validate a recasting of the corresponding 8 TeV ATLAS analysis.

## Notes

### Acknowledgements

We are grateful to Josselin Proudom and Paolo Torrielli for useful discussions and comments in the early stage of this work, to Nishita Desai, Stefan Prestel and Peter Skands for comments on the color junction implemented in Pythia 8 and to Ivan Mikulec and Cristina Suárez for clarifying details on the CMS exclusion limits of Ref. [57]. We also thank Jun Guo and Khristian Kotov for their help in recasting the Run 1 CMS monotop analysis. AD and GC acknowledge partial support from the Labex-LIO (Lyon Institute of Origins) under grant ANR-10-LABX-66, FRAMA (FR3127, Fédération de Recherche ”André Marie Ampère”). BF and HSS are supported by French state funds managed by the Agence Nationale de la Recherche (ANR), in the context of the LABEX ILP (ANR-11-IDEX-0004-02, ANR-10-LABX-63).

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