Xu-Xu Yang¹, Hang Zhou^,2, Tian-Peng Tang¹, Ning Liu^,11Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing, 210023, China
²School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164, China

First author contact: ^*Authors to whom any correspondence should be addressed.
Received:2020-10-9Revised:2020-11-9Accepted:2020-11-13Online:2021-01-25

Fund supported:

National Natural Science Foundation of Chinahttps://doi.org/10.13039/501100001809.11705093

Abstract
Searching for the top squark (stop) is a key task to test the naturalness of SUSY. Different from stop pair production, single stop production relies on its electroweak properties and can provide some unique signatures. Following the single production process ${pp}\to {\tilde{t}}_{1}{\tilde{\chi }}_{1}^{-}\to t{\tilde{\chi }}_{1}^{0}{\tilde{\chi }}_{1}^{-}$, the top quark has two decay channels: leptonic channel and hadronic channel. In this paper, we probe the observability of these two channels in a simplified minimal supersymmetric standard model scenario. We find that, at the 27 TeV LHC with the integrated luminosity of ${ \mathcal L }=15\,{\mathrm{ab}}^{-1}$, ${m}_{{\tilde{t}}_{1}}\lt 1900\,\mathrm{GeV}$ and μ<750 GeV can be excluded at 2σ through the leptonic mono-top channel, while ${m}_{{\tilde{t}}_{1}}\lt 1200\,\mathrm{GeV}$ and μ<350 GeV can be excluded at 2σ through the hadronic channel.
Keywords： top squark;mono-top signature;HE-LHC


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Xu-Xu Yang, Hang Zhou, Tian-Peng Tang, Ning Liu. Mono-top signature from stop decay at the HE-LHC. Communications in Theoretical Physics, 2021, 73(2): 025201- doi:10.1088/1572-9494/abcfb7

1. Introduction

The discovery of Higgs [1, 2] made 2012 a landmark year of particle physics. It marks a significant success for the Standard Model (SM) and the efforts of particle physicists for nearly half a century have also been rewarded. This is very inspiring but there are still several dark clouds floating in the sky that make particle physicists disturbed and yearning at the same time, which all imply the existence of new physics and promote physicists to propose new models beyond the SM. Naturalness problem is one of the dark clouds and the weak scale supersymmetry (SUSY) is one of the most promising solutions. SUSY constructs a symmetry between fermions and bosons by introducing superpartners of the SM particles and then cancel the Higgs boson mass quadratic divergence naturally. We can make a bold assumption that μ<200 GeV and ${m}_{{\tilde{t}}_{\mathrm{1,2}}}\lt 1.5$ TeV within the framework of minimal supersymmetric standard model (MSSM) [3-7]. So if we want to test SUSY naturalness, searching for light stops in collider is very important [8-24].

LHC was built initially to search for Higgs boson but now we can also use it to search for new physics, including stops mentioned above. The null results of searching can exclude the low energy range and promote us to search for stops in a relatively high energy scale [25, 26]. On the basis of analysis on 139 fb⁻¹ data from 13 TeV LHC, the current exclusion limits for stop mass have been reached to 400-1250 GeV depending on the mass of LSP at 95% CL [27]. While the exclusion limits for chargino ${\tilde{\chi }}_{1}^{\pm }$ and neutralino ${\tilde{\chi }}_{2}^{0}$ vary from 180 to 740 GeV depending on a varying LSP mass at 95% CL with 36.1 fb⁻¹ [28] and 139 fb⁻¹ [29-31] data. Moreover, the large gap between the electroweak energy scale and the Planck energy scale drives the new physics to appear at TeV scale. Therefore, as the LHC cannot cater for the demand for new physics, proposals have been made to build High Energy LHC (HE-LHC), which is designed to run at collision energy of 27 TeV with the integrated luminosity of 15 ab⁻¹. In this work, we propose to search for stops through single stop production via electroweak interaction at the HE-LHC (figure 1). Following the production process, the stop can decay into the SM top quark which then can go through two decay channels: hadronic channel and leptonic channel. The search for stop by these two channels has been studied in [32] at the 14 TeV LHC, we now explore their observability at the 27 TeV LHC. Generally, the stop pair production is considered as the discovery channel, but the single production can manifest the electroweak coupling between stop and neutralino, which can be used as a complementary study to the QCD pair production. After the stop mass can be determined through its pair production in the future, the single production search becomes a good way to identify the natures of electroweakinos. In addition, single production has distinct signatures at the LHC that are not present in pair production, which can serve as further confirmation of the discovery of stop [32-35].

Figure 1.

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Figure 1.Feynman diagrams for the single stop production at LO.


We assume a simplified scenario of the [36-40] in our research in which the only sparticles are the stop and charginos. Bino, winos and higgsinos constitute the electroweakino sector where the neutralinos ${\tilde{\chi }}_{1,2,3,4}^{0}$ are formed as mass eigenstates of the neutral components. Their mass matrix can be written as(1)$\begin{eqnarray}{{\boldsymbol{M}}}_{{\chi }^{0}}=\left(\begin{array}{cccc}{M}_{1} & 0 & -{c}_{\beta }{s}_{W}{m}_{Z} & {s}_{\beta }{s}_{W}{m}_{Z}\\ 0 & {M}_{2} & {c}_{\beta }{c}_{W}{m}_{Z} & -{s}_{\beta }{c}_{W}{m}_{Z}\\ -{c}_{\beta }{s}_{W}{m}_{Z} & {c}_{\beta }{c}_{W}{m}_{Z} & 0 & -\mu \\ {s}_{\beta }{s}_{W}{m}_{Z} & -{s}_{\beta }{c}_{W}{m}_{Z} & -\mu & 0\end{array}\right),\end{eqnarray}$from which we can infer that the neutralinos can be treated as bino-, wino- or higgsino-like with the mass parameters M₁,M₂ or μ, if the mass of Z boson can be neglected. In a similar way, the mass matrix of charginos ${\tilde{\chi }}_{1,2}^{\pm }$(2)$\begin{eqnarray}{{\boldsymbol{M}}}_{{\chi }^{\pm }}=\left(\begin{array}{cc}0 & {X}^{{\rm{T}}}\\ X & 0\end{array}\right),\quad \mathrm{with}\,{\boldsymbol{X}}=\left(\begin{array}{cc}{{M}}_{2} & \sqrt{2}{s}_{\beta }{m}_{W}\\ \sqrt{2}{c}_{\beta }{m}_{W} & \mu \end{array}\right),\end{eqnarray}$leads wino- or higgsino-like charginos with a negligible W mass. Through unitary matrices N,U and V, the above two mass matrices(1) and (2) can be diagonalized. A nearly degerate higgsino-like LSP (the lightest SUSY particle) can thus be obtained with U₁₂∼1, ${V}_{12}\sim \mathrm{sgn}(\mu )$, ${N}_{\mathrm{13,14,23}}=-{N}_{24}\,\sim 1/\sqrt{2}$, V₁₁,U₁₁,N_11,12,21,22∼0 and μ≪M_1,2. Moreover, we set $\tan \beta =50$ and ${m}_{{\tilde{U}}_{3R}}\ll {m}_{{\tilde{Q}}_{3L}}$ so that the top squark is right-handed, which can be seen from the mass-squared matrix of top squark(3)$\begin{eqnarray}{{\boldsymbol{M}}}_{\tilde{t}}^{2}=\left(\begin{array}{cc}{m}_{{\tilde{t}}_{L}}^{2} & {m}_{t}{X}_{t}^{\dagger }\\ {m}_{t}{X}_{t} & {m}_{{\tilde{t}}_{R}}^{2}\end{array}\right),\end{eqnarray}$with(4)$\begin{eqnarray}{X}_{t}={A}_{t}-\mu \cot \beta ,\end{eqnarray}$(5)$\begin{eqnarray}{m}_{{\tilde{t}}_{R}}^{2}={m}_{{\tilde{U}}_{3R}}^{2}+{m}_{t}^{2}+\displaystyle \frac{2}{3}{m}_{Z}^{2}{\sin }^{2}{\theta }_{W}\cos 2\beta ,\end{eqnarray}$(6)$\begin{eqnarray}{m}_{{\tilde{t}}_{L}}^{2}={m}_{{\tilde{Q}}_{3L}}^{2}+{m}_{t}^{2}+{m}_{Z}^{2}\left(\displaystyle \frac{1}{2}-\displaystyle \frac{2}{3}{\sin }^{2}{\theta }_{W}\right)\cos 2\beta ,\end{eqnarray}$where A_t is the trilinear parameter. The branching ratio of ${\tilde{t}}_{R}\to t{\tilde{\chi }}_{1,2}^{0}$ is assumed to be 50% [35]. Because the mass splitting between ${\tilde{\chi }}_{1}^{\pm }$ and neutralino is very small, the leptons from ${\tilde{\chi }}_{1}^{\pm }$ decay are so soft that they will give a unique signature which is identified as transverse missing energy at the collider. In addition, with the conserved R-parity, the lightest neutralino ${\tilde{\chi }}_{1}^{0}$ may serve as a dark matter particle. And for a wino- or higgsino-like LSP, the mass of the LSP should be of TeV scale to account for the observed dark matter relic density, due to the large annihilation rates [41]. While for a light higgsino-like LSP in the natural MSSM, alternative schemes have been proposed to produce the required relic density through the standard thermally way, such as making an axion-higgsino admixture as the dark matter candidate [42, 43].

We use the following softwares for Monte-Carlo simulation: MadGraph5_aMC@NLO for event generation at parton level, Pythia [44] for hadronization and parton showering, Delphes [45] for detector simulation and CheckMATE2 [46] as a processor connecting the above tools. And we also include the effects of QCD corrections at next-to-leading order by applying a K-factor of 1.4 [33, 47, 48]. SUSYHIT is used to calculate the sparticles mass spectrum. To cluster jets, we use anti-k_t algorithm with a cone radius ΔR=0.4 [49].

This paper is organized as follows. In section 2, we present the study of the leptonic channel from single stop production at the HE-LHC. And section 3 is on the hadronic channel. In section 4, we draw a conclusion on our work.

2. Mono-top signature of leptonic channel from single stop production at the HE-LHC

In this section, we investigate the mono-top signature of leptonic channel from single stop production:(7)$\begin{eqnarray}{pp}\to {\tilde{t}}_{1}{\tilde{\chi }}_{1}^{-}\to t{\tilde{\chi }}_{1}^{0}{\tilde{\chi }}_{1}^{-}\to {\tilde{\chi }}_{1}^{0}{\tilde{\chi }}_{1}^{-}{{bl}}^{+}\nu \,.\end{eqnarray}$The dominant background for this process is the SM $t\bar{t}$ production from semi- or full-leptonic decay of top quark, since the system of limited jet energy resolution and missing leptons can be miss-tagged as ${{/}\!\!\!\!{E}}_{T}$. Another background comes from the single top production due to the undetected final leptons. We neglect some possible backgrounds, such as diboson production, because their cross sections are relatively small.

The signature of equation (7) consists of a hard b jet and a charged lepton plus missing transverse energy ${{/}\!\!\!\!{E}}_{T}$, from which we find several kinematic variables that can be used to separate signal and background, including the number of lepton N_ℓ and b-jet N_b, the transverse momentum of the leading b-jet p_T(b₁), missing transverse energy ${{/}\!\!\!\!{E}}_{T}$ and the transverse mass of lepton plus missing energy M_T^l. We also construct the variable H_T3 [50] as the scalar sum of the transverse momentum of the third to fifth jet, to suppress the $t\bar{t}$ background, since the signal has less hard jets. We present the distributions of N_ℓ, N_b, p_T(b₁), ${{/}\!\!\!\!{E}}_{T}$, M_T^l and H_T3 for the signal and background events at the 27 TeV LHC. The benchmark point is μ=200 GeV and ${m}_{{\tilde{t}}_{1}}=1000\,\mathrm{GeV}$. As shown in figure 2, lepton number of the signal events is more likely to center around N_ℓ=1 while the backgrounds around N_ℓ=0. Because of the boost effect of the b-jet from the stop decay, the leading b jets in signal events tend to be harder than that in the background events. The distributions of ${{/}\!\!\!\!{E}}_{T}$ and M_T^l in the larger region for the signal are natural consequences as a result of the massive ${\tilde{\chi }}_{1}^{\pm }$, which are well separated from the backgrounds.

Figure 2.

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Figure 2.Normalized distributions of N(l), N(b), p_T(b₁), ${{/}\!\!\!\!{E}}_{T}$, M_T^l, and H_T3 for the leptonic channel at 27 TeV LHC. The benchmark point is set as μ=200 GeV and ${m}_{{\tilde{t}}_{1}}=1000\,\mathrm{GeV}$.


After the above discussion, we select the events with the following cuts: (1) exact one lepton in the final state is required; (2) we require at least one b-jet and that the leading b-jet satisfies p_T(b₁)>200 GeV; (3) ${{/}\!\!\!\!{E}}_{T}\gt 500\,\mathrm{GeV}$ and ${M}_{T}^{l}\gt 650\,\mathrm{GeV}$ are required; (4) H_T3<200 GeV is required to further suppress the $t\bar{t}$ background; (5) to finally reduce multi-jet events in the $t\bar{t}$ background, we apply a cut as the minimum azimuthal angle between any of the jets and the missing transverse momentum ${\rm{\Delta }}\phi (j,{{/}\!\!\!\!{\vec{p}}}_{T})\gt 0.6$. We present the cutflow based on the above event cuts in table 1 for the leptonic channel of single stop production as well as for the SM backgrounds. As we can see from the table, the most effective cut is by the large ${{/}\!\!\!\!{E}}_{T}$, which can suppress single-top and $t\bar{t}$ backgrounds by about ${ \mathcal O }({10}^{2})$. To estimate the statistical significance α, we use $\alpha =S/\sqrt{B}$ where S (B) is the events number after the above cuts applied. In figure 4(a), we present the 2σ exclusion limits for the leptonic channel on the plane of higgsino mass parameter μ versus stop mass ${m}_{{\tilde{t}}_{1}}$, from which we can find that ${m}_{{\tilde{t}}_{1}}\lt 1900\,\mathrm{GeV}$ and μ<750 GeV can be excluded at 2σ level.


Table 1.
Table 1.A cut flow analysis of the cross sections (in unit of fb) for the leptonic channel events at the HE-LHC.

Cut	Signal	Background
$m({\tilde{t}}_{1},\mu )$ [GeV]	(1000, 200)	Single-top	$t\bar{t}$
Nl=1	8.179	3.1·105	8.75·105
Nb≥1	6.296	2.31·105	8.08·105
pT(b1)>200 [GeV]	3.262	7.9·103	4.45·104
${{/}\!\!\!\!{E}}_{T}\gt 500$ [GeV]	1.067	79.75	135.35
${M}_{T}^{l}\gt 650$ [GeV]	0.473	37.89	39.63
HT3<200 [GeV]	0.101	0.507	0.955
${\rm{\Delta }}\phi (j,{{/}\!\!\!\!{\vec{p}}}_{T})\gt 0.6$	0.0524	0.2537	0.2387

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3. Mono-top signature of hadronic channel from single stop production at the HE-LHC

In this section, we investigate the mono-top signature of hadronic channel from single stop production:(8)$\begin{eqnarray}{pp}\to {\tilde{t}}_{1}{\tilde{\chi }}_{1}^{-}\to t{\tilde{\chi }}_{1}^{0}{\tilde{\chi }}_{1}^{-}\to {\tilde{\chi }}_{1}^{0}{\tilde{\chi }}_{1}^{-}{bjj}.\end{eqnarray}$In addition to $t\bar{t}$ and single top background, another dominant background is Z+jets because light-flavor jets can fake the signal b-jet in the final state.

In figure 3, we present the distributions of N_b, p_T(b₁), ${{/}\!\!\!\!{E}}_{T}$ and H_T3 . From the kinematic distributions, we can find that signal has more events than background centered around N_b = 1. Similar to the case of leptonic channel, the boost of the leading b-jet from the stop decay leads to a larger p_T(b₁) for the signal and the massive ${\tilde{\chi }}_{1}^{\pm }$ leads to a larger ${{/}\!\!\!\!{E}}_{T}$ of the signal events than the backgrounds. H_T3 can also be used to distinguish between signal and background due to less hard jets in the signal.

Figure 3.

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Figure 3.Normalized distributions of N(b), p_T(b₁), ${{/}\!\!\!\!{E}}_{T}$, and H_T3 for hadronic channel events at 27 TeV LHC. The benchmark point is set as μ=200 GeV and ${m}_{{\tilde{t}}_{1}}=1000\,\mathrm{GeV}$.


Then we use the following cuts after the above analysis on the kinematic distributions: (1) we require no leptons in the final states; (2) we require at least one b-jet and the leading b-jet satisfies p_T(b₁)>200 GeV; (3) ${{/}\!\!\!\!{E}}_{T}\gt 700\,\mathrm{GeV}$ is required; (4) we require p_T(j₁)>650 GeV; (5) H_T3<350 GeV is required; (6) ${\rm{\Delta }}\phi (j,{{/}\!\!\!\!{\vec{p}}}_{T})\gt 0.6$ where ${\rm{\Delta }}\phi (j,{{/}\!\!\!\!{\vec{p}}}_{T})$ is defined in the same way as in the last section. In table 2, we can see that the large ${{/}\!\!\!\!{E}}_{T}$ requirement can suppress single-top and $t\bar{t}$ backgrounds most effectively by about ${ \mathcal O }({10}^{3})$, with about 10% signal events surviving.


Table 2.
Table 2.A cut flow analysis of the cross sections (in unit of fb) for the hadronic channel events at the HE-LHC. Note that S/B for this channel is tiny due to the large SM backgrounds and the sensitivity is worse than that of the leptonic channel, as shown in figure 4.

Cut	Signal	Background
$m({\tilde{t}}_{1},\mu )$ [GeV]	(1000, 200)	Single-top	$t\bar{t}$	Z+jets
Lepton veto	8.976	3.1·105	9.15·105	1.01·108
Nb≥1	6.863	2.34·105	7.65·105	2.15·107
pT(b1)>200 [GeV]	3.8	7.9·103	4.74·104	1.6·105
${{/}\!\!\!\!{E}}_{T}\gt 700$ [GeV]	0.39	25.46	12.41	455
pT(j1)>650 [GeV]	0.26	21.06	10.98	364
HT3<200 [GeV]	0.085	1.35	1.19	156
${\rm{\Delta }}\phi (j,{{/}\!\!\!\!{\vec{p}}}_{T})\gt 0.6$	0.045	0.93	1.19	65

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The same formula $\alpha =S/\sqrt{B}$ is adopted to evaluate the statistical significance and the contour on the plane of μ versus ${m}_{{\tilde{t}}_{1}}$ is shown in figure 4(b) to present the 2σ exclusion limits for the hadronic channel. The higgsino mass parameter and stop mass can be excluded at 2σ to ${m}_{{\tilde{t}}_{1}}\lt 1200\,\mathrm{GeV}$ and μ<350 GeV, respectively. It should be noted due to the large background for the hadronic channel, the sensitivity of this channel is worse than that of the leptonic channel, as can be seen from the contours in figure 4.

Figure 4.

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Figure 4.The statistical significance $S/\sqrt{B}$ for the processes: (a) leptonic channel and (b) hadronic channel, on the plane of stop mass ${m}_{{\tilde{t}}_{1}}$ versus the higgsino mass parameter μ at the HE-LHC.


In both cases of leptonic and hadronic channels, the systematic uncertainties caused by high pile-up will lead to lower statistical significance and we can resort to real performance of upgraded detectors. And new developed analysis methods including the machine-learning ones [51-54] may be used to improve our results in such searches at hadron colliders.

Finally we mention that, as a complete research, we have also perform studies on the search for another decay mode of the stop, which is the mono-b channel [5, 55]: ${pp}\to {\tilde{t}}_{1}{\tilde{\chi }}_{1}^{-}\to b+{{/}\!\!\!\!{E}}_{T}$. The stop mass can be excluded below 1.9 TeV at 27 TeV LHC with ${ \mathcal L }=15\,{\mathrm{ab}}^{-1}$ and below 3.9 TeV at the 100 TeV hadron colliders such as FCC-hh or SPPC with ${ \mathcal L }=3000\,{\mathrm{fb}}^{-1}$.

4. Conclusion

In this work, we investigate the sensitivity of the leptonic and hadronic channel from single stop production in a simplified MSSM scenario at the 27 TeV LHC with the integrated luminosity of ${ \mathcal L }=15\,{\mathrm{ab}}^{-1}$. As a complementary study to the traditional pair production, the single stop production presents some unique signatures from which we construct several useful kinematic variables to distinguish the signal from backgrounds. 2σ exclusion limits for both cases are presented: ${m}_{{\tilde{t}}_{1}}\lt 1900\,\mathrm{GeV}$ and μ<750 GeV for the leptonic channel, while ${m}_{{\tilde{t}}_{1}}\lt 1200\,\mathrm{GeV}$ and μ<350 GeV for the hadronic channel.

Acknowledgments

Xu-Xu Yang would like to thank Yuchao Gu for helpful discussions. This work was supported by the National Natural Science Foundation of China (NNSFC) under Grant No. 11 705 093, and by the Jiangsu Planned Projects for Postdoctoral Research Funds, Grant No. 2019K197.

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