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. 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 as1 ) 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, N11,12,21,22 ∼ 0 and μ ≪ M1,2. 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
$\begin{eqnarray}{{\boldsymbol{M}}}_{{\chi }^{0}}=\left(\begin{array}{cccc}{M}_{1} & 0 & -{c}_{\beta }{s}_{W}{m}_{Z} & {s}_{\beta }{s}_{W}{m}_{Z}\\ 0 & {M}_{2} & {c}_{\beta }{c}_{W}{m}_{Z} & -{s}_{\beta }{c}_{W}{m}_{Z}\\ -{c}_{\beta }{s}_{W}{m}_{Z} & {c}_{\beta }{c}_{W}{m}_{Z} & 0 & -\mu \\ {s}_{\beta }{s}_{W}{m}_{Z} & -{s}_{\beta }{c}_{W}{m}_{Z} & -\mu & 0\end{array}\right),\end{eqnarray}$
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 ${\tilde{\chi }}_{1,2}^{\pm }$ $\begin{eqnarray}{{\boldsymbol{M}}}_{{\chi }^{\pm }}=\left(\begin{array}{cc}0 & {X}^{{\rm{T}}}\\ X & 0\end{array}\right),\quad \mathrm{with}\,{\boldsymbol{X}}=\left(\begin{array}{cc}{{M}}_{2} & \sqrt{2}{s}_{\beta }{m}_{W}\\ \sqrt{2}{c}_{\beta }{m}_{W} & \mu \end{array}\right),\end{eqnarray}$
leads wino- or higgsino-like charginos with a negligible W mass. Through unitary matrices N, U and V, the above two mass matrices ( $\begin{eqnarray}{{\boldsymbol{M}}}_{\tilde{t}}^{2}=\left(\begin{array}{cc}{m}_{{\tilde{t}}_{L}}^{2} & {m}_{t}{X}_{t}^{\dagger }\\ {m}_{t}{X}_{t} & {m}_{{\tilde{t}}_{R}}^{2}\end{array}\right),\end{eqnarray}$
with $\begin{eqnarray}{X}_{t}={A}_{t}-\mu \cot \beta ,\end{eqnarray}$
$\begin{eqnarray}{m}_{{\tilde{t}}_{R}}^{2}={m}_{{\tilde{U}}_{3R}}^{2}+{m}_{t}^{2}+\displaystyle \frac{2}{3}{m}_{Z}^{2}{\sin }^{2}{\theta }_{W}\cos 2\beta ,\end{eqnarray}$
$\begin{eqnarray}{m}_{{\tilde{t}}_{L}}^{2}={m}_{{\tilde{Q}}_{3L}}^{2}+{m}_{t}^{2}+{m}_{Z}^{2}\left(\displaystyle \frac{1}{2}-\displaystyle \frac{2}{3}{\sin }^{2}{\theta }_{W}\right)\cos 2\beta ,\end{eqnarray}$
where At 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-kt 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:
$\begin{eqnarray}{pp}\to {\tilde{t}}_{1}{\tilde{\chi }}_{1}^{-}\to t{\tilde{\chi }}_{1}^{0}{\tilde{\chi }}_{1}^{-}\to {\tilde{\chi }}_{1}^{0}{\tilde{\chi }}_{1}^{-}{{bl}}^{+}\nu \,.\end{eqnarray}$
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 Nℓ and b-jet Nb, the transverse momentum of the leading b-jet pT(b1), missing transverse energy ${{/}\!\!\!\!{E}}_{T}$ and the transverse mass of lepton plus missing energy MTl. We also construct the variable HT3 [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 Nℓ, Nb, pT(b1), ${{/}\!\!\!\!{E}}_{T}$, MTl and HT3 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 Nℓ=1 while the backgrounds around Nℓ=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 MTl 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. Normalized distributions of N(l), N(b), pT(b1), ${{/}\!\!\!\!{E}}_{T}$, MTl, and HT3 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 pT(b1) > 200 GeV; (3) ${{/}\!\!\!\!{E}}_{T}\gt 500\,\mathrm{GeV}$ and ${M}_{T}^{l}\gt 650\,\mathrm{GeV}$ are required; (4) HT3 < 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. 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 |
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:
$\begin{eqnarray}{pp}\to {\tilde{t}}_{1}{\tilde{\chi }}_{1}^{-}\to t{\tilde{\chi }}_{1}^{0}{\tilde{\chi }}_{1}^{-}\to {\tilde{\chi }}_{1}^{0}{\tilde{\chi }}_{1}^{-}{bjj}.\end{eqnarray}$
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 Nb, pT(b1), ${{/}\!\!\!\!{E}}_{T}$ and HT3 . From the kinematic distributions, we can find that signal has more events than background centered around Nb = 1. Similar to the case of leptonic channel, the boost of the leading b-jet from the stop decay leads to a larger pT(b1) for the signal and the massive ${\tilde{\chi }}_{1}^{\pm }$ leads to a larger ${{/}\!\!\!\!{E}}_{T}$ of the signal events than the backgrounds. HT3 can also be used to distinguish between signal and background due to less hard jets in the signal.
Figure 3. Normalized distributions of N(b), pT(b1), ${{/}\!\!\!\!{E}}_{T}$, and HT3 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 pT(b1) > 200 GeV; (3) ${{/}\!\!\!\!{E}}_{T}\gt 700\,\mathrm{GeV}$ is required; (4) we require pT(j1) > 650 GeV; (5) HT3 < 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. 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 |
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. 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.