Leptonic mono-top from single stop production at LHC

Top squark (stop) can be produced via QCD interaction but also the electroweak interaction at the LHC. In this paper, we investigate the observability of the associated production of stop and chargino, $pp \to \tilde{t}_1\tilde{\chi}^-_1$, in compressed electroweakino scenario at the 14 TeV LHC. Due to the small mass-splitting between the lightest neutralino ($\tilde{\chi}^0_1$) and chargino ($\tilde{\chi}^-_1$), such a single stop production can give a mono-top signature through the stop decay $\tilde{t}_1 \to t \tilde{\chi}^0_1$. Focusing on the leptonic mono-top channel, we propose a lab-frame observable $\cos\theta_{b\ell}$ to reduce the SM backgrounds in virtue of a boosted top quark from the stop decay. We find that the single stop production can be probed at $2\sigma$ level at the HL-LHC for $m_{\tilde{t}_1}<760$ GeV and $m_{\tilde{\chi}^0_1}<150$ GeV.

So far, ATLAS and CMS collaborations have performed extensive searches for stops at the LHC Run-1 and Run-2. The current search strategies are specialized for different kinematical regions. For example, when mt 1 mχ0 1 + m t , the top quarks from stop decays are usually energetic. With the endpoint observables, such as M T 2 [24,25], the stop pair can be discriminated from the tt background. But in the compressed regions, for example mt 1 ≈ mχ0 1 + m t , the decay products of the stop are very soft. In this region, the stop is searched for by using the monojet signature [26][27][28][29][30][31][32]. Based on recent Run-2 (∼ 15 fb −1 ) dataset, the stop mass has been excluded up to ∼ 1 TeV in simplified models [33][34][35][36][37][38][39][40]. Like the top quark, stops can be produced in pair, but also can be singly produced via the electroweak interaction, such as the associated production of the stop and chargino, bg →t 1χ − 1 (c.f. Fig. 1) [41][42][43]. When the stop and chargino are not heavy or the chargino is much lighter than the stop [41], the single stop production can have a sizable cross section at the LHC. Although the single stop may not be a good discovery channel as the stop pair production, the study of single stop is meaningful because it can serve as a complementary channel to probe the electroweak properties of the stop [42,43].
In this work, we explore the feasibility of probing the single stop production process pp →t 1 (→ tχ 0 1 )χ − 1 + X in a compressed SUSY scenario, where the charginoχ ± 1 is almost degenerate with the lightest neutralinoχ 0 1 . Such a spectrum is motivated by natural SUSY [4,5] or the well-tempered neutralino frameworks [44]. Due to the small mass splitting betweenχ ± 1 andχ 0 1 , the single stop production will give the mono-top signature [43,[45][46][47][48][49] and in Ref. [43] its full-hadronic final states with top tagging technique are studied. In this study, we focus on the leptonic mono-top channel of the process pp →t 1χ − 1 . In contrast with the full hadronic channel, the leptonic channel has no QCD background pollution. Besides, the cut on the leptonic m T can greatly reduce the tt and W + b backgrounds [47,48]. We also construct a new variable, which is the open angle of the charged lepton and b-jet from the top quark in the stop decay, to reduce the SM backgrounds.
This work is organized as follows. In Sec. II, we calculate the single stop production at the LHC and stop decays in compressed electroweakino scenarios. In Sec. III, we perform detailed Monte Carlo simulation for the leptonic mono-top signature from the single stop production at the LHC. Finally, we summarize our conclusions in Sec. IV.
We evaluate the mass spectrum and branching ratios of all sparticles with SUSY-HIT [60].
We use MadGraph5 aMC@NLO [61] to calculate the leading order cross section of the single stop production. The NNPDF23LO1 [62] parton distribution functions are chosen for our calculations. The renormalization and factorization scales are set as the default value. We include the NLO-QCD correction by applying a K-factor of 1.3 [41,43] to the cross section of the single stop production. It should be noted that the single stop production not only relies on the nature of the electroweakinos, but also is affected by the polarized states of the stop. To demonstrate this, we consider two cases: the left-handed stopt L by taking mŨ 3R = 2 TeV to decouple the right-handed component, and the right-handed stopt R by taking mQ 3L = 2 TeV to decouple the left-handed component. In the lower panel of Fig. 5, we present the branching ratios of stop decaying to the top quark and neutralinos. For higgsino case, it can be seen that a left-handed stopt L dominantly decays to tχ 0 1,2 at tan β = 10. The reason is that the decay width of bχ + 1 is proportional to y b and is suppressed for a small tan β. If the stop is right-handedt R , its couplings withχ 0 1,2 andχ ± 1 are proportional to y t , and the branching ratios oft R → tχ 0 1,2 andt R → bχ + 1 are about 50% and 50%, respectively. For the wino case, botht L andt R decay to tχ 0 1 with the same branching ratio. Besides, it can be seen that the cross section of stop pair production σ(tt * ) is about one order of magnitude larger than that of single stop production if stop mass is less than 300 GeV. With the increase of stop mass, the cross section of stop pair production decreases more rapidly than the single stop production due to the suppression of phase space. For example, when stop mass is 700 GeV, the ratio of σ(tt * )/σ(t RH − ) is about four. Considering the stop decay branching ratios, we find that the number of events oft 1t * 1 (→tχ 0 1,2 ) production is still about two times larger than that oft R (→ tχ 0 1,2 )H − production. While the expected number of events oft L (→ tχ 0 1,2 )H − andt L,R (→ tχ 0 1 )W − productions are less than that of t R (→ tχ 0 1,2 )H − . In the following, we will uset R (→ tχ 0 1,2 )H − production as an example to investigate the observability of the single stop production at the LHC.

III. LEPTONIC MONO-TOP SIGNATURE FROM SINGLE STOP PRODUC-TION AT THE LHC
Sinceχ ± 1 andχ 0 1,2 are the nearly degenerate higgsinos in our considered scenario, the mass splitting between them is small so thatχ ± 1 andχ 0 2 appear as missing transverse energy at the LHC. This leads to the mono-top signature for the single stop production at the LHC, which is In our simulation, we focus on the leptonic mono-top channel. In contrast with the full hadronic final states, the problematic QCD multijet background can be safely neglected in this leptonic channel. We use MadGraph5 aMC@NLO [61] to generate the parton level events. Then, we perform the parton shower and hadronization by Pythia [63]. The jets are clustered by the anti-k t algorithm with a cone radius ∆R = 0.4 [65]. We implement the detector effects with Delphes [64].
The SM backgrounds are dominated by the following processes: • The largest SM backgrounds are the semi-and di-leptonic tt productions, where the missing lepton and the limited jet energy resolution will lead to relatively large missing E T . The leading order cross section of tt production is normalized to its approximate next-to-next-to-leading-order value σ NNLOapprox tt = 920 pb [66].
• The subdominant background is the single top production, which is irreducible, up to a jet that could come from ISR. We include three production modes tj, tb and tW in our simulation.
There are other possible SM backgrounds, such as W + jets and the diboson production In Fig. 4, we show the jet multiplicity (N jets ) distributions of the signal and backgrounds.
We can see that most of events of tt and single top backgrounds have larger N jets than the single stop process. To suppress the backgrounds, we will veto the second hard jet in our event selection.
Another interesting observable is the opening angle θ b between the charged lepton and the b-jet in the lab-frame. After requiring exactly one lepton and one b-jet, we display the distribution of cos θ b in Fig. 5. We can see that most of the signal events fall in the region of cos θ b > 0, while the backgrounds have more events in the region of cos θ b < 0. This is because the the charged lepton and the b-quark from top quark in the stop decays are boosted so that they tend to move in the same direction when the mass splitting betweeñ • We require exact one hard lepton with p T ( ) > 30 GeV and |η | < 2.5.
• We require exact one b-jet with p T (b) > 75 GeV and |η b | < 2.5 and veto extra jets with p T (j) > 20 GeV to suppress the tt background.  In Table I,  In Fig. 6, we plot the dependence of the signal significance S/ √ B on mχ0 1 and m t 1 for the 14 TeV LHC with a luminosity L = 3000 fb −1 . From this figure we can see that the significance drops with the increase of mχ0 1 and m t 1 because of the reduction of the cross section. We find that the parameter range 100 GeV ≤ mχ0 1 ≤ 150 GeV and mt 1 ≤ 760 GeV can be covered at ≥ 2σ level with S/B > 3% at the HL-LHC, which is moderately better than the hadronic stop channel [43]. Given a discovery of the stop and a measurement of the single stop production cross section, we examine the discriminating power of single stop production with regard to the electroweak properties of the stop. In Fig. 7, we show the statistical significance S/ √ B of the process pp →t 1χ − 1 for a benchmark point mt 1 = 600 GeV, µ = 100 GeV and M 1,2 = 2 TeV on the plane of stop mixing angle cos θt 1 and tan β at 14 TeV LHC with L = 3000 fb −1 .
We can see that the mixing angle cos θt 1 0.5 ( right-handed-like stop) can be probed above 5σ level. While for cos θt 1 0.5 (left-handed-like stop), the significance S/ √ B depends on the value of tan β. This is because the cross section oft LH − production is sensitive to tan β (c.f. Fig. 2). When cos θt 1 > 0.7, the significance S/ √ B is be less than 3σ. On the other hand, ifχ − 1 is wino-like, we can expect that the large cos θt 1 region will have larger S/ √ B than the small cos θt 1 region at the HL-LHC since the cross section oft LW − production is much larger than that oft RW − production (c.f. Fig. 2).

IV. CONCLUSION
In this work we explored the observability of the associated production of stop and chargino in the compressed electroweakino scenario at 14 TeV LHC. Due to the small mass splitting betweenχ 0 1 andχ − 1 , such a production can lead to the mono-top signature via stop decayt 1 → tχ 0 1 . We analyze the leptonic mono-top channel pp →t 1χ − 1 → b + / E T , and construct a lab-frame observable cos θ b from the top quark in the stop decay to reduce the SM backgrounds. We found that the stop mass can be probed up to 760 GeV at 2σ level through the single stop production at 14 TeV LHC with L = 3000 fb −1 . We also find that the stop mixing angle can also be determined from the single stop production assuming a measurement of the single stop production cross section at HL-LHC.