Constraining the Compressed Top Squark and Chargino along the W Corridor
Abstract
Studying superpartner production together with a hard initial state radiation (ISR) jet has been a useful strategy for searches of supersymmetry with a compressed spectrum at the Large Hadron Collider (LHC). In the case of the top squark (stop), the ratio of the missing transverse momentum from the lightest neutralinos and the ISR momentum, defined as , turns out to be an effective variable to distinguish the signal from the backgrounds. It has helped to exclude the stop mass below 590 GeV along the top corridor where . On the other hand, the current experimental limit is still rather weak in the corridor where . In this work we extend this strategy to the parameter region around the corridor by considering the one lepton final state. In this case the kinematic constraints are insufficient to completely determine the neutrino momentum which is required to calculate . However, the minimum value of consistent with the kinematic constraints still provides a useful discriminating variable, allowing the exclusion reach of the stop mass to be extended to GeV based on the current 36 fb LHC data. The same method can also be applied to the chargino search with because the analysis does not rely on jets. If no excess is present in the current data, a chargino mass of 300 GeV along the corridor can be excluded, beyond the limit obtained from the multilepton search.
I Introduction
Weakscale supersymmetry (SUSY) has long been considered as the leading candidate for the new physics beyond the Standard Model (SM). Supersymmetric particles have been searched for at colliders for decades but unfortunately none of them has been found yet. The strong limits from the searches at the Large Hadron Collider (LHC) have raised concerns if SUSY can provide the solution to the hierarchy problem of the Higgs mass scale in SM, as the LHC probes the energy scale into the TeV range. For the hierarchy problem, the most relevant particles are the superpartners of the top quark, top squarks (or simply stops), because the top quark has the largest coupling to the Higgs field and hence gives the largest quadratic correction to the Higgs masssquared parameter. The stops are needed to be near the weak scale to cut off this contribution in order for the theory to be natural. The current lower bound on the stop has reached beyond 1 TeV in typical search channels at the LHC Aaboud:2017ayj ; Aaboud:2017bac ; Aaboud:2017nfd ; Sirunyan:2017cwe ; Sirunyan:2017wif ; Sirunyan:2017kqq ; CMS:2017zki ; Sirunyan:2017xse ; Sirunyan:2017leh , which would imply quite severe finetuning already.
Of course, there are cases where the stop mass limit is not as strong yet. In particular, the limit degrades if the masses difference between the stop and the lightest supersymmetric particle (LSP) that it decays to become smaller, i.e., they have a compressed spectrum. In this case, the visible SM particles from the stop decay will not carry a large amount of energy. The missing transverse momentum will also be suppressed because it is just the opposite of the sum of the visible transverse momentum. These signal events are more difficult to be distinguished from the SM backgrounds. The search strategies and search limits depend on how compressed the spectrum is and stop decay chains. For example, for highly compressed spectra (), the searches rely on 4body decays () Boehm:1999tr ; Das:2001kd ; Konar:2016ata ; Aaboud:2017bac ; Aaboud:2017nfd ; CMS:2017odo ; CMS:2016zvj ; Khachatryan:2016pxa or flavorchanging decays () Hikasa:1987db ; Muhlleitner:2011ww ; Khachatryan:2016pxa ; Sirunyan:2017kiw ; Aad:2014nra ; Aaboud:2016tnv , or even monojet Drees:2012dd . Before the LHC Run 2, the most difficult case used to be the top corridor, where . This is because the top quark and the neutralino from the stop decay carry little momenta in the stop rest frame and are boosted with the same velocity as the original stop particle. The stop pair is produced backtoback in the transverse plane, resulting in the cancellation of the two neutralinos’ transverse momenta, leaving no trace of their existence. Then the events look exactly like the large SM background. The analyses of the Run 1 data provided essentially no constraint along the top corridor.
The situation has completely changed in Run 2 with new techniques being employed to attack this parameter space region. An important observation is that if the stop pair is produced with a hard initial state radiation (ISR) jet, the two neutralinos will be boosted in the opposite direction to the ISR jet, giving missing transverse energy (MET) antiparallel to the ISR jet Carena:2008mj ; Hagiwara:2013tva ; An:2015uwa ; Macaluso:2015wja . A variable which measures the ratio the twoneutralino transverse momentum and the ISR transverse momentum provides a powerful discriminator between the signal and the backgrounds, as it should be equal to for the stop events while close to zero for the SM backgrounds. With a sophisticated method to determine the ISR system Jackson:2016mfb , the Run 2 analysis has been able to exclude the stop mass below 590 GeV along the top corridor with 36 fb of data Aaboud:2017ayj , assuming 100% branching fraction to . This is quite impressive, and the limit is even stronger than the nearby parameter region where the mass difference between and is somewhat off the top quark mass.
The analysis with the variable is based on the fully hadronic channel where there is no additional MET other than that carried by the two neutralinos. In this case is simply given by
(1) 
In semileptonic or dileptonic decays, however, the neutrino(s) coming from the decays give an additional contribution to MET, which ruin the relation in Eq. (1). One way to deal with this is to try to reconstruct the neutrino momentum so that it can be subtracted from the total MET to obtain the MET due to the neutralinos only. Then a modified variable related to can be defined analogously as a discriminating variable. For the semileptonic decay, it was shown Cheng:2016mcw that from the 3 mass shell conditions () together with the assumption that the perpendicular component of the relative to is entirely due to the neutrino, the neutrino momentum can be solved with a twofold ambiguity. After subtracting the solved neutrino momentum, the variable also provides a strong discriminator for the stop events in the semileptonic decay channel and makes it competitive with the fully hadronic result.
For the dileptonic channel with two final state neutrinos, there is one more unknown than the number of kinematic constraint equations, so we can not completely reconstruct the neutrino momenta. Instead, for each event we can only obtain a finite range of which can be consistent with that event. Nevertheless, the upper and lower limits of the allowed , denoted by and could provide potential variables for discriminating signals from backgrounds. In Ref. Cheng:2017dxe , it was found indeed that and provide more discriminating power than just using and MET. Although, for the case of stop decaying to top plus LSP, the dileptonic channel is not expected to compete with the allhadronic or semileptonic channels due to the small branching ratios, the dileptonic search can be useful if the SUSY spectrum is such that the stop decays mainly through the chargino and the slepton decays to the LSP, in which case the dileptonic final states can be dominant Cheng:2017dxe ; Konar:2017oah .
After the progress in stop search coverage along the top corridor, the corridor where remains relatively weakly constrained. In this case, the bottom quark, and from the stop decay are also static in the stop rest frame. The missing from the two ’s again cancels from the backtoback boost of the stoppair in the transverse plane. Such events are difficult to be distinguished from the SM backgrounds, resulting a poor reach in current LHC searches and the stop could still be as light as GeV around that region Aaboud:2017bac ; Aaboud:2017nfd . A natural thought is again to consider events with an ISR jet to boost the stoppair in the opposite direction so that the ’s will produce some MET. Then one can use the similar variables to distinguish signals from backgrounds. A main goal of this study is to explore whether this technique can help to improve the stop mass bound around the corridor.
We will focus on the semileptonic events where one decays leptonically and the other decays hadronically. The jets from the stop decays will be soft so they will not be useful due to low tagging efficiencies and large hadronic backgrounds. Compared with the semileptonic stop events along the top corridor, we lose a top quark mass shell constraint because the decay does not go through an onshell top quark. Therefore the neutrino momentum can not be completely reconstructed and a unique value can not be obtained. Nevertheless, the kinematic constraints still limit into a finite range. We can define the and variables just as for the case of the dileptonic stop events in the top corridor to examine whether they are useful in suppressing backgrounds. We will find out that does provide a useful discriminating variable in this case.
Since the jets are too soft to be useful in the corridor of the stop, the signal events look the same as the chargino pair production in the corridor () if one ignores the jets. The same analysis can be applied to the chargino search around the corridor. In SUSY, the chargino is usually accompanied by one or two neutralinos with similar masses, depending on whether it is winolike or higgsinolike. Hence, one should consider chargino and neutralino pair productions altogether. Under the assumption that the LSP is binolike and the chargino (neutralino) decays to the LSP plus an (oneshell or offshell) (), the current strongest constraints come from trilepton searches Sirunyan:2017lae ; CMS:2017sqn ; Aad:2014nua ; Aad:2014vma ; ATLAS:2017uun , where the production cross section is taken to be coming from the winos. However, for the same reason due to the large SM background, there is a search gap around , where the exclusion reach for is only about GeV CMS:2017sqn . We find that the search using variable with an ISR jet could compete with the trilepton search around that region.
This paper is organized as follows. In section II, we discuss the kinematic constraints for the stop pair production in the corridor with an ISR jet in the semileptonc channel. We define for this case and describe how to obtain the minimum and maximum allowed values from the constraint equations as the kinematic variables for the stop searches. In section III, we investigate the usefulness of the , variables for the stop searches in the corridor. A more detailed description of the analyses is given for a chosen benchmark stop mass at 450 GeV and it is shown that is quite useful in suppressing certain SM backgrounds. We then perform the study for a series of points along the corridor to obtain the signal significances in comparison with current search limits. In section IV we apply the similar analysis to the chargino (and second neutralino) pair productions and compare with the trilepton search limits. Section V contains our conclusions. A detailed description of the solutions for and from the kinematic constraints is presented in appendix A. In appendix B we compare the analyses with and without using the and variables and show that they indeed can improve the signal significances.
Ii Kinematics and Variables
For the stop pair production together with and ISR jet, the momentum conservation tells us that
(2) 
In the corridor where , the , and from the decay will simply be comoving with the same velocity as their mother particle . Therefore we have
(3) 
Together with Eq. (2) we obtain
(4) 
which is the kinematic variable that we would like to use for discriminating stop signals from backgrounds. However, for semileptonic decays, this quantity is not directly measurable, because the neutrino from the decay also contributes to the missing transverse momentum besides the two ’s. To obtain we need to know the neutrino momentum so that it can be subtracted from to get the total of the two ’s.
The neutrino momentum satisfies the two mass shell conditions:
(5)  
(6) 
In addition, the sum of the transverse momenta of the two ’s, , should be antiparallel to the ISR jet. If we decompose into components parallel and perpendicular to the direction, the perpendicular component should be attribute to the neutrino:
(7) 
which gives us one more constraint on the neutrino momentum once is determined. On the other hand, the parallel component receives contributions from both the ’s and the neutrino:
(8) 
Using Eq. (4), we can write
(9) 
where the quantities include signs which represent being parallel or antiparallel to the ISR.
We can see that there is one more unknown than the number of kinematic constraint equations, so we can not completely solve the constraint equations to obtain a unique or discrete solution.^{1}^{1}1In contrast, in the top corridor there is an additional mass shell condition of the top quark mass, , so the constraint equations can be solved to yield discrete solutions Cheng:2016mcw . However, the kinematic constraints still limit the solutions to a finite range. As in Ref. Cheng:2017dxe , the minimum and the maximum values of the allowed range of , and , provide potential variables for the signal and background discrimination. The detailed computation of and is presented in Appendix A. The combination of the kinematic constraints gives a quadratic equation for one neutrino component. To have real solutions, the discriminant of the quadratic equation is required to be . The discriminant is also quadratic in , so the two solutions of discriminant = 0 give and .
In the above discussion, the information of the jets from the stop decays is not used at all. In the corridor, the jets are typically too soft to be identified or to be useful. As a result, the same analysis also applies to the chargino pair production with the chargino decays to and . In SUSY, there is usually at least one neutralino () having a similar mass as that of the chargino, so the neutralinochargino pair production is also important at the same time. If decays to with decays hadronically and the from the chargino decays leptonically, our analysis can also apply. For the charginoneutralino production, the trilepton search traditionally provides the strongest constraint. We will perform a study based on our method in Sec. IV to compare it with the current trilepton search bound.
Iii Stop Searches along the W Corridor
iii.1 Signal and Background Generations
We use MadGraph 5 Alwall:2014hca and Pythia 6 Sjostrand:2006za to generate both the background and the signal events. MLM matching scheme Mangano:2002ea is applied for both the SM background and the SUSY signal production in order to prevent doublecounting between the matrix elements and the parton shower. The detector simulation is performed by Delphes 3 deFavereau:2013fsa , using the anti jet algorithm Cacciari:2008gp with the parameter . For the signals, the production cross sections are normalized to 13 TeV NLO+NLL results Borschensky:2014cia . The jet tagging efficiency is taken to be the same as one of the benchmark operating points shown in btagging , with the maximum efficiency .
Since we require exactly one lepton, large MET and hard extra jets, a number of SM processes can be responsible for such a final state. According to similar/related collider studies Sirunyan:2017mrs ; Aaboud:2017bac , we expect SM , , jets and diboson events to be our main backgrounds, since they can naturally provide a lepton and MET with large production rates. Other backgrounds, such as , jets and events either suffer from low production cross sections or low signal efficiencies. All SM backgrounds mentioned above are generated by the method aforementioned. Besides the SM backgrounds, the dileptonic decay of can be an irreducible background to the signal. However, this process has a much smaller cross section compared to the SM backgrounds and can be ignored for the rest of our discussion.
iii.2 Event Selection
For our benchmark studies, all events must satisfy the preliminary selection as described below. Each event is required to have at least 2 jets, 0 tautagged jet and exactly 1 isolated lepton with 20 GeV GeV and . The upper limit of the transverse momentum is imposed because our signal comes from a compressed spectrum and the bosons are not very boosted. Since we need a hard ISR jet, the leading jet is required to satisfy GeV while the rest of the jets must have GeV. A jet must have GeV and to be considered in the later analysis. The signal event is expected to have a substantial amount of missing transverse momentum from the neutralinos recoiled against the ISR jet. On the other hand, the missing transverse momentum of the SM backgrounds mainly comes from neutrinos. The requirement GeV is applied to eliminate most of the backgrounds. For toprelated backgrounds, decay provides hard jet(s) in the final states, thus we veto all tagged jets to reduce the impact of these backgrounds. Furthermore, to control the large jets background where the missing transverse energy is due to a single neutrino from the decay, a cut on the transverse mass GeV is imposed. It proved to be very effective to suppress + jets and other semileptonic backgrounds.
In our signal events, the neutralinos are recoiled against the ISR. To make sure that the leading jet is antiparallel to the sum of neutralinos’ momenta and is not from the decay of the stops, we require that and . To take into account the cases where there is more than one ISR jet, we define to be the vector sum of all jets’ that are inside the cone with the leading jet and outside with the lepton.
iii.3 Stop Benchmark Study
For an illustration, we describe in detail the analysis for a benchmark point “Stop450,” GeV, GeV along the corridor in the parameter space. For simplicity, we assume all other supersymmetric particles are decoupled and the stop’s decay branching ratio to through an offshell top is . Since the spectrum of interest is very compressed, the searches based on the types of variables are ineffective, which motivates us to explore the usefulness of the type of variables.
In Fig. 1 we plot the twodimensional distributions for the signal benchmark point Stop450 and SM backgrounds after the preliminary selection. As expected, the stop signal events mostly distribute at larger values, while SM backgrounds appear at both small and large values.
A closer look at the data shows that backgrounds with one single neurtrino as the source of their missing energy tend to give small . These “mononeutrino” backgrounds include + jets and semileptonic production, where there is no other invisible particle except one neutrino. In principle, these backgrounds should allow as a solution from the equation
(10) 
However, if the measured purely comes from , the corresponding transverse mass is bounded by the mass,
(11) 
which would have been removed by the GeV cut. The events that passed the cut must have some additional due to mismeasurements or lost particles, which generally renders a positive as shown in the figure. We also see that is a more useful variable to suppress these backgrounds than which has a wider distribution.
On the other hand, those backgrounds which can produce more than one neutrino such as and dileptonic likely give larger . This is because when leptons are not identified by the detector or neutrinos are pair produced from , the extra neutrino or lost lepton momentum becomes part of the MET. Consequently, the assumptions mentioned in Sec.II are violated. More often than not, these extra neutrinos are produced in the different hemisphere of the ISR system, the MET then becomes larger and tends to be more positive. Such an effect due to extra neutrinos also occurred for the topcorridor stop search Cheng:2016mcw . As a result, this type of background overlaps more with signals and the variables are less effective in removing them. Fortunately they are subdominant compared to the jets background which can be effectively suppressed by the variables.
For events that do not yield real solutions, one possibility is to simply discard them. However, there are quite some signal events which do not have real solutions, which may be caused by mismeasurements. In those cases, one might hope that the real part of the complex solutions of gives a reasonable approximation to the true value. To check if this helps to increase the signal significance, for those events that give complex solutions for , we simply define to be the real part of the complex solutions and plot its distributions for the signal and backgrounds in Fig. 2. The empirical variable turns out to be also useful as one can see that the background events (especially the dominant jets) have a lower distribution than that of the signal, although it is not as good as in the real solution case.
After seeing the usefulness of the variable, we plot the signal and background distributions against other variables, MET and in Figs. 3 and 4. We see that the dominant backgrounds generally also have lower values in MET and .
Based on these distributions, we make the following cuts to select two signal regions:

for events with 200 GeV MET 300 GeV, and GeV are required (SRL);

for events with MET GeV, and GeV are required (SRH).
For smaller MET where the backgrounds are large, we impose harder cuts on and to reduce the background events. For large MET, and cuts can be relaxed a bit to allow more signal events to pass them.
The numbers of events passing the above cuts for the benchmark signal and SM backgrounds, normalized to an integrated luminosity of 36 fb are shown in Table 1.
Initial  Prelim  SRL(R)  SRH(R)  SRL(C)  SRH(C)  
450 GeV  20.6  51.6  25.4  38.0  
W+jets  25.7  42.8  19.4  23.3  
diboson  33.1  56.0  61.1  56.2  
(Dilep)  1.97  40.5  18.6  62.3  19.6  
(Semilep)  7.86  9.2  0  0  0  0 
SM other  3.50  9.8  7.5  15.3  3.1  
SM total  109  125  158  102 
After the final selection, the largest background comes from the diboson which is dominated by +jets. This is because can decay to two neutrinos which imitates the neutralinos of the signal events.
To calculate the signal significances for the benchmark models, we use the likelihood method with the assumption that the overall number of background events in each signal region respects the normal distribution with a fractional uncertainty . The likelihood is defined to be
(12) 
where and are corresponding numbers of signal and background events, , and is the normalized normal distribution with the mean and a standard deviation . The final significance from this method is simply given by . For the case with no systematic error, , this equation simply reduces to the standard formula Cowan:2010js :
(13) 
For the Stop450 benchmark, we get a significance of for 36 fb with (without) a 10 background uncertainty. For current LHC SUSY searches also using onelepton final states Aaboud:2017bac , the systematic uncertainties for different signal regions vary from to , which mainly comes from uncertainties in modeling the SM backgrounds and MC simulations rather than the experimental uncertainties. In the future when the integrated luminosity increases from to , we expect that the systematic uncertainties will further decrease but the actual numbers are hard to predict. Here we use a 10% background systematic uncertainty to demonstrate its impact on the signal significances. The results with different background uncertainties can also be obtained easily from the numbers in Table 1.
One question of the analysis is how much the variables help the stop search in this case. One can imagine that a variable defined by the ratio MET/ISR gives a simple approximation of and hence the search can be done with the standard simple variables MET, ISR, and . To check this we plot the MET vs. ISR distributions of the signal and background in Fig. 5. One can see that there is some separation between signal and backgrounds, but compared to Fig. 1 it does not seem to be as good. In Appendix B, we perform an analysis without using the variables and find that indeed the signal significance is substantially inferior to the result obtained here with the variables.
iii.4 Stop Results at LHC 13TeV
The discussion of the last subsection demonstrated that the analysis based on the variables with a hard ISR can yield a large signal significance for a 450 GeV stop in the corridor with 36 integrated luminosity. To study the reach of this method, we perform the same analysis for a series of points along the corridor. The optimal signal regions may depend on the mass points, but for simplicity and easy comparison we use the same signal regions defined in the previous subsection. The results are shown in Table 2 and Fig. 6. We find that a stop mass below GeV in the corridor with the assumed decay mode can be excluded at the 95% CL by this method. In comparison, the current ATLAS 1lepton analysis only excludes stop mass up to GeV in the corridor Aaboud:2017bac , The ATLAS 2lepton analysis can exclude stop mass up to GeV just above the sum , but leaves a gap below that where the reach degraded to GeV Aaboud:2017nfd . They are far beneath the potential reach of the new approach studied here.
(GeV)  250  300  350  400  450  500  550 

27.9(37.4)  18.0(25.4)  11.8(17.2)  7.0(10.2)  4.3(6.3)  2.7(3.9)  2.1(3.0)  
37.6(47.8)  20.5(27.9)  10.9(15.8)  7.9(11.5)  4.2(6.1)  3.0(4.3)  2.2(3.2)  
20.1(28.0)  14.2(20.7)  10.8(16.1)  7.0(10.2)  3.7(5.4)  2.7(3.9)  1.6(2.3) 
We are also interested in the mass parameter region slightly away from the line to see the coverage of our method. We performed the same analysis for points along the lines of GeV. The results are also shown in Table 2. Away from the line, some of the kinematic assumptions used in Sec. II are no longer valid. For instance, when the mass gap between and is larger than , the bosons are still onshell, so Eq. (6) still holds. However, the neutralinos would no longer be static in the rest frame of the stops and consequently the sum of their momentum may no longer be strictly antiparallel to the ISR. Thus, our assumption that the neutrino is solely responsible for is no longer justified. This could further smear the distribution for the signal, hence reducing its discriminating power. We see that the significances for the points on the GeV line are generally somewhat worse than those on the line for the same stop mass. On the other hand, for a stop lighter than , the stop goes through the 4body decay and the mass shell condition Eq. (6) is no longer valid. However, the mass ratio is larger for the same . The distribution of for the signal also shifts to larger values, resulting in better separation from the backgrounds. The signal significances along the GeV line are still comparable to the points along the line. From these results, we conclude that this new approach can apply to a quite wide region around the corridor and will extend the coverage on the search gap present in the current experimental analyses.
Iv Chargino and Neutralino Searches along the W Corridor
The compressed chargino/neutralino that decay via or can also give the + jets + MET final state without jets, thus similar analysis can also be applied to chargino searches along the corridor. Due to the smaller production cross section, the experimental exclusion limit on and is weaker compared to stop searches. The current (36 ) reach of and is less than GeV in the compressed region from CMS in the channel, assuming and are winolike and decay to and plus respectively Sirunyan:2017lae ; CMS:2017sqn . (The higgsinolike , can also be constrained as long as they have the same spectrum and decay final states, but their production rate will be a few times smaller.) There is a gap around where the limit further degrades to GeV. The limit from the current ATLAS analysis is even weaker ATLAS:2017uun . There is no chargino/neutralino search using the channel from either ATLAS or CMS in the compressed region, which motivates us to explore the usefulness of the approach using in the chargino search.
We start with a benchmark (C1N2300) of 300 GeV degenerate , , with the production rate taken to be winolike. The LSP is assumed to be binolike and has a mass 215 GeV. , are produced through the electroweak process, then decay to with 100% branching ratio. The preliminary selection rules are mostly the same as ones applied in the stop study of the previous section, except for the MET requirement. Because the reach in the mass spectrum will be weaker than the stop case due to the smaller production cross section, for the same ISR momentum the recoiled momentum carried by the two ’s will be lower for smaller . With that observation, we lower the MET requirement to GeV.
In Fig. 7 we plot the twodimensional vs. distributions of 300 GeV 1 lepton signal vs. various SM backgrounds after the preliminary selection, normalized to 36 . Compared to Fig. 1, we can see that signal events of C1N2300 generally have smaller range relative to those of the Stop450 signal, in accordance with our expectation. Specifically, the theoretical value for C1N2300 is , smaller than that of Stop450 where . Similar to the stop case, the more useful variable is as it separates the signal and backgrounds better than , as we can see from Fig. 7.
Due to the smaller values for the signal, one may want to lower the cut in the signal region selection. However, the backgrounds is large at lower values so a lower cut would need to be accompanied by a harder cut on other variables such as MET. The MET and vs. distributions for the signal and backgrounds are shown in Fig. 8. We modify the two signal regions as follows:

for events with MET GeV, GeV and are required (SRL);

for events with MET GeV, GeV and are required (SRH).
Initial  Prelim  SRL(R)  SRH(R)  SRL(C)  SRH(C)  
6.7  6.2  5.9  2.4  
14.1  13.5  14.5  7.1  
3.3  2.6  2.1  1.7  
6.4  6.6  8.6  3.5  
+ jets  30.2  27.9  34.1  9.3  
diboson  54.2  35.5  119  31.1  
(Dilep)  60.1  6.6  96.1  8.7  
(Semilep)  7.86  0  0  0  0  
SM others  15.5  7.1  20.1  0.9  
SM total  160  77.5  269  50.0 
The numbers of events passing the above cuts are listed in Table 3. In the table we separate the signal events into the chargino pair production and the charginoneutralino production, and also events with real and complex solutions for . If we include the background uncertainty, the signal significance of the 300 GeV chargino benchmark would be around 2.3 including all channels. In other words, this mass point can be excluded if no excess is present in the current data. This exceeds the current multilepton bound on in the corridor, which is no higher than GeV Sirunyan:2017lae ; CMS:2017sqn ; ATLAS:2017uun .
To explore the potential power of this channel in the future, we project the analyses for several mass points along the corridor to a higher integrated luminosity of . Numerical results are presented in Table 4, also with their overall signal efficiency. It is clear that as the chargino becomes heavier, the expectation of also increases, rendering a larger MET and on average. As the result, the overall signal efficiency grows and partially compensates the reduction of the production cross section. From the results we can see that for 13 TeV LHC the reach in the chargino mass around the corridor could go beyond 400 GeV in the one lepton channel based on this method.
(GeV)  300  350  400  450 

Overall signal efficiency ()  3.4  6.1  7.9  8.8 
Significance ()  3.2  3.0  2.5  1.6 
V Conclusions
SUSY searches at the LHC have put strong bounds on the superpartner masses, generally beyond 1 TeV for colored states. However, it is important to cover the search holes at lower mass regions before one can declare that SUSY is too heavy to address the naturalness problem. The search holes at lower masses arise when the superpartners have a compressed spectrum. The visible particles and the missing transverse energy from the cascade decays of the superpartner are soft in this case. They are often difficult to be distinguished from the SM backgrounds, which results in the weaker limits. To improve the searches, a useful strategy is to consider the superpartner production together with a hard ISR jet. The LSPs recoiled against the ISR will produce a larger missing transverse energy, allowing better identification of the SUSY signals.
In the case of stop search, the (or ) variable that measures the ratio of the LSP mass and the stop mass has been shown to be a powerful discriminator for the signal and the backgrounds. It has been used to extend the exclusion reach to 590 GeV along the top corridor using the all hadronic channel. The semileptonic channel could have a similar reach, as the neutrino momentum can be solved from the kinematic constraints and hence its contribution to the MET can be subtracted to obtain the contribution from the LSPs. It is then natural to explore whether similar methods can be applied to smaller mass differences between the stop and the LSP, such as in the corridor where the current experimental limits are still quite weak.
In this paper we extend the strategy to the stop search in semileptonic decays around the corridor. In this case the jets are too soft to be useful and we lose the kinematic constraint from an onshell top intermediate state during the decay. As a result, the neutrino momentum can not be fully reconstructed and one can not obtain a unique value from the experimental measurements. Nevertheless, the rest of the kinematic constraints still impose a restriction on the allowed values consistent with an event. We found that the minimum value of of the allowed interval provides a good discriminator for the signal and the backgrounds. By combining with other standard variables like MET and , it can significantly extend the exclusion reach beyond the limits obtained from the current experimental analyses. The same analysis also applies to chargino/neutralino search in the corridor. The search reach of the chargino mass is not as good as the stop mass due to the smaller production cross section, but can still surpass the limits set by the current multilepton searches.
A lesson from these studies is that by fully utilizing the kinematic features and constraints of the signal and background events, one can construct discriminating variables that more effectively separate them, and therefore improve the search coverage. This is important for the difficult parameter regions where the signal and backgrounds have similar distributions in simple traditional variables. The stake of finding or excluding new physics is so high that no stone should be left unturned. Coming up with better search strategies at the LHC shall continue to be a high priority in high energy physics.
Acknowledgments
This work is supported in part by the US Department of Energy grant DESC000999. H.C. C. was also supported by The Ambrose Monell Foundation at the Institute for Advanced Study, Princeton.
Appendix A Solving for and
In this Appendix, we explain in details of how we calculate the allowed range from kinematic constraints and present the analytical formula for and .
Assuming that the missing transverse momentum comes purely from the two neutralinos and the neutrino, from Eq. (4), we can write the neutrino’s transverse momentum in terms of and the transverse momentum of ISR: :
(14) 
After substituting them into the mass shell equations, (5), (6),
(15) 
we obtain a quadratic equation of in the form of
(16) 
where coefficients are functions of given below:
(17) 
In order for the event process to be physical, the neutrino’s momentum must be real which means coefficients satisfy the following inequality
(18) 
From Eq. (17) we can see that is a linear function of , is a quadratic function of and is a constant. Thus, the left part of inequality (18) is actually a quadratic function of and can be written in the form
(19) 
with the coefficients given by
(20) 
One can show that the coefficient is negative as long as by the following equivalent relations:
(21) 
The coefficients can be calculated from the experimentally measured lepton momentum , transverse momentum of the ISR,