Stop Search in the Compressed Region via Semileptonic Decays

In supersymmetric extensions of the Standard Model, the superpartners of the top quark (stops) play the crucial role in addressing the naturalness problem. For direct pair-production of stops with each stop decaying into a top quark plus the lightest neutralino, the standard stop searches have difficulty finding the stop for a compressed spectrum where the mass difference between the stop and the lightest neutralino is close to the top quark mass, because the events look too similar to the large $t\bar{t}$ background. With an additional hard ISR jet, the two neutralinos from the stop decays are boosted in the opposite direction and they can give rise to some missing transverse energy. This may be used to distinguish the stop decays from the backgrounds. In this paper we study the semileptonic decay of such signal events for the compressed mass spectrum. Although the neutrino from the $W$ decay also produces some missing transverse energy, its momentum can be reconstructed from the kinematic assumptions and mass-shell conditions. It can then be subtracted from the total missing transverse momentum to obtain the neutralino contribution. Because it suffers from less backgrounds, we show that the semileptonic decay channel has a better discovery reach than the fully hadronic decay channel along the compressed line $m_{\tilde{t}} - m_{\tilde{\chi}}\approx m_t$. With 300 $\text{fb}^{-1}$, the 13 TeV LHC can discover the stop up to 500 GeV, covering the most natural parameter space region.


I. INTRODUCTION
The discovery of the Higgs boson [1,2] completes the Standard Model (SM), but also makes the hierarchy problem more eminent. The SM interactions of the Higgs field induce quadratically divergent contributions to its mass-squared, and the largest contribution comes from the top quark loop. In order to keep the electroweak symmetry breaking scale natural, new physics is expected to be present near the weak scale to cut off the divergent contributions. In supersymmetry (SUSY), the top quark loop is cancelled by the loops of its superpartners, the stops. It is hence natural that the stops belong to the most sought-after particles in new physics searches at the LHC.
After Run 1 and the initial 13 TeV run of the LHC, ATLAS and CMS experiments have put constraints on the stop mass up to ∼ 750 GeV, assuming the stop decays to a top quark and the lightest neutralinoχ 0 1 , which is assumed to be the lightest supersymmetric particle (LSP) and stable, with mχ0 1 200 GeV [3][4][5][6]. Similar but slightly weaker bounds were also obtained if some of the stops decay through a chargino or a heavier neutralino to the LSP. Run 2 is expected to extend the reach beyond 1 TeV, at which point SUSY as a solution to the hierarchy problem may be strongly questioned. However, the current searches leave some gaps in the lower stop mass region. In particular, if mt ≈ m t + mχ, the top quark and the neutralino from the stop decay are almost static in the stop rest frame. Consequently, in the lab frame the top and the neutralino will be collinear with pχ/pt ≈ mχ/mt. In such cases, the stop pair production events will look almost identical to the top quark pair production, as the two neutralinos tend to travel back to back, resulting in a cancellation of their momenta and leaving no trace ofχs. This is the reason why no experimental limit has been set upon this compressed region so far.
One possible way proposed in Refs. [7][8][9] to explore the compressed region is to consider events of stop pair production with a hard initial state radiation jet (J ISR ). From momentum conservation, therefore both neutralinos tend to be emitted in opposite direction to the ISR jet, resulting in a significant amount of missing transverse momentum ( / p T ). For the fully hadronic decay events, the / p T mainly comes from the neutralinos. Using Eq. (1), we see that the ratio between / p T and p T (J ISR ) (defined as R M in Ref. [8]) is roughly equal to the ratio between the neutralino and the stop masses, which is strictly between zero and one. It can be a useful kinematic variable to distinguish the stop events where R M should be close to mχ/mt from the SM top background events where R M is expected to be close to zero [7][8][9].
As for the semileptonic and dileptonic decays of the stops, R M becomes less informative if the neutrinos' contribution to / p T cannot be separated from that of neutralinos. However, for semileptonic events, if one exploits the kinematics unique to the compressed region, it is possible to reconstruct the top quark that decays leptonically, hence retrieving a relation similar to Eq. (2). Another benefit of requiring a lepton in the final states is that it vetoes QCD backgrounds, which suffer from large uncertainties under high jet multiplicities.
In this paper we demonstrate the reconstructions of semileptonic decays of the stop pair production in the compressed region, and show that it is very useful for stop searches. In Sec. II, we analyze the kinematics of the semileptonic events and discuss the reconstruction of missing transverse momenta from the neutrino and the neutralinos. In Sec. III we describe in detail a search done for the benchmark mass point mt = 400 GeV, m χ = 226.5 GeV as an example of our method. We also compare the significances obtained from our method and which we will assume to be the neutrino momentum component perpendicular to the ISR jet in the transverse plane for the following analyses. Once the J ISR is identified, p ⊥ T ν is uniquely determined from the experiment.
We first consider the case mt = m t + mχ. For the leptonically decaying top quark, there are three mass-shell equations in addition to Eq. (3): Given the measured momenta of the lepton and the b-jet, the three equations together with the p ⊥ T ν allow us to solve for p ν . Taking the differences of the 3 mass-shell equations followed by plugging in the p ⊥ T ν from Eq. (3), we can reduce them to one quadratic equation for E ν , the kinetic energy of the reconstructed neutrino.
The quadratic equation, if solvable, provides in general two different real solutions for E ν . We will discuss how we select the solution later. After E ν is determined, we substitute it back into the original mass-shell equations, then the full momentum of the reconstructed neutrino can be retrieved. Finally, with the knowledge of p T ν , the component of the neutrino momentum antiparallel to p T (J ISR ), we can subtract the neutrino contribution from / p T and get a relation similar to Eq. (2): where we define the variableR M as the modified R M adapted to the semileptonic decays.
With a set of proper kinematic cuts, a clear peak in theR M distribution for the stop pair production can be identified, as we will show later.
As we discussed above, the quadratic equation in general can give two possible solutions for E ν . To choose between them, we investigate the kinematics of semileptonic decays for tt + J ISR and its main background tt + J ISR . As an illustration, we generate these events at the parton level for a benchmark of mt = 400 GeV and m χ = 226.5 GeV. The charged lepton and the neutrino from the W decay on average have the same energy if the W boson is longitudinally polarized, because they tend to be emitted in directions perpendicular to the W momentum. On the other hand, for transverse W decays the neutrino tends to be more energetic than the charged lepton. Because W bosons coming from the top decays are dominantly longitudinally polarized, the energy distributions of the neutrino and the charged lepton are similar. We can see in Fig Details about these effects are beyond the scope of this paper. MET cut for both the stop and top pair production. All distributions are normalized to one. The minor asymmetry that appears in the log(E ν /E ) distribution without the MET cut is because of the spin correlation between the neutrino and the W boson.

III. A CASE STUDY
As an illustration of our method, we describe in details the search done for a point mt = 400 GeV, m χ = 226.5 GeV in the parameter space of the compressed region. The dominant SM backgrounds for the semileptonic decay oftt + J ISR are the semileptonic and dileptonic decays of tt + J ISR . The reason that the dileptonic decays are important is mainly due to the imperfect lepton isolation. Since the top and its decay products are highly boosted antiparallel to the hard ISR jet, the lepton tends to have a small ∆R separation from the b jet, therefore has a non-negligible probability of failing the lepton isolation criteria. Both of these backgrounds have a similar topology to the signal, consequently they have a good chance of solving Eqs. (3) to (6) and yielding a sensibleR M value lying between 0 and 1.
Other SM backgrounds include the single or pair production of vector bosons (V ) with jets and ttV . Even though V + jets and V V + jets have relatively large cross sections, they seldom produce sensible solutions for the equations imposed by the signal kinematics. The small fractions that give real solutions rarely pass our selection cuts either. As a result, they give much less yields compared to tt + J ISR . ttV , on the contrary, has the kinematic features akin to the signal, but suffers from a tiny cross section. As a result, contributions of other SM backgrounds are negligible compared to the main backgrounds. Because one isolated lepton is required in the final state, the hadronic decays of the top pair production and the pure QCD backgrounds are also negligible.
Besides the SM backgrounds, the dileptonic decay oftt + J ISR can be an irreducible background to the signal. However, this process has a much smaller cross section compared to the SM processes and it is effectively negligible.

A. Signal and background generations
We use MadGraph 5 [10] and Pythia 8 [11] to generate events for both the background and the signal events. MLM matching scheme is turned on to prevent double-counting between the matrix element calculation and the parton shower [12]. The detector simulation is performed by Delphes 3 [13] with the anti-k t jet algorithm [14]. We normalize the background cross sections to the LHC 13 TeV top production [15][16][17][18][19]. A K-factor of 1.29 is applied to both semileptonic and dileptonic decays of the tt backgrounds. For the signals, the production cross section is normalized to LHC 13 TeV NLO+NLL results [20].

B. Event selection
The selection for the events of interest starts with at least 4 jets with one or more btags and exactly one isolated lepton. The b-tagging efficiency is set to be 80% with a misidentification rate of 0.015 [21]. Events with τ -tagging are vetoed. The non-b-tagged jet with the hardest p T is our ISR jet candidate. In particular, it must satisfy p T ≥ 475 GeV. The second and third hardest jets must satisfy p T ≥ 60 GeV. In order to ensure that the ISR jet is approximately in the opposite direction of the neutralino momentum sum, we require that |φ J ISR − φ MET | ≥ 2. As shown in Fig. 1, a MET cut effectively eliminates most of the SM backgrounds whose missing momentum mainly comes from the neutrinos, hence an MET cut > 200 GeV is imposed. Another useful kinematic variable is ∆φ ,MET , the azimuthal angle difference between the lepton and the missing transverse momentum. Since the main source of the missing momentum for the backgrounds is from the neutrino, it tends to be more collinear with the lepton for the background events compared with the signal events. Fig. 2 shows the ∆φ ,MET distributions for the signal and the backgrounds for the benchmark. After a cut on ∆φ ,MET > 0.9, most of the semileptonic background can be suppressed. However, this cut is less effective on the dileptonic background, because its MET is the sum of two neutrinos' momenta, which results in a wider ∆φ ,MET distribution.
A more sophisticated estimate to take into account the difference between the shapes of the signal and background can be obtained by the likelihood method. The likelihood ratio between signal plus background hypothesis and background only hypothesis is given by The theoretical predictions for each bin {s} and {b} are taken from the MC simulation, i.e. Assuming that the background in each bin is a normal distribution around its central value b with an uncertainty σ b , the new expression for the likelihood ratio is obtained by The integration can be done numerically and the upper and lower bounds of the integration are chosen to be b ± 5σ b . The significance obtained is a function of the fractional uncertainty σ b /b exp , as shown in Fig. 4, where we see that the significance can still maintain as high as 5σ even with a 20% uncertainty in the background normalization.
To compare our result with the study based on fully hadronic final states, we repeat the analysis done by Ref. [8] for the benchmark. Fig. 3b shows the result obtained after applying the selections adopted in Ref. [8]: p T (J ISR ) > 700 GeV, 3 sub-leading jets with p T > 60 GeV, benefit from requiring a lepton in the final state, therefore enjoy a smaller background compared to the hadronic stop decays. After applying a cut at 1 ≥ R M ≥ 0.42, we get 57 signal yields and 232 background yields for the fully hadronic channel, which roughly corresponds to a 4σ significance.

IV. RESULTS AT LHC 13 TEV
We have demonstrated that our method can produce a large signal significance for a 400 GeV stop in the compressed region with 300 fb −1 integrated luminosity in the case study. To result, the sum of their momenta may no longer be strictly antiparallel to J ISR , thus our assumption that the neutrino is solely responsible for / p ⊥ T (Eq. (3)) is less valid. TheR M value obtained by solving these equations will be smeared by the error in Eq. (3) and the smearing is estimated to be On the other hand, when the stop is lighter than the sum of m t and mχ, it will decay via the virtual top quark. Since the LSPχ is a stable particle, it must be produced on shell.
The virtual top will be almost static in the rest frame of the stop, therefore Eq. Finally a scan of (mt, mχ) in the compressed region is performed based on our method.
The result is shown in Fig. 7. The scan is done along the mt − (mχ + m t ) = 30, 0, −30 GeV lines. The significances are calculated using the simple expression Eq. (8) after applying the selections discussed in Sec. III, which are: • The second and third hardest jets with p T > 60 GeV.
In Table I, we present the significances for all the points we studied in the compressed region. As expected, the mt − (mχ + m t ) = −30 GeV line achieves as great significances can be seen clearly that our method can cover a wide mass range when mt − mχ m t .
The curves are the exclusion limits from ATLAS [3] as the mt − (mχ + m t ) = 0 line. They even perform better for lighter stops. This is because the R theory M is higher for heavier mχ given the same mt, which means more events Overall, the final significances of the three lines agree well with our earlier observation from

V. CONCLUSIONS
In this paper we investigate the stop search from the direct stop pair production in the compressed region, using the semileptonic decay mode. With a hard ISR jet, the neutralinos  Compared with the fully hadronic decay channel, our method for the semileptonic channel requires more sophisticated kinematic reconstruction, but suffers from less SM backgrounds.
As a result, we show that the semileptonic channel can have a better reach than the fully hadronic channel along the compressed line mt − mχ = m t . For 300 fb −1 integrated luminosity at LHC 13 TeV, the semileptonic channel can have a discovery reach of the stop mass up to about 500 GeV, in comparison to ∼ 400 GeV for the fully hadronic channel. Even though our kinematic equations are strictly valid only for mt − mχ = m t , as long as the deviations from this relation is small, the kinematic reconstruction still works pretty well.
The reach is somewhat degraded for mt − mχ > m t but not for mt − mχ m t .
The stops hold the key to the SUSY solution to the hierarchy problem. Their searches are indisputably important. The traditional stop searches are ineffective for a spectrum of mt − mχ ≈ m t . By resorting to a hard ISR jet, one can construct kinematic variables which can be used to distinguish the stop signal from the very similar SM top backgrounds. Future LHC runs will have a significant coverage of the stop mass even in the compressed region, probing the heart of natural SUSY.

ACKNOWLEDGMENTS
We would like to thank Zhangqier Wang for discussion on the likelihood method. This work is supported in part by the US Department of Energy grant DE-SC-000999.