Revealing compressed stops using high-momentum recoils

Journal of High Energy Physics, Mar 2016

Searches for supersymmetric top quarks at the LHC have been making great progress in pushing sensitivity out to higher mass, but are famously plagued by gaps in coverage around lower-mass regions where the decay phase space is closing off. Within the common stop-NLSP/neutralino-LSP simplified model, the line in the mass plane where there is just enough phase space to produce an on-shell top quark remains almost completely unconstrained. Here, we show that is possible to define searches capable of probing a large patch of this difficult region, with S/B ∼ 1 and significances often well beyond 5σ. The basic strategy is to leverage the large energy gain of LHC Run 2, leading to a sizable population of stop pair events recoiling against a hard jet. The recoil not only re-establishes a signature, but also leads to a distinctive anti-correlation between the and the recoil jet transverse vectors when the stops decay all-hadronically. Accounting for jet combinatorics, backgrounds, and imperfections in measurements, we estimate that Run 2 will already start to close the gap in exclusion sensitivity with the first few 10s of fb−1. By 300 fb−1, exclusion sensitivity may extend from stop masses of 550 GeV on the high side down to below 200 GeV on the low side, approaching the “stealth” point at \( {m}_{\overline{t}}={m}_t \) and potentially overlapping with limits from \( t\overline{t} \) cross section and spin correlation measurements.

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Revealing compressed stops using high-momentum recoils

HJE Revealing compressed stops using high-momentum recoils Sebastian Macaluso 0 1 2 4 Michael Park 0 1 2 4 David Shih 0 1 2 4 Brock Tweedie 0 1 2 3 0 Pittsburgh , PA 15260 , U.S.A 1 Stanford , CA 94305 , U.S.A 2 Piscataway , NJ 08854 , U.S.A 3 PITT PACC, Department of Physics and Astronomy, University of Pittsburgh 4 NHETC, Department of Physics and Astronomy, Rutgers University Searches for supersymmetric top quarks at the LHC have been making great progress in pushing sensitivity out to higher mass, but are famously plagued by gaps in coverage around lower-mass regions where the decay phase space is closing o . Within the common stop-NLSP/neutralino-LSP simpli ed model, the line in the mass plane where there is just enough phase space to produce an on-shell top quark remains almost completely unconstrained. Here, we show that is possible to de ne searches capable of probing a large patch of this di cult region, with S/B Hadronic Colliders; Supersymmetry Phenomenology - 1 and signi cances often well beyond 5 . The basic strategy is to leverage the large energy gain of LHC Run 2, leading to a sizable population of stop pair events recoiling against a hard jet. The recoil not only re-establishes a 6ET signature, but also leads to a distinctive anti-correlation between the 6ET and the recoil jet transverse vectors when the stops decay all-hadronically. Accounting for jet combinatorics, backgrounds, and imperfections in 6ET measurements, we estimate that Run 2 will already start to close the gap in exclusion sensitivity with the rst few 10s of fb 1 . By 300 fb 1, exclusion sensitivity may extend from stop masses of 550 GeV on the high side down to below 200 GeV on the low side, approaching the \stealth" point at mt~ = mt and potentially overlapping with limits from tt cross section and spin correlation measurements. 1 Introduction 2 3 A Event generation 1 Introduction Proposed analysis and predicted coverage Discussion and outlook pp ! t~t~ ; t~ ! t( ) + ~ 0 (1.1) The visible composition of the nal state is then identical to that of tt, which serves as a copious background. The main kinematic handle exploited in most searches has been the additional injection of 6ET (or more properly 6pT ) from the neutralinos. For m~ t m ~, exclusion limits from tt + 6ET searches at Run 1 extend beyond 700 GeV [10]. However, such searches face a major challenge when confronted with lower-mass regions in the stopneutralino mass plane where the 6ET is squeezed out. In particular, much attention has recently been directed at the \top compression line" mt~ ' m ~ + mt, which de nes the boundary between two-body decays into an on-shell top quark and neutralino, and threebody decays via an o -shell top quark into W b ~0. Limits along this compression line are largely nonexistent over a roughly 20 GeV-wide gap in stop mass. Proposals to probe this region using the total tt cross section and spin correlations [ 20, 21 ] have led to some inroads near the so-called \stealth" point (mt~; m ~) = (mt; 0) [1, 4]. But theoretical limitations make it unclear if these searches can be pushed much further, and there are possibly unresolved subtleties in the interplay between top mass and cross section measurements in the presence of a stop signal [ 21, 22 ]. The relatively long { 1 { lifetimes of stops very near to the top compression line has led to a complementary suggestion to use the annihilation-decays of stoponium [23{25], which would lead to distinctive resonant diboson signatures (including, e.g., and Z ). Projections for Run 2 predict sensitivity up to stop masses of several hundred GeV, depending in detail on the stop chirality admixture. However, these searches become insensitive if the individual stops decay more quickly than the stoponium, which generally occurs as soon as the stop-neutralino mass di erence opens up to even O(GeV). Other approaches have sought to use the small amount of 6ET that is available within the bulk of the produced stop pair events. Very detailed measurements of the shapes of the tails of 6ET -sensitive observables [26] or their multivariate generalizations [27] may be promising, but a careful accounting of theoretical and experimental errors is not always available, and the one measurement of this type that has been carried out [2] (by ATLAS, in the l+jets channel) does not reach the compression line. A simple cut-and-count style search based on dileptonic mT 2 [28, 29] or related constrained mass variables [30] should still be viable due to a particularly sharp turno of the background, and is also sensitive near the stealth point. But the maximum mass reach of such a search is ultimately limited by low statistics and exhibits a signi cant dependence on stop chirality. It has also been suggested to utilize electroweak production of stop pairs via VBF, albeit with di culties in probing stops much heavier than mt [31, 32]. Given these various limitations, there remains a clear need to consider further alternative options, lest comprehensive exploration of the top compression line be deferred to future precision lepton colliders. To make progress, we may take some inspiration from another compression line, at the very lowest end of the stop mass range: mt~ ' m ~. There, not only the 6ET , but all visible activity is being squeezed out of the decay. Nonetheless, limits exist from the LHC, presently up to roughly 260 GeV [3, 16]. These are obtained using the classic trick of cutting into the region of production phase space where a sparticle pair is produced in association with a visible hard recoil particle, in this case a jet. For an almost completely compressed spectrum, the neutralinos go to zero velocity in the rest frames of their parents, but carry the full energy and therefore take up the full fourmomenta. For stop pair production, the 6ET vector in lab-frame is then automatically equal to the net t~t~ transverse momentum vector, which in turn approximately balances against the leading jet. For stop-neutralino spectra near the top compression line, we can de ne an analogous p~T (jet) ' p~T (t~t~ ), we get the following relation, trick, but now face several novelties. The neutralinos again approach zero velocity in their parent frames, but they share the four-momenta with (almost) on-shell sister top quarks, with fraction m ~=mt~ taken up by the neutralinos. Therefore, in the limit of perfectly compressed two-body decay t~ ! t ~0, and assuming a single dominant recoil jet with ~ 6ET ' p~T (jet) m ~ m~ t : (1.2) The 6ET is now attenuated relative to the recoil pT , by a factor that can nominally extend down to zero in the massless neutralino limit (corresponding to the stealth stops [ 20 ]). This attenuation will generally make searches much more challenging when m ~ mt~ along the { 2 { reach. For a given neutralino mass, the extra 2mt worth of energy required to make a stop pair also leads to much lower rates relative to conventionally compressed spectra with mt~ ' m ~, especially in association with a proportionately energetic recoil jet. This issue in particular will be greatly ameliorated with the higher beam energy of the upgraded LHC. Finally, the two stop decays produce two on-shell or o -shell top quarks, which add to the visible activity and can inject further 6ET if either W decays leptonically. Perhaps somewhat counterintuitively, the cleanest signal may then be the all-hadronic decay mode, where all of the 6ET comes from the neutralinos, and eq. (1.2) is most closely followed. However, this decay mode also maximizes possible QCD backgrounds, as well as our possible confusion over exactly which jets come from the recoil against the stop pair versus from their decays. The possible utility of high-momentum recoils in this respect was emphasized relatively recently in [33]. In the present paper, we seek to put these ideas on rmer phenomenological footing, including a novel set of cuts and treatment of jet combinatorics, a detailed accounting of the various backgrounds, and allowance for a range of possible 6ET measurement performances. Targeting all-hadronic stop decays, we typically nd a healthy S=B 1, ensuring robustness against systematic errors of up to O(10%). We proceed to make a detailed forecast for the possible discovery and exclusion coverage in the stopneutralino mass plane. Our results are summarized in gure 3, where the proposed search is seen to cover a large portion of the formerly inaccessible top compression line, acting as a bridge between the two-body and three-body search strategies. For the expected 300 fb 1 to be delivered through Run 3 of the LHC, exclusion sensitivity extends up to 550 GeV. On the lower end, shrinking 6ET poses a major complication, but we nd that exclusion sensitivity down to mt~ ' mt + O(10 GeV) may be possible. This would merge our forecasted coverage with that of tt cross section measurements and other techniques that perform well in the stealth region, allowing for unbroken coverage. If this can be achieved, it would be a major accomplishment of the LHC, and a further demonstration that the enormous luminosity and broad bandwidth of accessible energies there provides unique opportunities, even for relatively low-mass physics with subtle kinematics. Our paper is organized as follows. The next section outlines our proposed analysis strategy and presents our estimated signal sensitivities. Section 3 discusses the results and possible extensions. More details of the generation of our event samples are presented in appendix A. 2 Proposed analysis and predicted coverage Our proposed analysis requires only a few ingredients: A veto on isolated leptons. A high multiplicity of jets and at least two b-tags. An energetic \ISR-jet" candidate. Coarsely-reconstructed top-candidates whose masses are not signi cantly above mt. { 3 { A strong anticorrelation of ISR-jet and 6E~T directions. A \signi cant" amount of missing energy, 6ET =pHT , localized near a value set by the ISR-jet pT cut and m ~=mt~. In more detail, our full reconstruction and selection, applied to 13 TeV simulated data (appendix A), proceeds as follows. Reconstructed electrons (muons) are rst selected starting from truth leptons with pT;` > 10 GeV and j `j < 2:5, and at identi cation e ciency of 0:90 (0:95). (The precise choices for the ID e ciencies are not crucial.) Electrons are then isolated by rst computing Pi jpT;ij R<0:2 (where the sum is over all other particles within R < 0:2 of the electron) and requiring pT;` Pi jpT;ij R<0:2 < 0:1 : (2.1) Electrons that fail this isolation criterion, as well as all other unidenti able leptons, are returned to the particle list as \hadrons" to be used in jet clustering. Additionally, there must be no jets (de ned below) within 0:4 of either an electron or muon. Otherwise, the lepton is vector-summed into the closest jet.1 Events that contain any surviving isolated leptons are then discarded. This lepton veto signi cantly reduces important backgrounds where the 6ET arises from a W boson decay, especially l+jets tt events and leptonic W +jets. More aggressive approaches than ours are also possible, using anti-tagging and/or vetoes on more loosely-identi ed leptons. Ultimately, we nd that our backgrounds containing W s are moderately dominated by . Jets are clustered from all truth hadrons, photons, and unidenti ed leptons (including electrons that fail the initial isolation step). The anti-kT algorithm [34] in FastJet [35] is applied with R = 0:4, an initial pT threshold of 15 GeV, and j j < 5:0. Jets from this stage are used for the lepton isolation above. Individual jet energies are then smeared with gaussians according to the expectation for the Run 2 & 3 conditions of 50 simultaneous pileup events, as projected in the Snowmass 2013 simulation note [36]: (pT )=pT = (8:2 GeV)=pT (0:55 GeV1=2)=ppT 0:02.2 Subsequently, an event must favoring the all-hadronic t~t~ +jet signal topology and further reducing backgrounds.3 have at least seven reconstructed jets with smeared pT above 20 GeV and j j < 2:8, highly Jets with j j < 2:5 are b-tagged according to an assumed working point with an e ciency of 0:70 (0:10) for truth b-jets (c-jets). Jets are rst truth avor-tagged by looking for the heaviest overlapping b- or c-hadron in the event record, and then assigned 1While these steps do not explicitly fold in pileup, signi cant drops in lepton reconstruction and isolation e ciencies in the coming LHC runs are unlikely, especially given the availability of isolation methods that are more tracker-based. It is also important to note that, because of the high recoil pT cut demanded below, leptons in the dominant backgrounds tend to be quite energetic. 2As of this writing, the most recent version (v1) contains a shifted-decimal typo for the noise coe cient in the written formula. 3We do not model \pileup jets" consisting mostly of di use pileup particles, of which O(2) per event are expected [ 37 ] given our pT threshold and before dedicated pileup-jet rejection. We anticipate that these will be rejected with reasonable enough e ciency (see, e.g., [ 38 ]) so as not to have a major impact on our analysis, though higher thresholds on the individual jet pT s would also be an option if necessary. { 4 { a reconstruction-level identity (b-jet or light- avor jet) based on the above e ciencies. Mistags of light- avor jets are not incorporated, nor are backgrounds with less than two heavy- avor partons in the hard event (see appendix A). Light- avor mistags are of subleading importance for both the stop signal and top backgrounds. For W=Z+jets and especially multijets, a complete analysis with light- avor mistags requires extensive simulation, which we have not undertaken. However, we do not expect this omission to have signi cant impact on the validity of our background estimates. As a speci c corroborating example, we refer which the W=Z+jets backgrounds are dominated by events with two truth b-jets.4 to the detailed background composition of the Higgs search (W=Z)H ! (W=Z)(bb) [39], in analysis. We employ a nominal model based on 6 H~T Pj p~T (j). This model implicitly Modeling of the 6ET vector is potentially a delicate issue for the low-mass region of this incorporates the e ects of pileup via the jet energy smearing, and preserves some of the correlations between the 6ET vector and over/under-measured jets. However, it does not account for additional re nements that could come from adding in activity that is not clustered into jets. To provide an approximate indication of how our 6ET modeling a ects our results, we also include some comparisons against truth-6ET , denoted 6E~T de nitions, 6E~T is not allowed to point along the p~T of any of the leading three jets, with a . For both truth requirement j j > 0:55. In practice, such a cut is used experimentally to avoid fake 6ET from under-measured jets, as well as real 6ET from heavy avor decays inside of jets. Within our own multijets samples, the cut is still somewhat advantageous when using 6HT . The advantage with 6ETtruth is minor, but we continue to apply the cut to maintain consistency and a higher degree of realism. Identi cation of the ISR jet exploits the kinematics of top decay in a simple way. For a b-quark produced in a hadronic top decay, adding in either of the quarks produced in the sister W 's decay will produce a subsystem with a mass less than mt, and more speci cally less than q mt2 m2W ' 153 GeV at leading-order with narrow W . These inequalities continue to hold even when the top is below its mass-shell, as the kinematic boundary only becomes lower. The leading two b-jets in the event are taken to be the b-quark candidates. A list of remaining jets in the event is formed which satisfy m(b + j) > 200 GeV for both b-quark candidates. The highest-pT jet from this list is then the ISR candidate. Only events with pT (ISR-jet) > 550 GeV are kept in our analysis. (For an indication of how the signal rate changes with the recoil pT threshold, see [33].) Individual top quarks are reconstructed using a procedure borrowed from [5]. Excluding the two leading b-jets and the ISR-jet candidate, the two closest jets in the - plane are added to form a \W boson." This in turn is added to the closest b-jet to form a \top quark." The procedure is then repeated amongst the remaining jets and b-jet. In the absence of smearings and combinatoric confusions, both top-candidates constructed in this manner would satisfy m ' mt if on-shell, and m < mt if o -shell. We make a somewhat 4To give some rough sense of accounting, the \penalty" for QCD to produce a pair of hard, well-separated heavy quarks from a gluon splitting is O( s= ), which is overall percent-scale. This easily beats the chances of a double-mistag of truth light- avor jets, which is O(10 4). For single-mistag events containing one bquark at the hard event level, the O(10 2 ) mistag would need to be combined with the very small b PDFs. (Practically such events are paying both s= and the mistag rate.) { 5 { Baseline Cuts lepton veto jets ISR-jet jet/6ET overlap 6HT =pHT tops 6ET =pHT window ISR-jet/6ET anti-alignment no isolated ID'ed leptons with pT (l) > 10 GeV, j (l)j < 2:5 pT (j) > 20 GeV, j (j)j < 2:8; N (j) >= 7, N (b-tag) >= 2 pT (ISR-jet) > 550 GeV j (j1;2;3; 6ET )j > 0:55 6HT =pHT > 3 GeV1=2 (including 6ETtruth analysis) Additional Cuts m(top-candidates) < 250 GeV j Finally, we employ the relation in eq. (1.2), which, as per [33], we decompose into angle 6ET =HT or the \signi cance" ratio 6ET =pHT . We and magnitude. For the angular component, a strong anticorrelation between the ISR-jet and 6ET directions is demanded: j (ISR-jet,6ET )j > 2:95. For the magnitude, we expect that the signal 6ET will be approximately equal to pT (ISR-jet) (m ~=mt~). Because of the interplay of the hard pT (ISR-jet) cut and the rapidly-falling production pT distributions, the signal will appear as a localized bump in 6ET . Raw 6ET can serve as an adequate discriminating variable here, as can other standard 6ET -sensitive variables such as the ratio nd the last option to be slightly more e ective than the others at separating signal from background (at the 10% level in S=B), and choose this for our analysis. is also applied in the 6ETtruth-based analysis.) several of the discriminating variables for backgrounds and some example signal points, illustrating the cumulative puri cation of the signal. Table 2 shows the integrated event counts. Note that, to maintain e cient Monte Carlo generation, a cut of 6HT =pHT > 3 GeV1=2 has been applied to de ne a baseline reconstructed sample. (This 6HT -based cut The analysis thus de ned, we scan through the model space of the stop-neutralino mass p plane, with ner-grained steps near the top compression line (of order the top quark width). The signi cance S=pS + B. We de ne exclusion threshold as S=pS + B = 2, and discovery nal 6ET =pHT window is optimized per sample to maximize the naive statistical threshold as S= B = 5. Figure 3 shows our nominal exclusion and discovery contours for 300 fb 1, indicating a near complete closure of the current compression line gap. Figure 4 shows the luminosity required to achieve exclusion-level sensitivity along the compression line. While our simulations are done under Run 2 & 3 conditions, we have also naively extrapolated as far as the HL-LHC luminosity of 3 ab 1. We include as well in gure 5 a { 6 { 1 ) baseline cuts through ISR pT > 550 GeV 0 0 0 multijet top W/Z+jets 1 ) b f top b f 0 0 3 ( s t n e ev10 # 1 10-1 1 1.5 2 2.5 3 Δφ(ISR,HT) nominal 6HT -based analysis, with cumulative cuts. The baseline cuts include the lepton veto, jet counting, ISR-jet pT cut, jet/6ET overlap removal, and a cut 6HT =pHT > 3 GeV1=2 used to de ne the simulation samples. scan of the signal and background rates at 300 fb 1 along the top compression line. This indicates S=B 1 over most of the range that we study, suggesting good resilience to systematic errors, which we have not attempted to estimate. Finally, in gure 6 we provide a closer view of the exclusion sensitivity near the stealth point, via a series of scans over mt~ at xed neutralino masses. 3 Discussion and outlook pression line beyond 400 GeV at discovery-level signi cance, and perhaps up to 550 GeV at exclusion-level signi cance, over the current phase of LHC running. These numbers already start to approach what was done for non-compressed stops at Run 1. However, unlike those searches, for us the sensitivity is maximized on the top compression line. This complementarity is made possible by focusing on the unique kinematic con gurations that { 7 { 1 ) b f s t multijet top + Δφ(ISR,Etruth) > 2.95, Etruth analysis T 1 ) b f for the nominal 6HT -based analysis (left) and the reference 6ETtruth-based analysis (right). All other cuts have been applied. multijet top W=Z+jets top+W=Z (mt~; m~) = (275; 102) baseline cuts + m( rst top) < 250 GeV + m(second top) < 250 GeV + j example compressed signal point and its optimized 6HT =pHT window. start to open up at Run 2. It is rather remarkable that the persistent sensitivity gap at the top compression line, which has become a modern benchmark of di culty in new physics searches, can be covered so quickly and so broadly. Figure 4 indicates that the gap will start to close already with a data set comparable in size to Run 1, which should be achievable before the end of 2016. On the low side, our search very closely surrounds the stealth point (mt~; m ~) = (mt; 0), as indicated in detail in gure 6. In fact, we have found that the exclusion-level contour there depends only moderately on whether we use 6HT or 6ETtruth, though gure 5 illustrates that this choice does strongly a ect the S=B there. We emphasize the caveat that we have not folded in systematic errors. Ultimately, the major question is how well the multijet background can be controlled and modeled. Given this uncertainty, it is di cult for us to make very concrete statements near the stealth point. But following the discussion in the introduction, it seems highly likely that multiple search strategies will come into play. Even the present state-of-the art searches based on tt cross section and spin correlation measurements [1, 4] already overlap with our projections, completing the coverage at exclusion-level. { 8 { Ž Χ exclusion H300 fbL discovery H300 fbL ATLAS 1407.0583 CMS SUS-14-011 CMS SUS-13-011 b m W + m m Žtt m ŽΧ= m ŽΧ= m Žtm HJEP03(216)5 200 400 600 800 1000 exclusion sensitivities for our nominal 6HT -based analysis. The reference 6ETtruth-based analysis (not shown) yields very similar exclusion contours, but somewhat stronger discovery contours at lower masses. Note that our simulation grid does not extend all the way down to the W compression line mt~ ' m~ + mb + mW nor below, where the decay kinematics transitions to four-body. (We also do not indicate existing exclusions in that region. For the stealth exclusions, see gure 6.) 3000 fb 300 fb 30 fb 400 200 300 500 600 700 800 900 our nominal 6HT -based analysis (solid) and our reference 6ETtruth-based analysis (dashed), assuming 13 TeV and Run 2 & 3 pileup and detector conditions. (Projections beyond 300 fb 1 are naive extrapolations, not using HL-LHC conditions.) Our search is also very e ective at covering large portions of the three-body region. While our simulated model points do not extend below the W compression line at mt~ ' m ~ + mb + mW , and into the four-body region, it seems quite likely that we even continue to have some coverage there. This leaves open the possibility of linking up with monojet { 9 { 200 300 400 500 600 700 for both our nominal 6HT -based analysis (solid) and our reference 6ETtruth-based analysis (dashed). Signal Background mΧŽ = 20 GeV mΧŽ = 10 GeV mΧŽ = 0 GeV 140 160 180 200 220 240 260 stop masses from the dedicated ATLAS search for stealth stops [1]. The 6ETtruth-based analysis (not mt, for our nominal 6HT -based analysis. The gray shaded region indicates the excluded shown) yields very similar signi cances in the dip near the top compression line, but up to O(1) higher signi cances away from it. and other searches in that region. (See as well [28] for a recast of a soft dilepton search at 7 TeV that already makes some surprising inroads there.) An approach that requires fewer jets and looser hadronic top reconstructions would also likely be fruitful, a possibility that we save for future work. More generally, we have only very coarsely optimized our analysis, rst by xing most of our selection criteria by-eye on a small subset of model points, and then by selectively scanning over only our nal 6ET =pHT window. With the principle proven, a more carefully optimized suite of cuts would certainly achieve better results, especially for the stealthier model points. Breaking the search into more analysis regions, e.g. binned over pT (ISR-jet) (or t over multiple variables), could also be bene cial. An obvious further extension of the analysis includes HL-LHC, with up to 3 ab 1 of luminosity. The very high pileup would likely be a major concern there, as the rate of fake jets rises signi cantly, and the resolution on 6ET further degrades. Certainly, pushing further into the stealth region will be di cult, although the much higher event rates may allow for more highly-crafted cuts. On the high-mass side, if we naively extrapolate up our 300 fb 1 analysis as per gure 4, we nd discovery (exclusion) reach extending to about 800 GeV. Along similar lines, projections for a 100 TeV proton collider are also interesting to pursue. However, as we ultimately scan up to m~ t mt, we e ectively return to the fully compressed situation m ~ ' mt~. All of the compression lines may then practically blur together using more standard \monojet"+6ET style searches, perhaps supplemented by the additional \soft" activity from the t( ) decays. Such an analysis has been carried out in [40], nding sensitivity to compressed stops up to multiple TeV using the dilepton channel.5 Finally, all of our results readily generalize to those classes of fermionic top-partner models that exhibit either a conserved or approximately-conserved parity, and contain a neutral \LSP" boson which plays a role kinematically identical to ~0 [41]. The only major di erence relative to stops, from the perspective of our analysis, is their approximately six times larger cross section at a given mass, yielding commensurately stronger sensitivity. In conclusion, natural supersymmetry poses some interesting phenomenological challenges, as evidenced by the enduring gaps in coverage of one its simplest incarnations: an NLSP stop and LSP neutralino. While limits continue to push upward in mass in the favorable parameter regions that readily provide lots of 6ET , we have seen here that an appropriately constructed analysis at the upgraded LHC, along the lines suggested in [33], can qualitatively extend sensitivity to this model into the more di cult compressed regions at lower masses. Combined, these approaches will leave very little \natural" parameter space unexplored. With its next major phase in progress, the LHC appears poised to provide us with a much more comprehensive perspective on the possible role of supersymmetric top quarks in Nature. Note added. While this paper was nearing completion, [ 42 ] appeared, which has significant overlap with our results. Their proposed RM variable (a very close variant of what was originally proposed in [33]) is highly correlated with the 6ET =pHT variable that we use here, and in general with any variable proportional to 6ET in the presence of a hard ISR-jet pT cut. There are a number of other di erences in our analysis strategy, which lead to a higher S=B with comparable formal statistical signi cance, and somewhat di erent sensitivity contours. (E.g., near the speci c mass point mt~ = m + mt ' 350 GeV, we nd S=B ' 2, versus the S=B ' 1 found in [ 42 ].) We also pay additional attention to the approach to the stealth region and the possible role of 6ET resolution. However, we do not make a dedicated study around the W compression line. 5If we naively scale the energies and cross sections from the existing monojet+6ET searches for fully compressed stops [3, 16] from an 8 TeV machine to a 100 TeV machine (without running the PDFs), we would 3 ab 1. Suggestively, this coarse estimate is very close to that of [40] on the top compression line. expect an exclusion of (260 GeV) (100=8) ' 3 TeV after accumulating a luminosity of 20 fb 1 (100=8)2 ' HJEP03(216)5 Acknowledgments We thank Ayres Freitas, Matthew Buckley, Kaoru Hagiwara, Eva Halkiadakis, George Redlinger, and Scott Thomas for discussions, and Olivier Mattelaer for help debugging MadGraph matching at high kT . SM was supported by NSF grant No. PHY-1404056. MP was supported by the LHC-TI grant NSF No. PHY-0969510 and by the VPUE at Stanford University. DS was supported by DoE grant No. DE-SC0003883. BT was supported by DoE grant No. DE-FG02-95ER40896 and by PITT PACC. A Event generation Our event generation is performed using MadGraph5 aMC@NLO [ 43 ] at 13 TeV and showered with PYTHIA 6 [44], using leading-order matrix elements (without K-factors). We set the top quark mass to 173 GeV, and width to 1.5 GeV. For our signal samples, we choose mostly-right-handed stop and mostly-Bino neutralino. (Spin e ects on our all-hadronic analysis are expected to be modest.) Most samples are generated as t~t~ j, with only a parton-level cut of 400 GeV on the accompanying jet. Both stops are decayed using three-body phase space t~ ! W b ~0, regardless of mass point, which is crucial for modeling the kinematic transition at the top compression line. A complete decay chain is therefore, e.g., t1 > W+ b n1, W+ > j j. The stop width for each model point is computed separately using 1 ! 3 parton-level decay simulations. A subset of models along the compression line have been simulated over their full production phase space, using kT -MLM matching with a threshold of 100 GeV. Perhaps unsurprisingly, the events passing our nal selections are highly dominated by the 1j subsample, and are in close agreement with our simple unmatched simulations. Similarly, we nd very low relative pass rates for decay modes other than all-hadronic. The backgrounds are generated as follows.6 Our tt sample is matched up to one (two) jets for all-hadronic (partially leptonic or ) decays, again using a 100 GeV threshold. We also generate ttW and ttZ matched up to one jet. For W=Z+jets and multijet backgrounds, we concentrate on production with at least two heavy quarks (bottom or charm) in the hard event. Because of the di culties of computing very high-multiplicity matrix elements, we mainly use the parton shower to generate extra partons, and do not employ any matching. The W=Z+jets sample speci cally starts with W=Z (decaying to l , , or ) plus three hard partons, while the multijet sample starts with four hard partons. We have also crosschecked the multijets against AlpGen [45] samples, generated with identical criteria. For each sample we impose cuts at the parton level that treat the b and j partons democratically, R(j; j) > 0:4 (where j here includes b) as well as a pT cut on the requiring pT (j) > 15, hardest jet of 350 GeV. 6We do not generate single-top nor diboson backgrounds, which, given our reconstruction criteria, we expect to be subdominant to tt and W=Z+jets, respectively. Cf. the background composition in ATLAS's all-hadronic stop search [5]. Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. [1] ATLAS collaboration, Measurement of Spin Correlation in Top-Antitop Quark Events and Search for Top Squark Pair Production in pp Collisions at p s = 8 TeV Using the ATLAS Detector, Phys. Rev. Lett. 114 (2015) 142001 [arXiv:1412.4742] [INSPIRE]. 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Sebastian Macaluso, Michael Park, David Shih. Revealing compressed stops using high-momentum recoils, Journal of High Energy Physics, 2016, 151, DOI: 10.1007/JHEP03(2016)151