Single top squark production as a probe of natural supersymmetry at the LHC
aa r X i v : . [ h e p - ph ] J a n Single top squark production as a probe of natural supersymmetry at the LHC
Ken-ichi Hikasa, ∗ Jinmian Li, † Lei Wu, ‡ and Jin Min Yang § Department of Physics, Tohoku University, Sendai 980-8578, Japan ARC Centre of Excellence for Particle Physics at the Terascale,Department of Physics, University of Adelaide, Adelaide, SA 5005, Australia ARC Centre of Excellence for Particle Physics at the Terascale,School of Physics, The University of Sydney, NSW 2006, Australia State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Academia Sinica, Beijing 100190, China (Dated: October 10, 2018)Light top squarks (stops) and light higgsinos are the key features of natural SUSY, where thehiggsinos ˜ χ ± and ˜ χ , are nearly degenerate and act as the missing transverse energy ( /E T ) at theLHC. Besides the strong production, the stop can be produced via the electroweak interaction. Thedetermination of the electroweak properties of the stop is an essential task for the LHC and futurecolliders. So in this paper, we investigate the single stop (˜ t ) production pp → ˜ t + /E T in the naturalSUSY at the LHC, which gives the monotop signature t + /E T from ˜ t → t ˜ χ , or the monobottomsignature b + /E T from ˜ t → b ˜ χ +1 . We perform Monte Carlo simulations for these signatures andobtain the results: (1) The signal b + /E T has a better sensitivity than t + /E T for probing naturalSUSY; (2) The parameter region with a higgsino mass 100 GeV . µ .
225 GeV and stop mass m ˜ t .
620 GeV, can be probed through the single stop production with S/ √ B > . S/B . − . INTRODUCTION
The search for supersymmetry (SUSY) is a long-standing important task in particle physics. One primemotivation for weak-scale SUSY is that it protects theHiggs vacuum expectation value without unnatural fine-tuning of the theory parameters. In the minimal super-symmetric standard model (MSSM), only a small subsetof the supersymmetric partners strongly relates with thenaturalness of the Higgs potential [1]. This can be seenfrom the minimization of the Higgs potential [2]: M Z m H d + Σ d ) − ( m H u + Σ u ) tan β tan β − − µ ≃ − µ − ( m H u + Σ u ) , (1)where µ is the higgsino mass parameter, and m H d and m H u denote the weak scale soft SUSY breaking masses ofthe Higgs fields. A moderate or large tan β ≡ v u /v d is as-sumed in the last approximate equality. Σ u and Σ d arisefrom the radiative corrections to the Higgs potential, andthe one-loop dominant contribution to Σ u is given by [3]Σ u ∼ Y t π × m t i log m t i Q − ! . (2)In order to obtain the observed value of M Z without largecancelations in Eq. (1), each term on the right hand sideshould be comparable in magnitude. Thus, the higgsinomass µ must be of the order of ∼ −
200 GeV and therequirement of Σ u ∼ M Z / m H u at two-loop level, it is also upperbounded by the naturalness [9] (however, the direct LHCsearches have pushed the gluino up to TeV scale [10, 11]while the recent ATLAS Z-peaked excess may indicate agluino around 800 GeV [12]).So to test SUSY naturalness, the crucial task is tosearch for light stops or higgsinos. The search strat-egy for the pair productions of these nearly degeneratehiggsinos has been recently studied [13–26]. During theLHC run-1, the ATLAS and CMS collaborations haveperformed the extensive searches for the stops throughthe gluino-mediated stop production [27, 28] or the directstop pair production [29, 30]. Meanwhile, many theoret-ical studies that aim for improving the LHC sensitivityto a light stop have been proposed [31–46]. The currentLHC constraints indicate a stop mass bound of hundredsof GeV [47–57], however, those results are affected bythe stop polarization states and branching ratios. Theconstraints on the right-handed stop from the LHC run-1 direct searches [29, 30] are usually weakened by thebranching ratio suppression, which can still be as lightas 230 GeV in some compressed region [58]. If the stopmass is heavier than about 450 GeV, it is allowed in mostparameter space. So in our work, we require the stopmass be heavier than 450 GeV [58].Usually, the stop pair production provides the mostsensitive way to search for the stop at the LHC. However,the stop can also participate in the electroweak inter-action processes. The determination of the electroweakproperties of the stop is an essential task for the LHCand future colliders. In this work, we study the singlestop production pp → ˜ t + /E T in the natural SUSY atthe LHC. The observation of the single stop productionwill test the electroweak properties of the stop and thenaturalness of the supersymmetry. In the following, wewill perform the Monte Carlo simulations for the singlestop production and examine its sensitivity at the LHC.
200 400 600 800 100010 -3 -2 -1 ~~ ~ t - ( L O ) ( pb ) m t (GeV) = 100 GeVLHC-14 TeV t t * ( N L O ) ~~~ t - ( N L O ) ~ Figure 1: The cross sections of ˜ t ˜ t ∗ and ˜ t ˜ χ − productions atthe 14 TeV LHC for tan β = 50 and degenerate higgsinos withmass µ = 100 GeV. The contribution of conjugate process˜ t ∗ ˜ χ +1 is included. CALCULATIONS AND SIMULATIONS
At the LHC, the single stop production is induced bythe electroweak interaction and proceeds through the fol-lowing process (see Fig. 1 for the corresponding Feynmandiagrams): pp → ˜ t ˜ χ − . (3)Since in natural SUSY the light higgsinos are nearly de-generate, the decay products of ˜ χ − → W ∗ χ will carrysmall energies and, hence, are too soft to be observed inthe detector. Thus, the associated production of ˜ t ˜ χ − can be identified as ˜ t + /E T , which provides a distinctivesignature at the LHC.In Fig. 1, we show the next-to-leading order (NLO)cross sections of the stop pair and the single stop pro-ductions for µ = 100 GeV at 14 TeV LHC by using thepackages Prospino2 [59] and
MadGolem [60], respectively.The renormalization and factorization scales are taken asthe half average of the final states masses. In the calcu-lations of ˜ t ˜ χ − , we use the LO and NLO parton densitiesgiven by CTEQ6L1 and CTEQ6M with five active flavors[61]. The contribution of the conjugate process ˜ t ∗ ˜ χ +1 isincluded. Except for the higgsino mass parameter µ andright-handed stop soft mass m U , we assume other softsupersymmetric masses at 1 TeV, and use the packages SOFTSUSY-3.3.9 [62] and
MSSMCalc [63] to calculatemasses, couplings and branching ratios of the sparticles. Since the cross section of single stop production is notsensitive to tan β , we take tan β = 50 for simplicity. Wefind that the single stop cross section can still reach about200 fb when m ˜ t ≃
450 GeV. The NLO K -factor of theprocess pp → ˜ t ˜ χ − ranges from 1.25 to 1.33. When thestop becomes heavy, the single stop production cross sec-tion will decrease, but slower than the pair production,due to the kinematics.Next, we investigate the LHC observability of the sin-gle stop signatures with the sequent decays ˜ t → t ˜ χ , and ˜ t → b ˜ χ +1 : pp → ˜ t ˜ χ − → t ˜ χ , ˜ χ − → bjj + /E T , (4) pp → ˜ t ˜ χ − → b ˜ χ +1 ˜ χ − → b + /E T . (5)For the decay ˜ t → t ˜ χ , , the SM backgrounds to thesignal bjj + /E T are from the semi- and full-hadronic t ¯ t events [64–66] , where the undetected lepton and the lim-ited jet energy resolution will lead to the relatively largemissing transverse energy. The processes W + jets and Z + jets can fake the signal when one of those light-flavorjets are mis-tagged as a b -jet. Also, the single top canmimic our signal when the lepton from the W boson de-cay is missed at the detector. While t ¯ t + V backgroundsare not considered in our simulations due to their smallmissing energy or cross sections compared to the abovebackgrounds. (top)/GeV T p0 100 200 300 400 500 600 700 800 ( t op ) T d N / d p -4 -3 -2 -1 = 400 GeV t~ m = 500 GeV t~ m = 600 GeV t~ m = 700 GeV t~ m =100 GeV µ Figure 2: The parton-level p T distribution of the top quarkin the channel ˜ t → t ˜ χ , for µ = 100 GeV at 14 TeV LHC. Hadronic monotop has received special attention since its signa-ture offers the possibility to use top reconstruction as a tool toreject the backgrounds. In contrast, the leptonic monotops isbelieved to be more challenging since the branching fraction ofthe leptonic top quark decay is smaller and since there are twodifferent sources of missing transverse energy, namely a neutrinocoming from the top quark decay and the new invisible state. InRef.[65], the authors comparatively studies these two channelsand found that the sensitivity of both channels are very similar.
In Fig. 2, we present the parton-level p T distributionof the top quark in the channel ˜ t → t ˜ χ , for µ = 100GeV at 14 TeV LHC. It can be seen that, with the in-crease of stop mass, the top quark produced from stopdecay is boosted and has larger p T . So, in the analysis of˜ t → t ˜ χ , channel, we respectively adopt HEPTopTagger [32] and normal hadronic top reconstruction methods foreach sample to identify the top quark in the final statesand present our results with the best one. The detailedanalysis strategies are the followings: • Events with any isolated leptons are rejected; • Method-1 : We use Cambridge-Aachen (CA) algo-rithms [67] in
Fastjet [68] to cluster the jets with R = 1 . top-jet candidates. Eachcandidate must have the top quark substructurerequired by the HEPTopTagger . The b -tagging isalso imposed in the top-jet reconstruction. Otherenergy deposits outside the top-jet are further re-constructed as the normal jets by using anti- k t al-gorithm with R = 0 . < m t <
200 GeV. While the W window is taken as the default value in HepTop-Tagger ; • Method-2 : In normal hadronic top quark recon-struction, a pair of jets is selected with the invariantmass m jj >
60 GeV and the smallest ∆ R . A thirdjet closest to this di-jet system is used to consti-tute the top quark candidate. Among these threejets, at least one b -jet and ∆ φ ( /E T , p T ( b )) > k t algorithm is used for jet clus-tering with R = 0 . • We keep the events with the exact one recon-structed top quark and require 150 GeV < m rec t <
200 GeV; • The extra leading jet j outside the reconstructedtop quark object is vetoed if p T ( j ) >
30 GeV and | η ( j ) | < . • We define the signal regions according to( /E T , p T ( j top )) cuts: (200, 100), (250, 150), (300,200), (350, 250) for Method-1, and ( p T ( b ) , /E T )cuts: (200, 50), (250, 50), (300, 100), (350, 100)GeV for Method-2.For the decay ˜ t → b ˜ χ +1 , the SM backgrounds to thesignal b + /E T are dominated by the processes W + jetsand Z + jets when the light-flavor jets are mis-identifiedas b -jets [70]. The t ¯ t events become the sub-leading back-grounds due to their large multiplicity. The signal eventsare selected to satisfy the following criteria: • Events with any isolated leptons are rejected; • We require exact one hard b -jet in the final states,but allow an additional softer jet with p T ( j ) < φ ( /E T , p T ( j )) >
2. Since the hardnessof b -jet from stop decay depends on the mass split-ting between ˜ t and ˜ χ − , we define three signal re-gions for each sample according to ( /E T , p T ( b )) cuts:(100, 70), (150, 100) and (250, 200) GeV.Finally, we use the most sensitive signal region (with thehighest S/ √ B ) for each decay mode and show our re-sults in Fig. 3 and Fig. 4, respectively. In our study, weomitted the QCD multijet backgrounds, whose correcttreatment needs the experimental data-driven methodsand hence depends on the realistic detector environmentsof the 14 TeV LHC. As discussed in [65, 70, 71], the re-quirements of high p T ( b ) and large /E T with a seperation∆ φ ( /E T , p T ( j )) can usually be expected to greatly re-duce the fake contamination from the QCD backgroundsand allow for a good signal selection efficiency.The parton level signal and background events are gen-erated with MadGraph5 [72], where
W/Z +jets is matchedup to 3 jets by using MLM matching scheme [73] and set-ting xqcut = 30 GeV. For the value of qcut in matching,we take it to max ( xqcut + 5 , xqcut ∗ .
2) [74] in our simu-lation. We perform parton shower and fast detector sim-ulations with
PYTHIA [75] and
Delphes [76]. We assumethe b -jet tagging efficiency as 70% [77] and a misiden-tification efficiency of c -jets and light jets as 10% and0.1%, respectively. The cross section of t ¯ t is normalizedto the approximately next-to-next-to-leading order value σ t ¯ t = 920 pb [78]. RESULTS AND DISCUSSIONS
Table I: The cross sections of V +jets, t ¯ t and ˜ t ( → t ˜ χ , ) ˜ χ − fora benchmark point ( m ˜ t , µ ) = (611 , β = 10in Method-1 and Method-2 at 14 TeV LHC with L = 3000fb − . The cross sections are in unit of fb.cuts W + jets Z + jets t ¯ t tW S S/B S/ √ B Method-1 < − . < − . In Table I, we compare the results of pp → ˜ t ( → t ˜ χ , ) ˜ χ − for a benchmark point ( m ˜ t , µ ) = (611 , Z + jets background inMethod-1 is smaller than in Method-2, while the t ¯ t back-ground in Method-1 is larger than in Method-2. However,the signal events can be more kept in Method-1 than inMethod-2. So the overall effects make the Method-1 havea better sensitivity in reconstructing the top quark in theregion with large mass splitting between ˜ t and ˜ χ − . At14 TeV LHC with L = 3000 fb − , the statistical signif-icance S/ √ B for our benchmark point can reach 3 . σ (2 . σ ) with S/B = 4 .
0% (3 . Table II: The cross sections of V +jets, t ¯ t and ˜ t ( → b ˜ χ +1 ) ˜ χ − fora benchmark point ( m ˜ t , µ ) = (496 , β = 10at 14 TeV LHC with L = 3000 fb − . The cross sections arein unit of fb. W + jets Z + jets t ¯ t S S/B S/ √ B< − . In Table II, we show the cross sections of V + jets, t ¯ t and ˜ t ( → b ˜ χ +1 ) ˜ χ − for a benchmark point ( m ˜ t , µ ) =(496 , t → t ˜ χ , channel, Z + jets background is dominant over t ¯ t since only one hard b -jet is required in the final state.From Table II we can see that S/ √ B and S/B can reach5 . .
1% for L = 3000 fb − , respectively.
500 550 600 650 700 750 80075100125150175200225250275300325350
LHC-14 TeV, Lum.=3000 fb -1 ~ ( G e V ) m t (GeV) m t = + m t ~ t t~ ~ S/ B Figure 3: The dependence of the significance of the channel˜ t → t ˜ χ , on the higgsino mass µ and stop mass m ˜ t at the14 TeV LHC with L = 3000 fb − . In Fig. 3, we display the dependence of statistical sig-nificance S/ √ B of the channel ˜ t → t ˜ χ , on the higgsinomass µ and stop mass m ˜ t at 14 TeV LHC with L = 3000fb − . We can see that values of S/ √ B decrease withthe increase of µ because of the cut efficiency reduction.When the stop becomes heavy, the cross section of ˜ t ˜ χ − is suppressed. However, as a result of the application of HEPTopTagger method, more signal events can be kept,in particular in the mass range 450 GeV . m ˜ t . µ .
150 GeV, the stop mass m ˜ t .
610 GeV can be probed at & σ statistical significancewith S/B . S/ √ B of the chan-nel ˜ t → b ˜ χ +1 is presented on the plane of higgsino mass µ versus stop mass m ˜ t at 14 TeV LHC with L = 3000fb − . It can be seen that the sensitive stop region lies in450 GeV . m ˜ t .
620 GeV, where a hard b -jet ( p T > /E T ( /E T >
250 GeV) can be used to
500 550 600 650 700 750 80075100125150175200225250275300325350
LHC-14 TeV, Lum.=3000 fb -1 S/ Bt b ( G e V ) m t (GeV) ~~ ~ Figure 4: Same as Fig. 3, but for the decay channel ˜ t → b ˜ χ +1 . effectively suppress the backgrounds. But when the stopmass increases, S/ √ B will rapidly decrease. We see thatthe higgsino mass 100 GeV . µ .
225 GeV and the stopmass m ˜ t .
620 GeV can be covered at & σ statisticalsignificance with S/B varying from 4% to 19%.
CONCLUSIONS even its exclusion limit for the stop may be not asgood as the pair production. However, the stop can par-ticipates in the strong interaction processes but also inthe electroweak interaction processes, the determinationof the electroweak properties of the stop is an essentialtask for the LHC and future colliders. In this work wepropose to probe natural SUSY by using the electroweaksingle-stop production pp → ˜ t + /E T at the LHC (here themissing energy is from the nearly degenerate higgsinos).By analyzing the decay channels of the stop ˜ t → t ˜ χ , and ˜ t → b ˜ χ +1 , we obtain the obervations: (1) The de-cay ˜ t → b ˜ χ +1 has a better sensitivity than ˜ t → t ˜ χ , ; (2) The parameter region with a higgsino mass 100GeV . µ .
225 GeV and the stop mass m ˜ t .
620 GeVcan be covered with S/ √ B > . S/B .
19% at14 TeV HL-LHC with an integrated luminosity of 3000fb − . So the searches for the single stop production willdirectly test the naturalness of the supersymmetry andthe electroweak properties of the stop. ACKNOWLEDGMENTS
Lei Wu thanks David Lopez-Val and Dorival Goncalvesfor providing us the
MadGolem package. This work waspartly supported by the Grant-in-Aid for Scientific Re-search (No. 24540246) from Ministry of Education, Cul-ture, Sports, Science and Technology (MEXT) of Japan,by the Australian Research Council, by the CAS Cen-ter for Excellence in Particle Physics (CCEPP), by theNational Natural Science Foundation of China (NNSFC)under grants Nos. 11305049, 11275057, 11375001,11405047, 11275245, 10821504 and 11135003, and bySpecialized Research Fund for the Doctoral Program ofHigher Education under Grant No.20134104120002. ∗ Electronic address:[email protected] † Electronic address:[email protected] ‡ Electronic address:[email protected] § Electronic address:[email protected][1] R. Barbieri and G. F. Giudice, Nucl. Phys. B , 63(1988).[2] R. Arnowitt and P. Nath, Phys. Rev. D 46, 3981 (1992).[3] H. Baer, et al. , Phys. Rev. D , 115028 (2013).[4] S. F. King, M. Muhlleitner and R. Nevzorov, Nucl. Phys.B , 207 (2012).[5] Z. Kang, J. Li and T. Li, JHEP , 024 (2012).[6] T. 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