Search for 3-and 4-body decays of the scalar top quark in pp-collisions at root s = 1 . 8

We have searched for the signature of 3and 4-body decays of pair-produced scalar top quarks (stop) in the inclu state containing an electron, a muon, and significant missing transverse energy using a sample of pp̄ events correspondin to 108.3 pb−1 of data collected with the DØ detector at Fermilab. The search is done in the framework of the m supersymmetric standard model assuming that the neutralino ( χ̃0 1) is the lightest supersymmetric particle and is stable. evidence for a signal is found and we derive cross-section upper limits as a function of stop ( t̃) and neutralino masses different decay scenarios leading to the b νχ̃0 1 final state.  2004 Published by Elsevier B.V. mead SY um eir st ew evark tric rk r-

Supersymmetry SUSY 1 is a hypothetical symmetry between bosons and fermions that could lead to an extension of the standard model SM. SUSY predicts additional elementary particles with quantum numbers identical to those of the SM, except for their spins which di er by a half unit. Their masses must also di er since no evidence has been found for new particles with masses equal to those of the SM. In several SUSY models, the large mass of the top quark induces a strong mixing between the supersymmetric partners of the two chirality states of the top quark leading naturally to two physical states of very di erent mass 2 . The lightest stop, denotedt in this Letter, could therefore be signi cantly lighter than the other squarks rendering it a particularly auspicious choice for a direct search.
The production of a pair of stops at the Tevatron proceeds through gluon fusion or quark-antiquark annihilation, and its cross-section, for a given stop mass mt, is known at next-to-leading order NLO with a precision of 8 3 . The phenomenology of stop decays depends on the assumptions made in the SUSY model. In the framework of the minimal supersymmetric standard model MSSM 4 with R-parity 5 conservation, the lightest SUSY particle LSP is stable. In a previous publication 6 we performed this search assuming that the scalar neutrino sneutrino, is the LSP and derived exclusion limits reaching higher stop masses than those of previous similar searches 7, 8 . In this Letter we assume that the neutralino is the LSP.
We consider alternative scenarios to what has been done in most of the searches at the CERN LEP collider 8 or at the Fermilab Tevatron 9, 10, 11 . Those studies searched for the 2-body decays,t ! c~ 0 1 ort ! b~ + 1 where~ + 1 is the lightest chargino of the MSSM; it has been recently realized 12 that even if thet ! b~ + 1 decay is kinematically forbidden, as will be assumed in the following, thet ! c~ 0 1 channel may not be the dominant one for stop masses accessible at LEP or the Tevatron mt 90 GeV when the ratio of the two v acuum expectation values of the Higgs elds is not large tan 5 13 . The 3-body decayst ! bW~ 0 1 and ort ! b` could be kinematically allowed, and if not, the corresponding 4-body decayst ! bf f 0~ 0 1 where f f 0 originate from the decay of the virtual W boson produced byt ! b~ + 1 followed by~ + 1 ! W~ 0 1 andt ! b`~ 0 1 with ~ 0 1 from the decay of the virtual sneutrino produced by~ + 1 ! are generally allowed, i.e. as soon as mt m~ 0 1 + m b + m`. Thus, as the stop can dominantly decay to 3 or 4 bodieswhen tan 5, the search strategies must be modi ed.
The experimental signature for such decays of at t pair consists of two b quarks, two fermions, and missing transverse energy. Since our search is based on the presence of charged leptons in the nal state, we have access only to the case where the fermion f f 0 is a neutral charged lepton. The nal states of all these 3-and 4-body decays are thus identical b`~ 0 1 . The underlying process depends on the SUSY parameters, and can bea mixture of the described processes. In the following, the analysis is performed assuming the complete dominance of each of these four cases in turn, and will be referred to as 3-or 4-bodydecay in the W" or light" exchange scenario.
In our search, the leptons can bee; or , but leptons are considered only if they decay i n to e or . We place no requirements on the presence of jets and use only the eE T = signature since it has less background than the eeE T = or E T = channels. The missing transverse energy E T = represents the measured imbalance in transverse energy due to the 4 escaping neutrinos and neutralinos, and is obtained experimentally from the vector sum of the transverse energy measured in the calorimeter and in the muon spectrometer system. The event sample corresponds to 108:3 pb ,1 of data collected by the D experiment at Fermilab during the Run I of the Tevatron. A detailed description of the D detector and its triggering system can be found in Ref. 14 . This analysis is mainly based on three subsystems: the uranium liquidargon calorimeter for identifying electron candidates and measuring electromagnetic and hadronic energies; the inner detector for tracking charged particles and to di erentiate photons from electrons; and the muon spectrometer to identify and measure the required muon.
The data and pre-selection criteria are identical to those published in Ref. 6 , however for the new channels considered in this analysis W exchange scenario, and 4-body decay in the light sneutrino scenario, we apply a stricter nal selection. The initial selection requires events having one or more isolated electrons with transverse energy E e T 15 GeV, one or more isolated muons with E T 15 GeV, and E T = 20 GeV. A lepton is isolated if its distance in the -' plane from the closest jet is greater than 0.5, where and ' are the standard pseudorapidity and azimuthal angle variables. Jets are found using a cone algorithm with a radius of 0.5 in the -' plane. We also require 15 e ' 165 and e 2:0. e ' j' e , ' j, where '`` is the azimuthal angle pseudorapidity of the lepton`, and e j e + j are two kinematic quantities which increase rejection of the SM background 15 . The distributions of these kinematic quantities after these requirements are shown in Fig. 1a,b,c,e,f.
For the nal selection, we apply an additional requirement compared to those in Ref. 6 : if the event has one two or more jets with transverse energy greater than 15 GeV, we require that the distances in the -' plane D l 1 ;j 1 ' and D l 2 ;j 2 ' 1:5. D l 1 ;j 1 ' is de ned as the smaller of the two distances between the highest energy jet and each of the two leptons. D l 2 ;j 2 ' is de ned as the distance between the second highest energy jet and the lepton that was not used to de ne D l 1 ;j 1 ' . This requirement reduces the SM background by about a factor of two and removes only a small part 5 of the signal in the present analysis. The distributions of the transverse energy of any associated jets and D l 1 ;j 1 ' are shown in Fig. 1d,g, before applying this requirement.
The dominant SM processes that result in the eE T = signature are, in order of decreasing importance: i multi-jet processes called QCD" in the following with one jet misidenti ed as an electron and one true muon originating from another jet muon misidenti cation in our nal sample is negligible; ii Z ! ! e ; iii W W ! e ; iv t t! e j j . The Drell-Yan process DY ! ! e contributes less than 0.02 events after the nal event selection. The QCD background is determined using the data, following the procedure described in Ref. 16 . The other SM backgrounds are estimated using MC samples processed through the full data analysis chain.
For simulation of the signal, we use the pythia 17 event generator with its standard hadronization and fragmentation functions and the CTEQ3M 18 parton distribution functions. The stop decay is generated using comphep 19 . Detector simulation is performed using the fast D simulation reconstruction program, which agrees with reference samples passed through the full D analysis chain. Thet t samples are simulated for stop neutralino masses varying between 80 30 and 145 85 GeV. The chargino mass is set equal to 140 GeV, to prevent the possibility o f 2-body decay. The samples are produced separately for the W exchange and for the light sneutrino scenarios. In the light sneutrino scenario, the mass of the sneutrino is varied between 40 and 80 GeV for the 3-body decay, a n d i s s e t to mt , m b for the 4-body decay.
The expected cross-sections for the background processes and the numbersof events passing the nal selection are given in Table 1, and compared to the expected 4-body decay stop signal for mt m~ 0 1 = 120 60 GeV in the light sneutrino and W exchange scenarios. The e ciency for selecting the signal varies between 1 and 4 and is largest for high stop masses and low neutralino masses. The most signi cant sources of uncertainties on the number of signal events passing the selection criteria are given in Ref. 6 and combine to approximately 18. The total systematic error for the background is about 10. This error is dominated by the uncertainty on the QCD background 7 and on the cross-sections for the background processes 10 17.
The agreement between the number of observed events and the expected SM background allows us to set cross-section upper limits on stop pair production. We make the assumption that all non-SM processes, except the ones speci cally searched for, can be neglected. This translates to more conservative limits. The 95 con dence level C.L. limits are obtained using a Bayesian approach 20 that takes statistical and systematic uncertainties into account.
In the following we assume that the loop-induced stop decay,t ! c~ 0 1 , is negligible compared to the processes induced byt ! b~ + 1 , where~ + 1 is virtual. This is true for a large variety of MSSM models in which thet is the next-to-lightest supersymmetric particle and tan 5 12, 13 , or when the 3-body decayt ! b` is kinematically allowed. The two main scenarios that we study are dependent on the sneutrino mass: if m is large m 2m W the decay~ + 1 !` can be neglected, and only the decay~ + 1 ! W~ 0 1 contributes signi cantly, leading to the so-called W exchange scenario. Otherwise, the decay~ + 1 !` plays a signi cant role, and is assumed to be dominant in the so-called light sneutrino scenario, as is the case for instance if m m W 15 . The exact proportion of the two scenarios depends on the MSSM parameters; we treat them separately, assuming 100 branching ratio in each mode. Experimentally the light sneutrino scenario has an advantage since leptons are always present in the nal state; this is the case for only about one-third of the stops decaying via W exchange.
Cross-section limits in the W exchange scenario are shown in Fig. 2 for three di erent neutralino masses, m~ 0 1 = 4 0 ; 5 0 a n d 6 0 G e V . E v en at low m~ 0 1 and mt, the limits are about a f a c t o r o f t wo higher than the expected cross-section, so this 4-body decay scenario cannot be excluded with these data. The limits for the 3-body decay i.e. when mt m W + m b + m~ 0 1 are also shown, but are about an order of magnitude larger than the expected cross-section. Our results are compared to those of the CDF collaboration 7 obtained assumingt ! b~ + 1 followed by~ + 1 ! f f 0~ 0 1 via a virtual W boson, with m~ + 1 m~ 0 1 = 9 0 40 GeV.
Cross-section upper limits in the light sneutrino scenario are shown in Fig. 3 assuming m~ 0 1 m = 60; 80 GeV m~ 0 1 = 50; 60 GeV, and m = mt , m b for the 3-4-body 6 decay. The limits are stronger than those obtained for the W exchange scenario since two charged leptons are always present in the nal state. The cross-section limits are below the expected cross-section for some part of the mt; m 0 1 plane: for instance, for m~ 0 1 = 50 GeV the 4-body decay scenario is excluded for 90 mt 120 GeV. The limits for the 3-body decay are stronger, extending to mt = 140 GeV for m~ 0 1 = 6 0 G e V . The resulting exclusion contours for the light sneutrino scenario are displayed in Fig. 4 in the mt,m~ 0 1 plane assuming 3-or 4-body decay with a light sneutrino mass equal, respectively, to m~ 0 1 and mt , m b . The results obtained by CDF 10 and at LEP 21 assuming 100 branching ratio fort ! c~ 0 1 are also shown indicating that if the sneutrino is of comparable mass to the stop, or lighter, the intersection of the CDF exclusion contour and our 4-body light sneutrino exclusion contour provides a model-independent exclusion limit, i.e. up to stop neutralino masses approximately equal to 115 50 GeV. However, without an assumption of the m value, as we are not able to place exclusion limits in the W exchange scenario, the current limit in the mt; m 0 1 p l a n e i s m o d e l dependent above approximately 90 GeV. While we were preparing this Letter, ALEPH has reported the rst search at LEP for 4-bodydecays of the stop 22 . Their limit, when assuming 100 branching ratio fort ! b`~ 0 1 , is about 95 GeV for m~ 0 1 ' 75 GeV, and is also shown in GeV is excluded in the MSSM for m~ 0 1 50 GeV. If the sneutrino mass is smaller than 60 GeV, the mass exclusion domain extends up to a stop mass of 140 GeV. Without any assumptions on the sneutrino mass, the present analysis emphasizes that there is no model-independent exclusion limit on the stop mass above a p p r o ximately 90 GeV. We t h us provide new cross-section upper limits in the W exchange scenario up to mt = 140 GeV.  Figure 1: Distributions after initial selection cuts for the total background open histogram, the sum of the total background and the expected 4-body decay stop signal for mt m~ 0 1 = 120 60 GeV in the light sneutrino scenario shaded histogram, and the data points of a the transverse energy of the electron, b the transverse energy of the muon, c the missing transverse energy, d the transverse energy of any jets present, e the di erence in azimuthal angle between the two leptons, f the absolute value of the sum in of the two leptons, and g the smallest lepton to jet distance in the event when at least one jet is reconstructed, h the distance between the lepton and jet that have not beenused in g, when two jets are reconstructed. For the nal selection, all events having distances i n g o r h above 1.5 are rejected.