Search for scalar top quarks in the acoplanar charm jets and missing transverse energy final state in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV

We present a search for the pair production of scalar top quarks, $\tilde{t}$, using 995 pb$^{-1}$ of data collected in $p\bar{p}$ collisions with the D0 detector at the Fermilab Tevatron Collider at $\sqrt{s} = 1.96$ TeV. Both scalar top quarks are assumed to decay into a charm quark and a neutralino ($\tilde{\chi}^{0}_{1}$), where $\tilde{\chi}^{0}_{1}$ is the lightest supersymmetric particle. This leads to a final state with two acoplanar charm jets and missing transverse energy. We find the yield of such events to be consistent with the standard model expectation, and exclude sets of $\tilde{t}$ and $\tilde{\chi}^{0}_{1} $ masses at the 95% C.L. that substantially extend the domain excluded by previous searches.

(Dated: March 14, 2008) We present a search for the pair production of scalar top quarks,t, using 995 pb −1 of data collected in pp collisions with the D0 detector at the Fermilab Tevatron Collider at √ s = 1.96 TeV. Both scalar top quarks are assumed to decay into a charm quark and a neutralino (χ 0 1 ), whereχ 0 1 is the lightest supersymmetric particle. This leads to a final state with two acoplanar charm jets and missing transverse energy. We find the yield of such events to be consistent with the standard model expectation, and exclude sets oft andχ 0 1 masses at the 95% C.L. that substantially extend the domain excluded by previous searches.
PACS numbers: 14.80.Ly; 12.60.Jv Supersymmetry (SUSY) may provide a solution to the hierarchy problem if the SUSY particles have masses less than 1 TeV, strongly motivating the searches for supersymmetric objects at the Fermilab Tevatron Collider. SUSY predicts the existence of partners with identical quantum numbers to all standard model (SM) particles except for spin. There exist two spin zero SUSY partners of the top quark corresponding to the latter's left and right handed states. Several arguments exist in favor of a light scalar top quark (t). Thet mass mt receives negative contributions proportional to the top quark Yukawa coupling in the renormalization group equations. This makes thet weak eigenstates lighter than other squarks [1]. Mixing between the left and right handed superpartners of the top quark, being proportional to the top quark mass m t , leads to a large mass splitting between the two physical eigenstates. This makes one of thet considerably lighter than the other. Additionally, a lightt that strongly couples to the Higgs boson could also generate a large enough CP violating phase to explain the mechanism for electroweak baryogenesis [2].
In R-parity conserving models [3], the lightest supersymmetric particle (LSP) is stable, and cosmological constraints indicate that it should be neutral and colorless [4]. In the following we assume conservation of Rparity and takeχ 0 1 , the lightest of four SUSY particles that result from the mixing between the SUSY partners of the SM neutral gauge and Higgs bosons, to be the LSP.
In the search reported in this Letter, we consider the range mt < m b + mχ+ 1 and mt < m W + m b + mχ0 1 , where m b is the b quark mass, mχ0 1 is theχ 0 1 mass and mχ+ 1 is theχ + 1 mass, withχ + 1 being the lighter of two mass eigenstates resulting from the mixing of the SUSY partners of charged gauge and Higgs bosons. The dominantt decay mode in this model is the flavor changing processt → cχ 0 1 and is assumed to occur with 100% branching fraction. Thet → tχ 0 1 decay is kinematically forbidden over thẽ t mass range accessible in this search, and the tree level four-body decayst → bff ′χ0 1 can be neglected [5]. In pp collisions,t pairs are produced via quarkantiquark annihilation and gluon fusion. Thet pair production cross section (σtt) primarily depends on mt, and a weak dependence on other SUSY parameters affects only the higher-order corrections. At √ s = 1.96 TeV which is the centre-of-mass energy available at the Fermilab Tevatron collider, σtt at next-to-leading-order (NLO), calculated with prospino [6], ranges from 15 pb to 1 pb for 100 ≤ mt ≤ 160 GeV. These cross sections are calculated using cteq6.1m parton distribution functions (PDFs) [7] and equal renormalization and factorization scales µ rf = mt. A theoretical uncertainty of ≈ 20% is estimated due to scale and PDF choices. Thett event topology consists of two acoplanar charm jets and missing transverse energy (/ E T ) from the neutralinos that escape detection. Searches fort pair production in the jets plus missing transverse energy mode have been reported by collaborations working at the CERN LEP collider [8], and the CDF [9,10] and D0 [11,12] collaborations. The highest excluded mass to date is mt < 134 GeV (95% C.L.) for mχ0 1 = 48 GeV [12]. Thet search is performed in the data collected with the D0 detector during Run IIa of the Tevatron and corresponds to an integrated luminosity of 995 ± 61 pb −1 [13]. A detailed description of the D0 detector can be found in [14]. The central tracking system consists of a silicon microstrip tracker and a fiber tracker, both located within a 2 T superconducting solenoidal magnet. A liquid-argon and uranium calorimeter covers pseudorapidity |η| 4.2, where η = − ln[tan(θ/2)], and θ is the polar angle with respect to the proton beam direction. An outer muon system, covering |η| < 2, consists of layers of tracking detectors and scintillation counters on both sides of 1.8 T iron toroids.
The data sample collected from April 2003 to February 2006 with the jets+/ E T triggers was analyzed for thet search. The trigger conditions require the / H T and its separation from all jets to be greater than 30 GeV and 25 • , respectively, where / H T is the transverse energy computed only from jets. Jets are reconstructed using an iterative midpoint cone algorithm with radius R cone = 0.5 [15]. The data set is reduced to a sample of 1.5 million events by requiring at least two jets with p T > 15 GeV and / E T > 40 GeV.
Signal samples are simulated using pythia 6.323 [16] for mt ranging from 95 GeV to 165 GeV andχ 0 1 masses from 45 GeV to 90 GeV. The largest expected backgrounds for this search are W and Z bosons produced in association with jets, denoted as V+jets. The V+jets and tt processes are simulated using alpgen 2.05 [17] interfaced with pythia for the generation of initial and final state radiation and hadronization. The background samples for single top quark and diboson production are simulated using comphep [18] and pythia, respectively. The PDF set cteq6l1 is used for both signal and background samples, and all generated events are subjected to full geant-based [19] simulation of the detector response. Simulated signal and background events are overlaid with recorded unbiased beam crossings to incorporate the effect of multiple interactions that occur in a single beam crossing. After reconstruction, simulated events are weighted properly to ensure that the instanta-neous luminosity distribution is the same in data and the simulated Monte Carlo (MC) samples. A parametrization of the trigger efficiency measured from the data is applied to simulated MC events in order to fold in trigger effects. The multijet background, not included in the MC samples, is directly estimated from data.
A large data sample of Z/γ * (→ ee) + jets events, corresponding to an integrated luminosity of 1067±65 pb −1 , from the same data period as thet search, is used to improve the prediction of V+jets backgrounds. For this study, Z boson candidates are selected using two high transverse energy (E T > 15 GeV) clusters that deposit more than 90% of their energy in the electromagnetic calorimeter, have shower shapes consistent with expectations for electrons, are matched with tracks reconstructed in the central tracker, and form an invariant mass between 65 GeV and 115 GeV. At least two jets with p T > 15 GeV and |η det | < 2.5 are required, where |η det | is the jet pseudorapidity calculated using the assumption that the jet originates from the detector center. The predicted number of Z/γ * (→ ee)+ ≥ 2 jets events is calculated using alpgen after correcting for differences in electron and jet reconstruction efficiencies between data and MC and normalizing the MC to the inclusive number of Z boson events in data. The alpgen prediction is corrected in each jet multiplicity bin by a reweighting function that depends on the transverse momentum of the Z boson to obtain better agreement between the model and data. The reweighting function is derived by fitting the ratio of the transverse momentum distribution of Z boson data to that from the MC prediction. After reweighting, all other kinematical variables in the Z/γ * (→ ee)+ ≥ 2 jets sample applicable to thet search are well described by MC.
The multijet background in Z/γ * (→ ee) + jets events is estimated from a fit to the dielectron invariant mass distribution. The ratio of the number of ee events produced by γ * to the number of Z +γ * events is determined from MC and used to extract the multijet contribution by fitting the dielectron invariant mass in data with an exponential function for the multijet+γ * contribution and a Breit-Wigner convolved with a Gaussian for Z boson events.
For thet search, the predicted SM background from V+jets sources is normalized to the number of Z/γ * (→ ee) + 2 jets events after subtracting the multijet background, N data Z(ee)+2 . As an example, the normalization weight assigned to simulated Z(→ νν) events with n light partons is Here N MC Z(νν)+n is the number of simulated Z(→ νν)+ n light parton jets events; σ ALP Z(νν)+n and σ ALP Z(ee)+2lp are the cross sections predicted by alpgen for Z(→ νν)+ n and Z/γ * (→ ee)+ 2 light parton jets, respectively; and ǫ Z(νν)+n and ǫ Z(ee)+2lp are the corresponding detection efficiencies. The factor f = 0.89 ± 0.02 is applied to correct for three effects: the absence of γ * contribution to Z(νν)+ jets events, the normalization of MC light jets to a data sample that contains all flavors of jets, and the difference in the luminosities of the data set used for thẽ t search (995 pb −1 ) and the Z/γ * (→ ee) + 2 jets data set (1067 pb −1 ).
The normalization weight assigned to simulated W (→ ℓν)+n light partons is is the product of the ratio of the normalized differential cross sections for W and Z bosons production at NLO [20] and predicted by alpgen, respectively. The motivation behind using this technique is to lower the luminosity times cross section uncertainty (≈ 6.1% ⊕ 15%) on the predicted number of events towards the 5% statistical uncertainty of the Z/γ * (→ ee)+2 jets normalization sample. The combined 15% uncertainty on the theoretical cross section for various background processes is mainly due to the choice of PDF and the renormalization and factorization scale. The signal and smaller backgrounds such as tt, diboson, and single top quark production are normalized using the measured absolute luminosity. For these processes NLO cross sections were computed with mcfm 5.1 [21].
The search strategy fort involves three steps which include the application of the selection criteria on kinematical variables, heavy flavor (HF) tagging and optimization of the final selection depending ont andχ 0 1 masses. The data set for thet search is reduced to a sample of 2288 potentialtt candidates, by applying the 15 selection criteria denoted by C1 − C15 and summarized in Table I. The main motivation for C1 is to reduce the multijet background. Requirements C2 to C7 help in reducing the W +jets and multijet backgrounds. The condition on the charged particle fraction (CPF) in C8 requires that at least 85% of the jets' charged particle transverse momenta be associated with tracks originating from the selected primary vertex in the event. This track confirmation requirement removes events with spurious / E T due to the choice of an incorrect primary vertex. C9 − C11 are applied to reject W +jets background with isolated leptons from W boson decay. For an electron to be isolated, the energy deposited in the calorimeter in a cone of radius 0.4 in η − φ around the electron direction should not be more than 15% of the energy deposited  in the electromagnetic layers inside a cone of radius 0.2. A muon is declared isolated if the sum of the energies of all tracks other than the muon in a cone of radius 0.5 is less than 2.5 GeV, and the calorimeter energy deposited in a hollow cone with inner and outer radii 0.1 and 0.4 around the muon direction is less than 5 GeV. A track with p T > 5 GeV is considered isolated if no other track with p T > 1.5 GeV is found in a hollow cone of inner and outer radii 0.1 and 0.4 around the track considered. This condition also helps suppress backgrounds with τ leptons where the τ decays hadronically. Remaining instrumental background is removed using a quantity defined by the angular separation between all jets and the / E T of the event, D = ∆φ max − ∆φ min , where ∆φ max (∆φ min ) is the largest (smallest) azimuthal separation between a jet and / E T ; and an asymmetry variable defined as A = (/ E T − / H T ) / (/ E T + / H T ). The requirements applied on these variables are given by C12 and C13. Figure 1 shows that both of these variables are very effective in eliminating multijet background which dominates in data for large D and negative A.
The 2288 events selected in data can be compared to the 2199 ± 18 +316 −321 events predicted from the simulation normalized to Z/γ * (→ ee)+2 jets events or 2292±19 +527 −532 events predicted using absolute luminosity normalization, with the first quoted uncertainty due to finite MC statistics and the second due to systematic effects described in more detail below. The small remaining multijet background in thet search analysis is estimated after applying all analysis conditions shown in Table I except that on / E T . The background subtracted / E T distribution is fitted in the control region (40 ≤ / E T ≤ 60 GeV) with exponential and power law functions, and the estimated contribution is extrapolated into the signal region (/ E T > 60 GeV). The average of the two results is taken as the multijet background estimate, while the difference between the two fit results is taken as the systematic uncertainty. This amounts to 14.4 ± 10.7 (stat) ± 5.1 (sys) events contributed by multijet background before HF tagging and optimization of selection cuts.
After selecting candidate events on the basis of topology, HF tagging is used to identify charm jets in the final state. A neural network (NN) tagging tool [22] that combines information from three different D0 HF taggers to maximize the b quark tagging efficiency (≈ 73%) is used for this purpose.
The first tagger converts information from the impact parameter of the tracks identified in a jet into a probability that all tracks originate from the primary vertex, where the impact parameter is the distance of closest approach to the interaction point in a plane perpendicular to the beam axis. The second tagger identifies the presence of vertices that are significantly displaced from the primary vertex and associated with a jet. The third tagger makes use of the number of tracks with large impact parameter significance, where the significance is defined as the ratio of the impact parameter to its uncertainty. The result of the combination is a NN output. A requirement on the NN output is made that preserves high efficiency for detection of charm jets (≈ 30%) with a ≈ 6% probability for a light parton jet to be mistakenly tagged. The efficiency for c jet tagging is obtained by scaling the b jet tagging efficiency measured in the data by the c-tagging-to-b-tagging efficiency ratio computed in the MC.
At the final stage of the analysis, additional selection criteria on three kinematic variables; / E T , S = ∆φ max + ∆φ min , and H T , with H T defined as the scalar sum of the p T of all jets, are optimized by maximizing the expected lower limit on the neutralino mass for a given mt. The variable S after requiring at least one jet in the event to be HF tagged is shown in Fig. 2.
Minimum values of H T are varied from 60 GeV to 140 GeV in steps of 20 GeV, while those for / E T are var-  ied from 60 GeV to 100 GeV in steps of 10 GeV. Events having the values of these quantities above the minima are kept. Maximum values of S are tested between 240 • and 320 • in steps of 20 • , and events having S below the minimum are retained. For each set of requirements, the expected value of the signal confidence level CL s [23] under the hypothesis that only background is present is evaluated using allt andχ 0 1 mass combinations, taking into account systematic uncertainties. The set of criteria that return CL s = 0.05 for the highest neutralino mass corresponding to a given mt are chosen to be the optimal ones.
The optimized values of the selections for different mt are given in Table II along with the number of events observed in data and expected SM background. In all cases a requirement of / E T ≥ 70 GeV is imposed. No contamination remains from multijet background at this point in the analysis; it is therefore neglected while setting the limit. Efficiencies for three signal mass points along with the expected numbers of events are shown in Table III. The distribution of H T after optimization but with the constraint on H T removed is shown in Fig. 3. The final distribution of / E T is shown in Fig. 4. The detailed SM  background composition is given in Table IV. Systematic uncertainties are evaluated for eacht and χ 0 1 mass combination for the optimized set of requirements. Sources of systematic uncertainty include jet energy scale, jet energy resolution, jet identification and reconstruction, the jet multiplicity requirement, trigger efficiency, data to MC scale factors, normalization of background, HF tagging, luminosity determination, choice of PDF, and W boson p T reweighting. The effect of the jet multiplicity requirement on the background is studied using Z/γ * (→ ee) + jets events. The spectrum of transverse momentum of the third jet in data events with three or more jets is observed to be very well described by the simulation generated with alpgen. The ≈ 1% statistical uncertainty of the lowest p T bin, where the bulk of the events are, is taken as a systematic uncertainty introduced by the jet multiplicity requirement. To study the effect of the same requirement on thet signal, where a third jet enters an event primarily through initial or final state radiation, the p T spectrum of the leading jet in simulated Z/γ * (→ ee) events generated with pythia is examined. Comparison between data and simulation shows a slight excess in data in the low p T bin; this discrepancy is used to estimate a systematic uncertainty of ±1.5% on the signal acceptance attributable to the jet multiplicity requirement. The uncertainty on the signal acceptance and background estimation due to the PDF choice was determined using the cteq6.1m PDF set. The combined 10% uncertainty on the background normalization includes: 5% uncertainty from Z/γ * (→ ee) + jets statistics assigned to all V+jets samples; 50% uncertainty on the NLO cross section assigned to the V + HF background; 6.1% luminosity uncertainty assigned to tt, diboson, and single top quark background; and 8%, 6% and 15% uncertainties on NLO cross sections for tt, diboson, and single top quark production, respectively. The uncertainty on the background estimation due to the W boson p T reweighting is estimated using two different methods to estimate the W +jets background. In the first method, the W +jets background is estimated using the expression given in Eq. 2. In the second method, the same reweighting function as applied to the Z boson was used to reweight the W boson p T which is equivalent to setting α(p T ) = 1 in Eq. 2. Detailed estimates of all systematic uncertainties are given in Table V.
Using the assumption thatt decays into a charm quark and a neutralino with 100% branching fraction and the nominalt pair production cross section, the largest mt excluded by this analysis is 155 GeV, for a neutralino mass of 70 GeV at the 95% C.L. With the theoretical uncertainty on thet pair production cross section taken into account, the largest limit on mt is 150 GeV, for mχ0 1 = 65 GeV. These results are shown in Fig. 5.
In summary, D0 has searched for scalar top quarks in jets plus missing transverse energy final states using 1 fb −1 of data. No evidence fort production has been found. This analysis substantially extends the excluded