The global topologies of inclusive three-- and four--jet events produced in $\pp$ interactions are described. The three-- and four--jet events are selected from data recorded by the D\O\ detector at the Tevatron Collider operating at a center--of--mass energy of $\sqrt{s} = 1800$ GeV. The measured, normalized distributions of various topological variables are compared with parton--level predictions of tree--level QCD calculations. The parton--level QCD calculations are found to be in good agreement with the data. The studies also show that the topological distributions of the different subprocesses involving different numbers of quarks are very similar and reproduce the measured distributions well. The parton shower Monte Carlo generators provide a less satisfactory description of the topologies of the three-- and four--jet events.

We present a measurement of $\sigma \cdot B(W \rightarrow e \nu)$ and $\sigma \cdot B(Z~0 \rightarrow e~+e~-)$ in proton - antiproton collisions at $\sqrt{s} =1.8$ TeV using a significantly improved understanding of the integrated luminosity. The data represent an integrated luminosity of 19.7 pb$~{-1}$ from the 1992-1993 run with the Collider Detector at Fermilab (CDF). We find $\sigma \cdot B(W \rightarrow e \nu) = 2.49 \pm 0.12$nb and $\sigma \cdot B(Z~0 \rightarrow e~+e~-) = 0.231 \pm 0.012$nb.

A search for a heavy charged gauge boson, W ′, using the decay channels W ′ → eν and W′ → τν → eνν ν is reported. The data used in the analysis were collected by the DØ experiment at the Fermilab Tevatron during the 1992-93 p p collider run from an integrated luminosity of 13.9 ± 0.8 pb −1 at s =1.8 TeV . Assuming that the neutrino from W ′ decay is stable and has a mass significantly less than m W ′ , an upper limit at the 95% confidence level is set on the cross section times branching ratio for p p → W′ → eν . A W ′ with the same couplings to quarks and leptons as the standard model W boson is excluded for m W ′ < 610 GeV/c 2 .

We report on measurements of the ϒ(1S), ϒ(2S), and ϒ(3S) differential, (d2σdPtdy)y=0, and integrated cross sections in pp¯ collisions at s=1.8 TeV using a sample of 16.6 ± 0.6 pb−1 collected by the Collider Detector at Fermilab. The three resonances were reconstructed through the decay ϒ→μ+μ−. Comparison is made to a leading order QCD prediction.

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We present results on the search for the top quark in pp¯ collisions at √s =1.8 TeV with an integrated luminosity of 13.5±1.6 pb−1. We have considered tt¯ production in the standard model using electron and muon dilepton decay channels (tt¯→eμ+jets, ee+jets, and μμ+jets) and single-lepton decay channels (tt¯→e+jets and μ+jets) with and without tagging of b quark jets. An analysis of these data optimized for top quark masses below 140 GeV/c2 gives a lower top quark mass limit of 128 GeV/c2. An analysis optimized for higher top quark masses yields 9 events with an expected background of 3.8±0.9. If we assume that the excess is due to tt¯ production, and assuming a top quark mass of 180 GeV/c2, we obtain a cross section of 8.2±5.1 pb.

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We have calculated the double and triple differential cross sections for electron ejection with energy of 14.6 eV in single ionization of H2 by 75 keV proton impact. A molecular version of the continuum distorted wave-eikonal initial state approach is applied, where the interaction between the projectile and the residual molecular ion is considered more properly than in previous applications of the method. For triple differential cross sections, the present results are in better agreement with the experimental data than those of other descriptions when large momentum transfer values are considered. For double differential cross sections the experimental data are reproduced quite well for both coherent and incoherent proton beams.

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We report on a search for second generation leptoquarks with the D\O\ detector at the Fermilab Tevatron $p\overline{p}$ collider at $\sqrt{s}$ = 1.8 TeV. This search is based on 12.7 pb$~{-1}$ of data. Second generation leptoquarks are assumed to be produced in pairs and to decay into a muon and quark with branching ratio $\beta$ or to neutrino and quark with branching ratio $(1-\beta)$. We obtain cross section times branching ratio limits as a function of leptoquark mass and set a lower limit on the leptoquark mass of 111 GeV/c$~{2}$ for $\beta = 1 $ and 89 GeV/c$~{2}$ for $\beta = 0.5 $ at the 95\%\ confidence level.

The distribution of the transverse energy in jets has been measured in p p collisions at s =1.8 TeV TeV using the DØ detector at Fermilab. This measurement of the jet shape is made as a function of jet transverse energy in both the central and forward rapidity regions. Jets are shown to narrow both with increasing transverse energy and with increasing rapidity. Next-to-leading order partonic QCD calculations are compared to the data. Although the calculations qualitatively describe the data, they are shown to be very dependent on renormalization scale, parton clustering algorithm, and jet direction definition and they fail to describe the data in all regions consistently.

We analyze a sample of W + jet events collected with the Collider Detector at Fermilab (CDF) in ppbar collisions at sqrt(s) = 1.8 TeV to study ttbar production. We employ a simple kinematical variable "H", defined as the scalar sum of the transverse energies of the lepton, neutrino and jets. For events with a W boson and four or more jets, the shape of the "H" distribution deviates by 3.8 standard deviations from that expected from known backgrounds to ttbar production. However this distribution agrees well with a linear combination of background and ttbar events, the agreement being best for a top mass of 180 GeV/c^2.

The E760 Collaboration performed an experiment in the Antiproton Accumulator at Fermilab to study the two photon decay of the ηc(1 1S0) charmonium state formed in p¯p annihilations. This resulted in a new measurement of the mass Mηc=2988.3−3.1+3.3 MeV/c2 and of the product B(ηc→p¯p)×Γ(ηc→γγ) =(8.1−2.0+2.9) eV. We performed a search for the process p¯p→ηc′(2 1S0)→γγ over a limited range of center-of-mass energies. Since no signal was observed, we derived upper limits on the product of branching ratios B(ηc′→p¯p)×B(ηc′→γγ) in the center-of-mass energy range 3584≤ √s ≤3624 MeV. We observed no signal for the nonresonant process p¯+p→γ+γ and obtain upper limits.

The inclusive cross sections times leptonic branching ratios for W and Z boson production in PbarP collisions at Sqrt(s)=1.8 TeV were measured using the D0 detector at the Fermilab Tevatron collider: Sigma_W*B(W->e, nu) = 2.36 +/- 0.07 +/- 0.13 nb, Sigma_W*B(W->mu,nu) = 2.09 +/- 0.23 +/- 0.11 nb, Sigma_Z*B(Z-> e, e) = 0.218 +/- 0.011 +/- 0.012 nb, Sigma_Z*B(Z->mu,mu) = 0.178 +/- 0.030 +/- 0.009 nb. The first error is the combined statistical and systematic uncertainty, and the second reflects the uncertainty in the luminosity. For the combined electron and muon analyses we find: [Sigma_W*B(W->l,nu)]/[Sigma_Z*B(Z->l,l)] = 10.90 +/- 0.49. Assuming Standard Model couplings, this result is used to determine the width of the W boson: Gamma(W) = 2.044 +/- 0.093 GeV.

The ratio of the number of W+1 jet to W+0 jet events is measured with the D0 detector using data from the 1992–93 Tevatron Collider run. For the W→eν channel with a minimum jet ET cutoff of 25 GeV, the experimental ratio is 0.065±0.003stat±0.007syst. Next-to-leading order QCD predictions for various parton distributions agree well with each other and are all over 1 standard deviation below the measurement. Varying the strong coupling constant αs in both the parton distributions and the partonic cross sections simultaneously does not remove this discrepancy.

This paper presents the first direct measurement of the $B$ meson differential cross section, $d\sigma/dp_T$, in $p\overline{p}$ collisions at $\sqrt{s}=1.8$ TeV using a sample of $19.3 \pm 0.7$ pb$~{-1}$ accumulated by the Collider Detector at Fermilab (CDF). The cross section is measured in the central rapidity region $|y| < 1$ for $p_T(B) > 6.0$ GeV/$c$ by fully reconstructing the $B$ meson decays $B~{+}\rightarrow J/\psi K~{+}$ and $B~{0}\rightarrow J/\psi K~{*0}(892)$, where $J/\psi \rightarrow \mu~+\mu~-$ and $K~{*0} \rightarrow K~+ \pi~-$. A comparison is made to the theoretical QCD prediction calculated at next-to-leading order.

We establish the existence of the top quark using a 67 pb^-1 data sample of Pbar-P collisions at Sqrt(s) = 1.8 TeV collected with the Collider Detector at Fermilab (CDF). Employing techniques similar to those we previously published, we observe a signal consistent with t-tbar decay to WW b-bbar, but inconsistent with the background prediction by 4.8 sigma. Additional evidence for the top quark is provided by a peak in the reconstructed mass distribution. We measure the top quark mass to be 176 +/-8(stat) +/- 10(sys.) GeV/c^2, and the t-tbar production cross section to be 6.8 +3.6 -2.4 pb.

We present an analysis of data from p p¯ collisions at a center-of-mass energy of √s =1800 GeV. A measurement is made of the ratio R≡σB(p p¯→W→eν)/σB(p p¯→Z0→ee). The data represent 19.6 pg−1 collected by the Collider Detector at Fermilab during the 1992–1993 collider run of the Fermilab Tevatron. We find R=10.90±0.32(stat)±0.29(syst), and from this value we extract a measurement of the W→eν branching ratio Γ(W→eν)/Γ(W)=0.1094±0.0033(stat)±0.0031(syst). From this branching ratio we set a limit on the top quark mass of mt>62 GeV/c2 at the 95% confidence level. In contrast with direct searches for the top quark, this limit makes no assumptions about the allowed decay modes of the top quark. In addition, we use a calculation of the leptonic width Γ(W→eν) to obtain a value for the W total decay width: Γ(W)=2.064±0.060(stat)±0.059(syst) GeV.

The DO collaboration reports on a search for the Standard Model top quark in pbar-p collisions at Sqrt(s)=1.8TeV at the Fermilab Tevatron, with an integrated luminosity of approximately 50pb-1. We have searched for t-tbar production in the dilepton and single-lepton decay channels, with and without tagging of b-quark jets. We observed 17 events with an expected background of 3.8+/-0.6 events. The probability for an upward fluctuation of the background to produce the observed signal is 2.0E-6 (equivalent to 4.6 standard deviations). The kinematic properties of the excess events are consistent with top quark decay. We conclude that we have observed the top quark and measure its mass to be 199~+19_21 (stat.)+/- 22 (syst.)GeV/c**2 and its production cross section to be 6.4 +/- 2.2 pb.

We have directly measured the ZZ-gamma and Z-gamma-gamma couplings by studying p pbar --> l+ l- gamma + X, (l = e, mu) events at the CM energy of 1.8$TeV with the D0 detector at the Fermilab Tevatron Collider. A fit to the transverse energy spectrum of the photon in the signal events, based on the data set corresponding to an integrated luminosity of 13.9 pb~-1 ($13.3 pb~-1) for the electron (muon) channel, yields the following 95% confidence level limits on the anomalous CP-conserving ZZ-gamma couplings: -1.9 < h~Z_30 < 1.8 (h~Z_40 = 0), and -0.5 < h~Z_40 < 0.5 (h~Z_30 = 0), for a form-factor scale Lambda = 500 GeV. Limits for the Z-gamma-gamma$ couplings and CP-violating couplings are also discussed.

The properties of two-, three-, four-, five-, and six-jet events with multijet masses >600 GeV /c2 are compared with QCD predictions. The shapes of the multijet-mass and leading-jet-angular distributions are approximately independent of jet multiplicity and are well described by the NJETS matrix element calculation and the HERWIG parton shower Monte Carlo predictions. The observed jet transverse momentum distributions for three- and four-jet events discriminate between the matrix element and parton shower predictions, the data favoring the matrix element calculation.

We have used 19 pb**-1 of data collected with the Collider Detector at Fermilab to search for new particles decaying to dijets. We exclude at 95% confidence level models containing the following new particles: axigluons with mass between 200 and 870 GeV, excited quarks with mass between 80 and 570 GeV, and color octet technirhos with mass between 320 and 480 GeV.

Fermilab experiment E735 located at the CO intersection region of the\(\sqrt s= 1.8\) TeV\(p\bar p\) collider analysed over 900 Φ→K+K− events. Measured were the transverse momentum spectrum, the correlation between the average transverse momentum <pt> and the charged particle multiphcityNc, as well as the probability of Φ production per charged track,NΦ/Nc, versusNc. We have also made an estinate of the total inclusive cross section for Φ mesons,\(\sigma (p\bar p \to \phi X) = 7.3 \pm 2.2 mb\).

We present the results of a search in p¯p collisions at s=1.8 TeV for the top quark decaying to a charged Higgs boson (H±). We search for dilepton final states from the decay chain tt¯→HH (or HW, or WW) + bb¯→ll+X. In a sample of 19.3 pb−1 collected during 1992-93 with the Collider Detector at Fermilab, we observe 2 events with a background estimation of 3.0 ± 1.0 events. Limits at 95% C.L. in the (Mtop,MH±) plane are presented. For the case Mtop<MW+Mb, we exclude at 95% C.L. the entire (Mtop,MH±) plane for the branching ratio B(H→τν) larger than 75%. We also interpret the results in terms of the parameter tan β of two-Higgs-doublet models.

This paper reports the measurement of the B meson and b quark cross sections through the decay chain B0→J/ψ K*(892)0, J/ψ→μ+μ−, K*(892)0→K+π−, using 4.3 pb−1 of data collected at the Collider Detector at Fermilab in p¯p collisions at qrts=1.8 TeV. We obtain σB=1.5±0.7(stat)±0.6(syst) μb for B0 mesons with transverse momentum PT>9.0 GeV/c and rapidity ‖y‖<1.0. Using this result, we find σb=3.7±1.6(stat)±1.5(syst) μb for b quarks with PT>11.5 GeV/c and rapidity ‖y‖<1.0. The b quark cross section is compared to next-to-leading order QCD calculations and previous measurements.

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The charge asymmetry has been measured using $19,039W$ decays recorded by the CDF detector during the 1992-93 run of the Tevatron Collider. The asymmetry is sensitive to the ratio of $d$ and $u$ quark distributions to $x<0.01$ at $Q~2 \approx M_W~2$, where nonperturbative effects are minimal. It is found that of the two current sets of parton distributions, those of Martin, Roberts and Stirling (MRS) are favored over the sets most recently produced by the CTEQ collaboration. The $W$ asymmetry data provide a stronger constraints on $d/u$ ratio than the recent measurements of $F_2~{\mu n}/F_2~{\mu p}$ which are limited by uncertainties originating from deutron corrections.

We report on a study of W+ photon production in approximately 20 pb−1 of p−p¯ collisions at s=1.8 TeV recorded with the Collider Detector at Fermilab. Our results are in good agreement with standard model expectations and are used to obtain limits on anomalous CP-conserving WWγ couplings of −2.3<Δκ<2.2 for λ=0 and −0.7<λ<0.7 for Δκ=0 at 95% C.L. We obtain the same limits for CP-violating couplings. These results provide limits on the higher-order electromagnetic moments of the W boson of 0.8<gW<3.1 for qWe=1 and −0.6<qWe<2.7 for gW=2 at 95% C.L.

A prompt photon cross section measurement from the Collider Detector at Fermilab experiment is presented. Detector and trigger upgrades, as well as 6 times the integrated luminosity compared with our previous publication, have contributed to a much more precise measurement and extended PT range. As before, QCD calculations agree qualitatively with the measured cross section, but the data has a steeper slope than the calculations.

The W+jet angular distribution is measured using W→eν events recorded with the Collider Detector at Fermilab (CDF) during the 1988-89 and 1992-93 Tevatron runs. The data agree well with both a leading order and a next-to-leading order theoretical prediction. The shape of the angular distribution is similar to that observed in photon + jet data and significantly different from that observed in dijet data.

We present the results of a search for the top quark in 19.3 pb−1 of p¯p collisions at √s =1.8 TeV. The data were collected at the Fermilab Tevatron collider using the Collider Detector at Fermilab (CDF). The search includes standard model tt¯ decays to final states eeνν¯, eμνν¯, and μμνν¯ as well as e+ν+jets or μ+ν+jets. In the (e,μ)+ν+jets channel we search for b quarks from t decays via secondary vertex identification and via semileptonic decays of the b and cascade c quarks. In the dilepton final states we find two events with a background of 0.56−0.13+0.25 events. In the e,μ+ν+jets channel with a b identified via a secondary vertex, we find six events with a background of 2.3±0.3. With a b identified via a semileptonic decay, we find seven events with a background of 3.1±0.3. The secondary vertex and semileptonic-decay samples have three events in common. The probability that the observed yield is consistent with the background is estimated to be 0.26%. The statistics are too limited to firmly establish the existence of the top quark; however, a natural interpretation of the excess is that it is due to tt¯ production. We present several cross-checks. Some support this hypothesis; others do not. Under the assumption that the excess yield over background is due to tt¯, constrained fitting on a subset of the events yields a mass of 174±10−12+13 GeV/c2 for the top quark. The tt¯ cross section, using this top quark mass to compute the acceptance, is measured to be 13.9−4.8+6.1 pb.

Color coherence effects in pp¯ collisions are observed and studied with CDF, the Collider Detector at the Fermilab Tevatron collider. We demonstrate these effects by measuring spatial correlations between soft and leading jets in multijet events. Variables sensitive to interference are identified by comparing the data to the predictions of various shower Monte Carlo programs that are substantially different with respect to the implementation of coherence.

We present a measurement of the ratio σB(W→eν)σB(Z0→e+e−) in p¯p collisions at s=1.8 TeV The data represent an integrated luminosity of 21.7 pb−1 from the 1992-1993 run of the Collider Detector at Fermilab. We find σB(W→eν)σB(Z0→e+e−)=10.90±0.32(stat)±0.29(syst). From this value, we extract a value for the W width, Γ(W)=2.064±0.061(stat)±0.059(syst) GeV, and the branching ratio, Γ(W→eν)Γ(W)=0.1094±0.0033(stat)±0.0031(syst), and we set a decay-mode-independent limit on the top quark mass mtop>62 GeV/c2 at the 95% C.L.

If quarks are composite particles then excited states are expected. We have searched in pp¯ collisions for excited quarks (q*) which decay to common quarks by emitting a W boson (q*→qW) or a photon (q*→qγ). The simplest model of excited quarks has been excluded for mass M*<540 GeV/c2 at 95% confidence level.

Antiproton-proton elastic scattering was measured at c.m.s. energies √s =546 and 1800 GeV in the range of four-momentum transfer squared 0.025<-t<0.29 GeV2. The data are well described by the exponential form ebt with a slope b=15.28±0.58 (16.98±0.25) GeV−2 at √s =546 (1800) GeV. The elastic scattering cross sections are, respectively, σel=12.87±0.30 and 19.70±0.85 mb.

We report a measurement of the diffraction dissociation differential cross section d2σSD/dM2dt for p¯p→p¯X at √s =546 and 1800 GeV, M2/s<0.2 and 0≤-t≤0.4 GeV2. Our results are compared to theoretical predictions and to extrapolations from experimental results at lower energies.

We report a measurement of the proton-antiproton total cross section σT at c.m.s. energies √s =546 and 1800 GeV. Using the luminosity-independent method, we find σT=61.26±0.93 mb at √s =546 GeV and 80.03±2.24 mb at √s =1800 GeV. In this energy range, the ratio σel/σT increases from 0.210±0.002 to 0.246±0.004.

We measure the Drell-Yan differential cross section d2σdMdy||y|<1 over the mass range 11<M<150 GeV/c2 using dielectron and dimuon data from p¯p collisions at a center-of-mass energy of s=1.8 TeV. Our results show the 1M3 dependence that is expected from the naive Drell-Yan model. In comparison to the predictions of recent QCD calculations we find our data favor those parton distribution functions with the largest quark contributions in the x interval 0.006 to 0.03.

We present a measurement of the b-quark cross section in 1.8 TeV p-p¯ collisions recorded with the Collider Detector at Fermilab using muonic b-quark decays. In the central rapidity region (‖yb‖<1.0), the cross section is 295±21±75 nb (59±14±15 nb) for pTb>21 GeV/c (29 GeV/c). Comparisons are made to previous measurements and next-to-leading order QCD calculations.

We report the full reconstruction of χc mesons through the decay chain χc→J/ψ γ, J/ψ→μ+μ−, using data obtained at the Collider Detector at Fermilab in 2.6±0.2 pb−1 of p¯p collisions at √s =1.8 TeV. This exclusive χc sample is used to measure the χc-meson production cross section times branching fractions. We obtain σ×B=3.2±0.4(stat)−1.1+1.2(syst) nb for χc mesons decaying to J/ψ with pT>6.0 GeV/c and pseudorapidity ‖η‖<0.5. From this and the inclusive J/ψ cross section we calculate the inclusive b-quark cross section to be 12.0±4.5 μb for pTb>8.5 GeV/c and ‖yb‖<1.

We present measurements of the bottom-quark production cross sections in pp¯ collisions at √s =1.8 TeV. From the inclusive electron production rate, we have determined the bottom-quark production cross sections to be 1010±270, 168±43, 37±10 nb for the rapidity range of ‖yb‖<1.0 and the transverse momentum ranges of pTb>15, 23, 32 GeV/c, respectively. In addition, from the associated electron-D0 production rate, we have determined the bottom-quark cross section to be 364±80(stat)±95(syst) nb for ‖yb‖<1.0 and pTb>19 GeV/c.

The W production cross section times the branching ratio for W→lν, l=e,μ decays has been measured as a function of the associated jet multiplicity. The data have been recorded at the Collider Detector at Fermilab during the 1988–89 run. A recent leading order QCD calculation agrees well with the data up to a jet multiplicity of 4.

The first prompt photon measurement from the CDF experiment at the Fermilab pp¯ Collider is presented. Two independent methods are used to measure the cross section: one for high transverse momentum (PT) and one for lower PT. Comparisons to various theoretical calculations are shown. The cross section agrees qualitatively with QCD calculations but has a steeper slope at low PT.

Data taken with the Collider Detector at Fermilab (CDF) during the 1988–1989 run of the Tevatron are used to measure the distribution of the center-of-mass (rest frame of the initial state partons) angle between isolated prompt photons and the beam direction. The shape of the angular distribution for photon-jet events is found to be significantly different from that observed in dijet data. The QCD predictions show qualitative agreement with the observed prompt photon angular distribution.

The dijet invariant mass distribution has been measured in the region between 120 and 1000 GeV/c2, in 1.8-TeV pp¯ collisions. The data sample was collected with the Collider Detector at Fermilab (CDF). Data are compared to leading order (LO) and next-to-leading order (NLO) QCD calculations using two different clustering cone radii R in the jet definition. A quantitative test shows good agreement of data with the LO and NLO QCD predictions for a cone of R=1. The test using a cone of R=0.7 shows less agreement. The NLO calculation shows an improvement compared to LO in reproducing the shape of the spectrum for both radii, and approximately predicts the cone size dependence of the cross section.

The yields and average transverse momenta of pions, kaons, and antiprotons produced at the Fermilab p¯p collider at s=300, 540, 1000, and 1800 GeV are presented and compared with data from the energies reached at the CERN collider. We also present data on the dependence of average transverse momentum 〈pt〉 and particle ratios as a function of charged particle density dNcdη; data for particle densities as high as six times the average value, corresponding to a Bjorken energy density 6 GeV/fm3, are reported. These data are relevant to the search for quark-gluon phase of QCD.

We present measurements from events with two isolated prompt photons in p¯p collisions at √s =1.8 TeV. The differential cross section, measured as a function of transverse momentum (PT) of each photon, is about 3 times what next-to-leading-order QCD calculations predict. The cross section for photons with PT in the range 10–19 GeV is 86±27(stat)−23+32(syst) pb. We also study the correlation between the two photons in both azimuthal angle and PT. The magnitude of the vector sum of the transverse momenta of both photons, KT=‖PT1+PT2‖, has a mean value of 〈KT〉=5.1±1.1 GeV.

Inclusive jet cross sections have been measured in p¯p collisions at √s =546 and 1800 GeV, using the Collider Detector at Fermilab. The ratio of jet cross sections is compared to predictions from simple scaling and O(as3) QCD. Our data exclude scaling and lie (1.5–2.4)σ below a range of QCD predictions.

The dijet angular distribution is measured in the Collider Detector at Fermilab. This measurement covers higher mass ranges and larger scattering angles than previously possible. Good agreement is observed between the data and both leading-order [O(αs2)] and next-to-leading order [O(αs3)] QCD calculations. A limit on quark compositeness of Λc>1.0 TeV is obtained.

We present a measurement of jet shapes in p¯p collisions at √s =1.8 TeV at the Fermilab Tevatron using the Collider Detector at Fermilab (CDF). Qualitative agreement is seen with the predictions of recent next-to-leading [O(αs3)] calculations and with leading logarithm QCD based Monte Carlo simulations. The dependence of the jet shape on transverse energy is studied.