$\pi^- p$ at 205 GeV/c: Multiplicities of Charged and Neutral Particles Production of Neutral Particles

Ljung, D. ; Bogert, D. ; Hanft, R. ; et al.
Phys.Rev.D 15 (1977) 3163, 1977.
Inspire Record 111665 DOI 10.17182/hepdata.24616

A study of 205-GeV/c π−p interactions has been made with a 48 800-picture exposure in the bare Fermilab 30-inch hydrogen bubble chamber. The average number of charged particles produced per inelastic interaction is 7.99±0.06. The elastic cross section is 3.18±0.13 mb and the total cross section is 24.19±0.44 mb. The inclusive cross sections for neutral-particle production are: σ(γ)=171.3±15.3 mb, σ(KS0)=3.64±0.61 mb (x<0.3), σ(Λ)=1.71±0.34 mb (x<0.3), and σ(Λ¯)=0.59±0.23 mb (x<0.1). The average number of π0's produced per inelastic collision is consistent with a linear rise with the number of charged particles, and about equal to the number of produced π− or π+. The average number of K0's, Λ's, and Λ¯'s is consistent with very little dependence on the number of charged particles. General characteristics of neutral-particle production are presented and compared with other experiments. For each topology the produced neutral energy is ∼13 of the incident energy.

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$\rho^0$ Production in $\pi^- p$ Interactions at 100-{GeV}/$c$, 200-{GeV}/$c$ and 360-{GeV}/$c$

Higgins, P.D. ; Shephard, W.D. ; Biswas, N.N. ; et al.
Phys.Rev.D 19 (1979) 65, 1979.
Inspire Record 7275 DOI 10.17182/hepdata.4591

Inclusive and semi-inclusive cross sections for gp0 production in 100, 200, and 360 GeV/c π−p interactions are presented. Differential cross sections for ρ0 production as functions of c.m. rapidity and transverse momentum are compared with the corresponding differential cross sections for pion production. Effects of various methods of estimating background on the values obtained for ρ0 production cross sections are discussed. About 10% of the final-state charged pions appear to come from ρ0 decay. Thus, while ρ0 production and decay is a significant source of final-state pions, other sources must contribute the majority of the produced pions.

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A Measurement of $J / \psi$ and $\psi^{\prime}$ Production in 300-GeV/c Proton, Antiproton and $\pi^{\pm}$ Nucleon Interactions

The E705 collaboration Antoniazzi, L. ; Arenton, M. ; Cao, Z. ; et al.
Phys.Rev.D 46 (1992) 4828-4835, 1992.
Inspire Record 338055 DOI 10.17182/hepdata.22667

Hadroproduction of the Jψ and ψ′ states has been studied in 300-GeV/c proton, antiproton, and π±Li interactions. Both total and differential cross sections in xF and pT have been measured for the Jψ for the π±, proton, and antiproton interactions. The ratio of ψ′ to Jψ production has been determined for the four types of beam particles.

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A Precision measurement of the prompt photon cross-section in p anti-p collisions at S**(1/2) = 1.8-TeV

The CDF collaboration Abe, F. ; Albrow, M.G. ; Amidei, D. ; et al.
Phys.Rev.Lett. 73 (1994) 2662-2666, 1994.
Inspire Record 375582 DOI 10.17182/hepdata.19680

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.

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A Prompt photon cross-section measurement in anti-p p collisions at s**(1/2) = 1.8-TeV

The CDF collaboration Abe, F. ; Albrow, M. ; Amidei, D. ; et al.
Phys.Rev.D 48 (1993) 2998-3025, 1993.
Inspire Record 353026 DOI 10.17182/hepdata.22677

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.

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A Study of the Energy Dependence of the Underlying Event in Proton-Antiproton Collisions

The CDF collaboration Aaltonen, Timo Antero ; Amerio, Silvia ; Amidei, Dante E ; et al.
Phys.Rev.D 92 (2015) 092009, 2015.
Inspire Record 1388868 DOI 10.17182/hepdata.70787

We study charged particle production in proton-antiproton collisions at 300 GeV, 900 GeV, and 1.96 TeV. We use the direction of the charged particle with the largest transverse momentum in each event to define three regions of eta-phi space; toward, away, and transverse. The average number and the average scalar pT sum of charged particles in the transverse region are sensitive to the modeling of the underlying event. The transverse region is divided into a MAX and MIN transverse region, which helps separate the hard component (initial and final-state radiation) from the beam-beam remnant and multiple parton interaction components of the scattering. The center-of-mass energy dependence of the various components of the event are studied in detail. The data presented here can be used to constrain and improve QCD Monte Carlo models, resulting in more precise predictions at the LHC energies of 13 and 14 TeV.

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Asymmetries between the production of D(s)- and D(s)+ mesons from 500-Gev/c pi- nucleon interactions as functions of x(F) and p-transverse**2

The E791 collaboration Aitala, E.M. ; Amato, S. ; Anjos, J.C. ; et al.
Phys.Lett.B 411 (1997) 230-236, 1997.
Inspire Record 447720 DOI 10.17182/hepdata.42197

This paper presents measurements of the production of Ds- mesons relative to Ds+ mesons as functions of x_F and square of p_t for a sample of 2445 Ds decays to phi pi. The Ds mesons were produced in Fermilab experiment E791 with 500 GeV/c pi- mesons incident on one platinum and four carbon foil targets. The acceptance-corrected integrated asymmetry in the x_F range -0.1 to 0.5 for Ds+- mesons is 0.032 +- 0.022 +- 0.022, consistent with no net asymmetry. The results, as functions of x_F and square of p_t, are compared to predictions and to the large production asymmetry observed for D+- mesons in the same experiment. These comparisons support the hypothesis that production asymmetries come from the fragmentation process and not from the charm quark production itself.

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Asymmetries between the production of D+ and D- mesons from 500-GeV/c pi- - nucleon interactions as a function of xF and p(t)**2

The E791 collaboration Aitala, E.M. ; Amato, S. ; Anjos, J.C. ; et al.
Phys.Lett.B 371 (1996) 157-162, 1996.
Inspire Record 415081 DOI 10.17182/hepdata.41684

We present asymmetries between the production of D+ and D- mesons in Fermilab experiment E791 as a function of xF and pt**2. The data used here consist of 74,000 fully-reconstructed charmed mesons produced by a 500 GeV/c pi- beam on C and Pt foils. The measurements are compared to results of models which predict differences between the production of heavy-quark mesons that have a light quark in common with the beam (leading particles) and those that do not (non-leading particles). While the default models do not agree with our data, we can reach agreement with one of them, PYTHIA, by making a limited number of changes to parameters used.

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Azimuthal correlations in Z+jets events in proton-proton collisions at $\sqrt{s}$ = 13 TeV

The CMS collaboration Tumasyan, Armen ; Adam, Wolfgang ; Andrejkovic, Janik Walter ; et al.
Eur.Phys.J.C 83 (2023) 722, 2023.
Inspire Record 2172990 DOI 10.17182/hepdata.133278

The production of Z bosons associated with jets is measured in pp collisions at $\sqrt{s}$ = 13 TeV with data recorded with the CMS experiment at the LHC corresponding to an integrated luminosity of 36.3 fb$^{-1}$. The multiplicity of jets with transverse momentum $p_\mathrm{T}$$\gt$ 30 GeV is measured for different regions of the Z boson's $p_\mathrm{T}$(Z), from lower than 10 GeV to higher than 100 GeV. The azimuthal correlation $\Delta \phi$ between the Z boson and the leading jet, as well as the correlations between the two leading jets are measured in three regions of $p_\mathrm{T}$(Z). The measurements are compared with several predictions at leading and next-to-leading orders, interfaced with parton showers. Predictions based on transverse-momentum dependent parton distributions and corresponding parton showers give a good description of the measurement in the regions where multiple parton interactions and higher jet multiplicities are not important. The effects of multiple parton interactions are shown to be important to correctly describe the measured spectra in the low $p_\mathrm{T}$(Z) regions.

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Comparison of the Z/gamma*+jets to gamma+jets cross sections in pp collisions at sqrt(s)= 8 TeV

The CMS collaboration Khachatryan, Vardan ; Sirunyan, Albert M ; Tumasyan, Armen ; et al.
JHEP 10 (2015) 128, 2015.
Inspire Record 1372730 DOI 10.17182/hepdata.72989

A comparison of the differential cross sections for the processes Z/gamma* + jets and photon (gamma) + jets is presented. The measurements are based on data collected with the CMS detector at sqrt(s) = 8 TeV corresponding to an integrated luminosity of 19.7 inverse femtobarns. The differential cross sections and their ratios are presented as functions of pt. The measurements are also shown as functions of the jet multiplicity. Differential cross sections are obtained as functions of the ratio of the Z/gamma* pt to the sum of all jet transverse momenta and of the ratio of the Z/gamma* pt to the leading jet transverse momentum. The data are corrected for detector effects and are compared to simulations based on several QCD calculations.

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Comparison of the isolated direct photon cross-sections in p anti-p collisions at s**(1/2) = 1.8-TeV and s**(1/2) = 0.63-TeV

The CDF collaboration Acosta, D. ; Affolder, T. ; Akimoto, H. ; et al.
Phys.Rev.D 65 (2002) 112003, 2002.
Inspire Record 581379 DOI 10.17182/hepdata.42882

We have measured the cross sections $d^2\sigma/dP_T d\eta$ for production of isolated direct photons in \pbarp collisions at two different center-of-mass energies, 1.8 TeV and 0.63 TeV, using the Collider Detector at Fermilab (CDF). The normalization of both data sets agree with the predictions of Quantum Chromodynamics (QCD) for photon transverse momentum ($P_T$) of 25 GeV/c, but the shapes versus photon $P_T$ do not. These shape differences lead to a significant disagreement in the ratio of cross sections in the scaling variable $x_T (\equiv 2P_T/\sqrt{s}$). This disagreement in the $x_T$ ratio is difficult to explain with conventional theoretical uncertainties such as scale dependence and parton distribution parameterizations.

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Cross-section and heavy quark composition of gamma + muon events produced in p anti-p collisions

The CDF collaboration Affolder, T. ; Akimoto, H. ; Akopian, A. ; et al.
Phys.Rev.D 65 (2002) 012003, 2002.
Inspire Record 557647 DOI 10.17182/hepdata.42881

We present a measurement of the cross section and the first measurement of the heavy flavor content of associated direct photon + muon events produced in hadronic collisions. These measurements come from a sample of 1.8 TeV ppbar collisions recorded with the Collider Detector at Fermilab. Quantum chromodynamics (QCD) predicts that these events are primarily due to Compton scattering process charm+gluon -> charm+photon, with the final state charm quark producing a muon. The cross section for events with a photon transverse momentum between 12 and 40 GeV/c is measured to be 46.8+-6.3+-7.5 pb, which is two standard deviations below the most recent theoretical prediction. A significant fraction of the events in the sample contain a final-state bottom quark. The ratio of charm to bottom production is measured to be 2.4+-1.2, in good agreement with QCD models.

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Cross-section for forward J / psi production in p anti-p collisions at S = 1.8-TeV

The CDF collaboration Acosta, D. ; Affolder, T. ; Akimoto, H. ; et al.
Phys.Rev.D 66 (2002) 092001, 2002.
Inspire Record 603674 DOI 10.17182/hepdata.22217

The inclusive cross section for J/ψ production times the branching ratio B(J/ψ→μ+μ−) has been measured in the forward pseudorapidity region: B×dσ[p¯+p→J/ψ(pT>10GeV/c,2.1<|η|<2.6)+X]/dη=192±9(stat)±29(syst)pb. The results are based on 74.1±5.2pb−1 of data collected by the CDF Collaboration at the Fermilab Tevatron Collider. The measurements extend earlier measurements of the D0 Collaboration to higher pTJ/ψ. In the kinematic range where the experiments partially overlap, these data are in good agreement with previous measurements.

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Cross-sections for the production of high mass muon pairs from 800-GeV proton bombardment of H-2

The E772 collaboration McGaughey, P.L. ; Moss, J.M. ; Alde, D.M. ; et al.
Phys.Rev.D 50 (1994) 3038-3045, 1994.
Inspire Record 372414 DOI 10.17182/hepdata.42501

Absolute cross sections as functions of kinematic variables are presented for the production of muon pairs from 800 GeV proton bombardment of H2. Drell-Yan (continuum) dimuons were recorded in the mass regions 4.5≤Mμ+μ−≤9 GeV and Mμ+μ−≥11 GeV, with an x-Feynman range -0.1≤xF≤0.75. This range corresponds to smaller masses and larger values of xF than previous 800 GeV Drell-Yan data. Cross sections for the Υ(1S) resonance are also given versus the transverse momentum and xF.

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DELTA++ AND ANTI-DELTA++ PRODUCTION IN 100-GEV/C ANTI-P P INTERACTIONS.

Ward, D.R. ; Ansorge, R.E. ; Bust, C.P. ; et al.
Nucl.Phys.B 141 (1978) 203-219, 1978.
Inspire Record 132549 DOI 10.17182/hepdata.8291

We present results on inclusive Δ ++ (1236) production in 100 GeV/ c p p interactions. In the region | t | < 1 GeV 2 we find a cross section of 1.29 ± 0.15 mb. Comparisons with pp interactions at high energies show Δ ++ production in pp and p p interactions to be very similar. The decay angular distributions of the Δ ++ are consistent with production predominantly through pion-exchange and the properties of the system recoiling from the Δ ++ are similar to those of real π + p interactions. However, the p π + background is found to show qualitatively similar behaviour. In contrast to the indications of Δ ++ production through pion exchange we also find evidence that events proceeding through diffraction dissociation are more likely to contain Δ ++ than other events. We present results on the forward production of Δ ++ in association with Δ ++ and protons.

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Dependence of inclusive jet production on the anti-$k_\mathrm{T}$ distance parameter in pp collisions at $\sqrt{s} =$ 13 TeV

The CMS collaboration Sirunyan, Albert M ; Tumasyan, Armen ; Adam, Wolfgang ; et al.
JHEP 12 (2020) 082, 2020.
Inspire Record 1795080 DOI 10.17182/hepdata.95241

The dependence of inclusive jet production in proton-proton collisions with a center-of-mass energy of 13 TeV on the distance parameter $R$ of the anti-$k_\mathrm{T}$ algorithm is studied using data corresponding to integrated luminosities up to 35.9 fb$^{-1}$ collected by the CMS experiment in 2016. The ratios of the inclusive cross sections as functions of transverse momentum $p_\mathrm{T}$ and rapidity $y$, for $R$ in the range 0.1 to 1.2 to those using $R = $ 0.4 are presented in the region 84 $\lt$ $p_\mathrm{T}$ $\lt$ 1588 GeV and $|y|$ $\lt$ 2.0. The results are compared to calculations at leading and next-to-leading order in the strong coupling constant using different parton shower models. The variation of the ratio of cross sections with $R$ is well described by calculations including a parton shower model, but not by a leading-order quantum chromodynamics calculation including nonperturbative effects. The agreement between the data and the theoretical predictions for the ratios of cross sections is significantly improved when next-to-leading order calculations with nonperturbative effects are used.

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Dependence of the $t\bar{t}$ production cross section on the transverse momentum of the top quark

The D0 collaboration Abazov, V.M. ; Abbott, B. ; Abolins, M. ; et al.
Phys.Lett.B 693 (2010) 515-521, 2010.
Inspire Record 842641 DOI 10.17182/hepdata.54975

We present a measurement of the differential cross section for $t\bar{t}$ events produced in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV as a function of the transverse momentum ($p_T$) of the top quark. The selected events contain a high-$p_T$ lepton ($\ell$), four or more jets, and a large imbalance in $p_T$, and correspond to 1 fb${}^{-1}$ of integrated luminosity recorded with the D0 detector. Each event must have at least one candidate for a $b$ jet. Objects in the event are associated through a constrained kinematic fit to the $t\bar{t}\to WbW\bar{b} \to \ell\nu b q\bar{q}'\bar{b}$ process. Results from next-to-leading-order perturbative QCD calculations agree with the measured differential cross section. Comparisons are also provided to predictions from Monte Carlo event generators using QCD calculations at different levels of precision.

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Differential cross section measurements for the production of a W boson in association with jets in proton-proton collisions at sqrt(s) = 7 TeV

The CMS collaboration Khachatryan, Vardan ; Sirunyan, Albert M ; Tumasyan, Armen ; et al.
Phys.Lett.B 741 (2015) 12-37, 2015.
Inspire Record 1303894 DOI 10.17182/hepdata.67318

Measurements are reported of differential cross sections for the production of a W boson, which decays into a muon and a neutrino, in association with jets, as a function of several variables, including the transverse momenta (pt) and pseudorapidities of the four leading jets, the scalar sum of jet transverse momenta (HT), and the difference in azimuthal angle between the directions of each jet and the muon. The data sample of pp collisions at a centre-of-mass energy of 7 TeV was collected with the CMS detector at the LHC and corresponds to an integrated luminosity of 5.0 inverse femtobarns. The measured cross sections are compared to predictions from Monte Carlo generators, MADGRAPH + PYTHIA and SHERPA, and to next-to-leading-order calculations from BLACKHAT + SHERPA. The differential cross sections are found to be in agreement with the predictions, apart from the pt distributions of the leading jets at high pt values, the distributions of the HT at high-HT and low jet multiplicity, and the distribution of the difference in azimuthal angle between the leading jet and the muon at low values.

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Differential cross sections of J/psi and psi' in 800-GeV/c p Si interactions.

The E-771 collaboration Alexopoulos, T. ; Durandet, C. ; Erwin, A.R. ; et al.
Phys.Rev.D 55 (1997) 3927-3932, 1997.
Inspire Record 446872 DOI 10.17182/hepdata.22271

We present the xF and pT differential cross sections of J/ψ and ψ′, respectively, in the ranges −0.05<xF<0.25 and pT<3.5 GeV/c. The data samples are constituted by about 12 000 J/ψ and 200 ψ′ produced in proton-silicon interactions at 800 GeV/c and decaying into opposite sign muons. The xF and pT distributions are compared with recent results from experiments E789 at the same energy and to leading order QCD predictions using the MRS D0 parametrization for the parton structure function. The measured shapes of the differential cross sections, except for the dσ/dxF at small xF, agree very well with the prediction, even though their value is quite a bit larger than the prediction. We also present the cosθ differential cross section of the J/ψ which indicates unpolarized production in contrast with color octet models predictions.

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Differential cross sections, charge production asymmetry, and spin-density matrix elements for D*(2010)+- produced in 500-GeV/c pi- nucleon interactions.

The Fermilab E791 collaboration Aitala, E.M ; Amato, S ; Anjos, J.C ; et al.
Phys.Lett.B 539 (2002) 218-226, 2002.
Inspire Record 587686 DOI 10.17182/hepdata.42892

We report differential cross sections for the production of D*(2010) produced in 500 GeV/c pi^- nucleon interactions from experiment E791 at Fermilab, as functions of Feynman-x (x_F) and transverse momentum squared (p_T^2). We also report the D* +/- charge asymmetry and spin-density matrix elements as functions of these variables. Investigation of the spin-density matrix elements shows no evidence of polarization. The average values of the spin alignment are \eta= 0.01 +- 0.02 and -0.01 +- 0.02 for leading and non-leading particles, respectively.

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Direct photon cross section with conversions at CDF

The CDF collaboration Acosta, D. ; Affolder, T. ; Albrow, M.G. ; et al.
Phys.Rev.D 70 (2004) 074008, 2004.
Inspire Record 648506 DOI 10.17182/hepdata.42869

We present a measurement of the isolated direct photon cross section in p-pbar collisions at sqrt(s) = 1.8 TeV and |eta| &lt; 0.9 using data collected between 1994 and 1995 by the Collider Detector at Fermilab (CDF). The measurement is based on events where the photon converts into an electron-positron pair in the material of the inner detector, resulting in a two-track event signature. To remove pi0 -> gamma gamma and eta -> gamma gamma events we use a new background subtraction technique which takes advantage of the tracking information available in a photon conversion event. We find that the shape of the cross section as a function of pT is poorly described by next-to-leading-order QCD predictions, but agrees with previous CDF measurements.

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Distributions of charged hadrons observed in deep-inelastic muon deuterium scattering at 490-GeV

The E-665 collaboration Adams, M.R. ; Aid, S. ; Anthony, P.L. ; et al.
Phys.Lett.B 272 (1991) 163-168, 1991.
Inspire Record 318993 DOI 10.17182/hepdata.29288

Longitudinal and transverse momentum spectra of final state hadrons produced in deep-inelastic muon-deuterium scattering at incident muon energy of 490 GeV have been measured up to a hadronic center of mass energy of 30 GeV. The longitudinal distributions agree well with data from earlier muon-nucleon scattering experiments; these distributions tend to increase in steepness as the center of mass energy increases. Comparisons with e + e − data at comparable center of mass energies indicate slight differences. The transverse momentum distributions show an increase in mean p T 2 with an increase in the center of mass energy.

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Evidence of b-jet quenching in PbPb collisions at sqrt(s[NN]) = 2.76 TeV

The CMS collaboration Chatrchyan, Serguei ; Khachatryan, Vardan ; Sirunyan, Albert M ; et al.
Phys.Rev.Lett. 113 (2014) 132301, 2014.
Inspire Record 1269454 DOI 10.17182/hepdata.68931

The production of jets associated to bottom quarks is measured for the first time in PbPb collisions at a center-of-mass energy of 2.76 TeV per nucleon pair. Jet spectra are reported in the transverse momentum (pt) range of 80-250 GeV, and within pseudorapidity abs(eta < 2). The nuclear modification factor (R[AA]) calculated from these spectra shows a strong suppression in the b-jet yield in PbPb collisions relative to the yield observed in pp collisions at the same energy. The suppression persists to the largest values of pt studied, and is centrality dependent. The R[AA] is about 0.4 in the most central events, similar to previous observations for inclusive jets. This implies that jet quenching does not have a strong dependence on parton mass and flavor in the jet pt range studied.

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GENERAL FEATURES OF CHARGED PARTICLE PRODUCTION IN ANTI-P P INTERACTIONS AT 100-GEV/C

Ward, C.P. ; Ward, D.R. ; Ansorge, R.E. ; et al.
Nucl.Phys.B 153 (1979) 299-333, 1979.
Inspire Record 146577 DOI 10.17182/hepdata.8129

We present new data on charged particle production in p p interactions at 100 GeV/ c . Comparisons are made between p p annihilations (estimated by differences) between corresponding p p and pp data samples) and e + e − annihilation into hadrons. A technique for separating the inclusive proton and pion spectra is described and the resulting pion spectra are studied in terms of Feynman x , rapidity and p T . Comparison with pp data allows us to estimate the pion spectra in p p annihilations and we find agreement with predictions of Mueller-Regge theory. We also present results on semi-inclusive π ± and proton production, give updated topological cross sections and describe further attempts to isolate effects due to annihilations. Finally we investigate the diffractive excitation of the antiproton into low-mass states by studying events with a slow recoil proton.

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High Mass Dimuon Production in anti-p n and pi- n Interactions at 125-GeV/c

Anassontzis, E. ; Katsanevas, S. ; Kiritsis, E. ; et al.
Phys.Rev.D 38 (1988) 1377, 1988.
Inspire Record 253413 DOI 10.17182/hepdata.23243

We have studied muon pairs with an invariant mass between 4 and 9 GeV/c2 produced in p¯N and π−N interactions at an incident momentum of 125 GeV/c. The experiment was performed at Fermilab using a tungsten target and a special beam enriched to contain 18% antiprotons. We compare differential distributions as functions of the dimuon invariant mass, Feynman x, transverse momentum, and decay angles of the dimuon to the predictions of the Drell-Yan model including QCD corrections. Quark structure functions for the p¯ and π− are extracted. Comparisons of the antiproton data to the Drell-Yan model are significant because the cross sections depend principally on the valence-quark structure functions which are accurately determined by deep-inelastic scattering measurements. The measured absolute cross section (integrated over positive Feynman x and all transverse momenta) is 0.106±0.005±0.008 nb/nucleon for the p¯N interaction and 0.107±0.003±0.009 nb/nucleon for the π−N interaction, where the quoted errors are statistical and systematic, respectively. Normalization (K) factors that are required to bring the naive Drell-Yan and first-order QCD predictions into agreement with the measurements are extracted, and the uncertainties involved in such comparisons are examined.

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