Current Fragmentation Region Research Articles

Quark Statistics and hadron spectra ine + e − annihilation and deep inelastic scattering

Predictions of Quark Combinatoric Calculus (QCC, alias Quark Statitstics) for baryon-tomeson ratio in quark jets are compared with hadron production datae+e− annihilation and deep inelastic μp collisons. It is shown that charm production data ine+e− annihilation provide us the impressive evidence confirming QCC which predict that in the jet formed byc-quark the probability to produce charmed baryons is equal to 1/3. The possibility of successful description of secondary hadron spectra\(\frac{s}{\beta } - \frac{{d\sigma }}{{dx_E }}\) (e+e−-hadrons) in the region 0.2<xE<0.9 in the framework of QCC approach is demonstrated. It is also shown that QCC agrees reasonably well with μp data forp/h+ and\(\bar p/h^ - \) ratios in the current fragmentation region.

Production of charmed particles in 250 GeV μ+-iron interactions

Dimuon and trimuon events produced by the interaction of 250 GeV muons in an iron target have been studied and are shown to originate predominantly from charm production. The data are used to measure the contribution of charm to the nucleon structure function F 2. The cross sections for real photoproduction ( Q 2=0) of charm in the current fragmentation region are derived as a function of photon energy and are found to be ∼0.6% of the total, hadronic photoproduction cross section in this energy range. The measured cross sections are found to be well represented by the photon-gluon fusion model. The charmed quark fragmentation function is obtained by using this model to fit the measured decay muon energy distribution and is found to be well represented by exp(1.6±1.6) Z. The data are used to study the momentum distribution of the gluons in the nucleon. An upper limit of 1.4% (90% confidence level) is set on the branching ratio D→ μν and a model-dependent upper limit on the branching ratio F→ μν is derived.

Multiplicity distributions inν¯μpinteractions

We present the multiplicity distributions of the hadrons produced in antineutrinoproton interactions. The data sample, which consists of 2025 charged-current events with antineutrino energy greater than 5 GeV, comes from exposures of the 15-foot hydrogen bubble chamber to the broad-band antineutrino beam at Fermilab. The distribution in hadronic mass $W$ has an average value of 3.7 GeV but extends up to 10 GeV. The mean multiplicity of charged hadrons depends on the hadronic mass $W$ and varies as $〈{n}_{\mathrm{ch}}〉=(\ensuremath{-}0.44\ifmmode\pm\else\textpm\fi{}0.13)+(1.48\ifmmode\pm\else\textpm\fi{}0.06)\mathrm{ln}{W}^{2}$ for ${W}^{2}&gt;4$ Ge${\mathrm{V}}^{2}$. The mean multiplicities for events with three or more charged tracks averaged over the total data sample are $〈{n}_{\ensuremath{-}}〉=1.68\ifmmode\pm\else\textpm\fi{}0.03$ and $〈{n}_{0}〉=1.11\ifmmode\pm\else\textpm\fi{}0.07$ for ${\ensuremath{\pi}}^{\ensuremath{-}}$ and ${\ensuremath{\pi}}^{0}$ production, respectively. The mean ${\ensuremath{\pi}}^{0}$ multiplicity is found to increase slowly with ${n}_{\ensuremath{-}}$. The integrated correlation coefficient ${f}_{2}^{\ensuremath{-}\ensuremath{-}}$ and the dispersion ${D}^{\ensuremath{-}}$ are given as a function of ${n}_{\ensuremath{-}}$. When compared to the distributions characteristic of other leptonic and hadronic reactions, we find a similarity between the $\overline{\ensuremath{\nu}}$ data and results from hadronic reactions that have no diffractive component. Multiplicity data for the heavier particles ${K}^{0}$, ${\ensuremath{\rho}}^{0}$, and $\ensuremath{\Lambda}$ are also summarized. The pion multiplicities in the current fragmentation region exceed those for the target fragmentation at all $W$ values. They also satisfy the isospin relation $2〈{n}_{0}〉=〈{n}_{+}〉+〈{n}_{\ensuremath{-}}〉$ required for the fragmentation of an $I=\frac{1}{2}$ quark when a $W&gt;4$ GeV selection is imposed.

Charge compensation in the quark jets

We sum cumulatively charges of hadrons produced over the range of rapidities in antineutrino-nucleon charged-current interactions and show that the hypothesis of local charge conservation is approximately valid above center-of-mass energies of 4 GeV. Charge compensation in the current fragmentation region seems to occur in a shorter rapidity interval than in proton-proton interactions at comparable center-of-mass energies.

Average transverse momentum behaviour of charged hadrons in charged current antineutrino-nucleon interactions

We have studied transverse momenta of charged hadrons in the current fragmentation region of charged current antineutrino- nucleon interactions observed in the Fermilab 15 ft bubble chamber. The measured momentum squared transverse to the vμ + plane (p out 2) of the negative hadrons varies as a function of Q 2, W 2 and x as expected from t he leading order perturbative QCD calculations. Positively charged hadrons show a different transverse momentum behaviour as a function of Q 2.

Net charge in deep inelastic antineutrino-nucleon scattering

We investigate the net change in the current fragmentation region in antineutrino-nucleon charged current interactions in the Fermilab 15 ft bubble chamber. Support is presented for the d-quark origin of the forward hadrons in the hadron center-of-mass system. An extrapolation of the net charge to infinite center-of-mass energy is performed giving as a result 〈Q〈 v =− (0.44 ± 0.09) . Combining this result with the result obtained using our v events in the same experiment we obtain the value 0.98 ± 0.15 for the charge difference between the fragmenting quarks in v and v charged current events.

Inclusive ϱ0 production in [formula omitted] charged-current interactions

Using data from the Fermilab 15 ft hydrogen bubble chamber, we have studied inclusive ϱ 0 production in antineutrino-proton charged-current interactions. We measure (0.21 ± 0.03) ϱ 0/event, corresponding to ϱ 0/ π −=0.12 ± 0.02. As a function of Q 2 and for hadronic masses above a threshold region, the ϱ 0/ π − ratio shows little variation. At least 50% of the ϱ 0's are consistent with coming from the current fragmentation region. The results agree reasonably well with the predictions of the quark fragmentation model of Feynman and field.

Properties of K 0 and Λ inclusive production in charged-current antineutrino-nucleon interactions

In this paper we discuss inclusive spectra of K 0's and Λ's produced in charged in charged-current ν μ N interactions in the Fermilab 15 ft bubble chamber filled with a 64% Ne-H 2 mixture. Data presented in terms of the invariant cross section show, when compared with results from experiments with other incident beams, that the behavior of these distributions is approximately the same. The K 0 and Λ fragmentation functions are presented and the shape of the K 0 fragmentation function is found to be consistent with the parametrization of Field and Feynman. The average K 0 and Λ transverse momentum squared as a function of Q 2, W 2, x and z is presented. Comparisons for the K 0's produced in the current fragmentation region are in qualitative agreement with QCD predictions. The value of the Λ polarization is measured and a positive normal polarization P N = 0.34±0.18 is found.

Meson Spectra in Forward Jets in Meson-Baryon and Deep-Inelastic Electron-Proton Scattering by a Simple Hadron Cascade Model

Momentum distributions of secondary particles in the beam fragmentation region in high energy meson· baryon collisions and current fragmentation region in electron-proton scattering are analyzed by a simple hadron cascade model. Our model is based upon such a scheme that the successive two body decay of quark pair into two quark pairs is the dominant mechanism in the hadronization of constituents after collisions. It is shown that satisfactory fit to the data is obtained for e-p scattering as well as hadron-hadron collisions.

Reactionsp¯p→pπ±Xand a comparison with leptoproduction and the quark-parton model

We have studied the inclusive reactions $\overline{p}p\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}X$ at 8.9 GeV/c and compared them to the lepton-induced processes ${e}^{\ensuremath{-}}p\ensuremath{\rightarrow}{e}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}X$ and the photoproduction reactions $\ensuremath{\gamma}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}X$. The naive quark-parton model is found to be quite successful in interpreting the results. The distribution of charge in the current-fragmentation region is consistent with production of ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ via absorption of the current by fractionally charged valence antiquarks of the antiproton.

Experimental Properties of Neutrino-Induced Jets

We analyze a sample of about 2000 charged-current neutrino-proton interactions with neutrino energy greater than 10 GeV produced in the 15 ft. hydrogen bubble chamber at Fermilab using a broad band neutrino beam. We study the details of the hadrons produced and find generally good agreement with the quark-parton model and present parametrizations of quark fragmentation (D) functions. The D functions are found to be independent of Q2 and W (total hadronic mass) for W > 4 GeV, in agreement with the model. The height of the rapidity plateau in the quark (current) fragmentation region is compared to that of the di-quark (target) fragmentation region and the two are found to agree. The mean transverse momentum PT of the hadrons is studied for its Q2 and Feynman-X dependence. We find a sizeable increase of ⟨PT2⟩ with Feynman-X which agrees, however, with our longitudinal phase space model. We find no statistically significant dependent of ⟨PT2⟩ on Q2, up to Q2 = 64 GeV2, although the highest momentum hadrons are consistent with a mild Q2 dependence. There are no effects of high "primordial" parton momentum apparent in the data. No effects of gluon radiation are found in the Q2 dependence of the phase space density of particle production near zero c.m. rapidity.

Experimental study of hadrons produced in high-energy charged-current neutrino-proton interactions

We analyze a sample of about 2000 charged-current neutrino-proton interactions with neutrino energy greater than 10 GeV produced in the 15-ft hydrogen bubble chamber at Fermilab using a broad-band neutrino beam. We study the details of the hadrons produced and find generally good agreement with the quark-parton model and present parametrizations of quark fragmentation ($D$) functions. The $D$ functions are found to be independent of ${Q}^{2}$ and $W$ (total hadronic mass) for $Wg4$ GeV, in agreement with the model. The height of the rapidity plateau in the quark (current) fragmentation region is compared to that of the diquark (target) fragmentation region and the two are found to agree. Detailed charge-correlation data are presented and compared to the Field-Feynman model of the $D$ functions, and also to a longitudinal-phase-space model, and are found to disagree with both. The mean transverse momentum ${P}_{T}$ of the hadrons is studied for its ${Q}^{2}$ and Feynman-$X$ dependence. We find a sizeable increase of $〈{{P}_{T}}^{2}〉$ with Feynman $X$ which agrees, however, with our longitudinal-phase-space model. We find no statistically significant dependence of $〈{{P}_{T}}^{2}〉$ on ${Q}^{2}$, up to ${Q}^{2}=64$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$, although the highest-momentum hadrons are consistent with a mild ${Q}^{2}$ dependence. The azimuthal angular distribution of the highest-momentum hadrons in high-${Q}^{2}$ events is examined for evidence of anisotropy of the type that has been predicted for effects of gluon radiation.

Anomalous current fragmentation in high-p⊥leptoproduction

The Bjorken-Kogut correspondence arguments are proved to be violated in the high-p/sub perpendicular/ final states in the deep-inelastic electroproduction or neutrino production. That is, there will be no secondary particles in the current-fragmentation region. Large gaps are possible in the hole-fragmentation region at small diffraction values of x = Q/sup 2//2m..nu...

Hard semi-inclusive processes in QCD

We present formulae resulting from a complete perturbative analysis of differential cross sections of (i) massive lepton pair production in hadron collisions, (ii) leptoproduction of a particle from the current fragmentation region, (iii) production of two particles from opposite jets in e +e − annihilation into hadrons. A new effective double logarithmic quark form factor is derived, which manifests itself in these processes. Experimental investigation of two-particle angle correlations in e +e − annihilation provides a possibility to measure directly this form factor and thus to make a nice test of QCD.

Deep-Inelastic Lepton Nucleon Scattering by New Type of Quark Cascade Model. II: Inclusive Spectra of vN -&gt; X in Current Fragmentation Region

Deep-Inelastic Lepton Nucleon Scattering by New Type of Quark Cascade Model. II: Inclusive Spectra of vN -&gt; X in Current Fragmentation Region

Final state hadrons in inclusive electroproduction processes

Inclusive deep inelastic electroproduction processes, in which one (or more) hadrons in the final state are observed in coincidence with the electron, are investigated using Regge-Mueller language, via the inclusive virtual photoproduction processes. The hadron distributions and generalized scaling laws are obtained. Assuming that Pomeron is the dominant Regge trajectory, it is a simple pole, and therefore factorizes at high energies. The contribution of the isospin-carrying secondary trajectories cause charge asymmetries in the central and current fragmentation regions, and these increase with Q 2, for fixed total energy. Average multiplicity grows logarithmically with energy, as in the hadronic case. However, in the Bjorken limit, the major contribution comes from the current fragmentation region, contrary to the hadronic case; and the contribution of central region scales, and increases with increasing ω −1. Finally, we show that the average transverse momentum of the produced particles is limited, and this limit depends on the density of the particles in the phase space (rate of increase of average multiplicity with ln s), and ω. All the predictions are consistent with the data.

Inclusive neutrino neutral current pion production in gauge-theoretic models

The description of the distribution of pions produced in the current fragmentation region in inclusive reactions such as e + N → e + π i + … and ν + N → μ − + π i + … in terms of a set of fragmentation functions D πi q ( z) is now well established. We use these functions, following Sehgal, and make predictions for π + π − , π 0 π ± ratios in the neutral current reactions ν + N → ν + π i + …. Predictions are given for the four-quark Weinberg-Salam model, the six-quark vector model, and the so-called hard-fact model, for both proton and isoscalar targets, with special reference to Fermilab experiments.

Jets in inclusive e +e − and leptoproduction

The assumption of jets with bounded p T leads to the following consequences: (a) In e +e − annihilation the coefficient of the cos 2 θ term (a) of single-particle inclusive distributions] exhibits a unique dependence on the observed particle momentum. This dependence provides a measure of 〈 p T 2〉 in a jet. (b) In two-particle inclusive annihilation the average of the squared relative p T is determined by the same parameter and by the momenta of the two particles. (c) The observation that in the current fragmentation region of leptoproduction the p T distribution of fast hadrons is broader than that of show ones is explained.

Comparison of neutrino- and electroproduced pions and tests of the parton model

Recent measurements on the inclusive distribution of electroproduced pions, when interpreted in the quark-parton model, yield a determination of the parton fragmentation functions D u π+ ( z) and D d π+ ( z) with an estimated uncertainty of 15% and 40% respectively. These functions provide predictions (of comparable uncertainty) for pion multiplicities in the current fragmentation region of neutrino-induced processes. We show, in particular, that the magnitude (and possibly the rising trend) of the π + π − ratio π+ ( z)/ N π− ( z) observed in ν + N → μ − + π ± + … can be reproduced. Predictions are made for the π +/ π − and π 0/ π ± ratios in the neutral current reactions, with special reference to the Gargamelle experiment.

Asymptotic domains in inclusive electroproduction

The behavior of current-induced single-particle inclusive amplitudes (current+hadron→hadron+anything,e.g. coincidence electroproduction) in the various Regge and scaling asymptotic domains is studied in a model-independent way. The Regge limits are those in which the amplitude is dominated by the exchange of single, double, or triple Regge or helicity poles and the scaling limits are those described by leading light-cone and short-distance singularities or parton dynamics. A unified treatment of these limits is presented and possible relations among the limits are deduced. The behavior in a number of further asymptotic domains is suggested from a study of overlapping domains. The main tool employed in the analysis is the systematic use of commutativity relations to relate and constrain the asymptotic behaviors. Many such relations can be deduced from integral representations (causal or Sommerfeld-Watson) but some relations are simply assumed. (It is not, however, assumed that different limits can be interchanged.) The result is a rather complete characterization of the amplitude in the interesting domains in terms of a few parameters. This characterization is illustrated in large multiple commutative diagrams which clearly display the many asymptotic domains and their relative structures and provide a comprehensive picture of the complicated multivariable dependence. Particular consequences of this approach are the smooth matching of the fragmentation and pionization regions and of the fragmentation and triple-Regge regions, the scaling behavior of the reggeon-current scattering amplitude, and a simple parametrization of the behavior in the current fragmentation region for large current mass. The final hadron multiplicity is discussed both in the Regge limit for large current mass and in the Bjorken limit. Any one of a number of further (but unproved) commutativity relations or limit interchanges are seen to lead to a logv multiplicity.