Single-particle Inclusive Distributions Research Articles

High-Energy Collisions of Heavy Nuclei

The profile function for the collision of two heavy nuclei is calculated. In principle, the method used sums all contributing diagrams. The single-particle inclusive distribution is predicted for very-high-energy collisions.

Inclusive Single Particle Distributions from the Dual Fermion Model

AbstractInclusive single particle distributions are calculated from the discontinuity of a phenomenological 4π NN amplitude obtained from the Neveu‐Schwarz‐Ramond dual fermion model. In contrast to former calculations using the conventional Veneziano B6‐function we get a correct triple Regge behaviour at x ≈ 1 with correct pole position in the t‐channel which is able to reproduce the data. The pomeron, not contained in the dual Born amplitude, is taken into account phenomenologically in the NN channel. Other pomeron contributions are subtracted from the data. We compare the inclusive pion distributions of the model in the beam fragmentation and central region with experimental data for reactions π + N → + X at 8 and 16 GeV/c.

One-, two-, and three-particle distributions inppcollisions at 205 GeV/c

Results of a Fermilab experiment using the 30-in. hydrogen bubble chamber are reported, with the main emphasis on pion production in the central region. Single-particle inclusive and semi-inclusive distributions in rapidity, Feynman $x$, and $p_{T}^{}{}_{}{}^{2}$ for both ${\ensuremath{\pi}}^{\ensuremath{-}}$ and ${\ensuremath{\pi}}^{+}$ are presented and compared with results of other experiments. Two-particle distributions are investigated using the correlation-function formalism. The relation between inclusive and semi-inclusive correlation functions is discussed. The semi-inclusive correlation functions in rapidity are found to have short-range character compatible with the ideas of independent-cluster-emission models. Evidence for effects due to Bose-Einstein statistics of like particles is found by comparing the joint correlation function in rapidity and azimuthal angle, as well as the charged multiplicity associated with transverse momentum in the like- and unlike-charge combinations. Data on the average associated transverse momentum are also presented. The inclusive and semi-inclusive three-particle distributions are presented for all charge combinations. The inclusive three-particle correlations are found to be small for events with more than four particles in the final state. Two independent ways were found in which three-particle densities can be expressed in terms of one- and two-particle densities.

Large transverse momenta from statistical bootstrap with spin

We show that statistical bootstrap models (SBM) with their prediction of exponentially decreasing p distributions (equivalently: constant maximal temperature τ 0 ≈ m π ) are not ruled out by the large p ⊥ observed above ≈ 100 GeV lab energy in hadron collisions. Usual SBM sum over all spin angular momenta of the decaying fireball; if a particular spin is fixed, SBM leads to large p ⊥. We discuss in this paper (after having justified a classical approach) several mechanisms yielding high-mass, high-spin fireballs, select arbitrarily one of these (single fireball excitation) and calculate in SBM with fixed spin the decay structure. The cross section dσ dM is taken to be an empirical function, fitted to existing p ⊥ data at one energy and then calculable at other energies. We can easily reproduce the p ⊥ distribution. Further results concern multiplicities rising with p ⊥, anisotropy of the single-particle inclusive distribution and various correlations. Unexpectedly, but a posteriori rather naturally a jet-like structure is found in the spin-orthogonal plane.

π+p,K+p, andpptopological cross sections and inclusive interactions at 100 GeV using a hybrid bubble-chamber-spark-chamber system and a tagged beam

${\ensuremath{\pi}}^{+}p$, ${K}^{+}p$, and $\mathrm{pp}$ interactions at 100 GeV are studied using the Fermilab hybrid 30-inch bubble chamber with associated downstream multiparticle spectrometer and an unseparated tagged positive beam. Topological cross sections and charged-particle-multiplicity moments are presented and good agreement is found with Koba-Nielsen-Olesen scaling. The charged-multiplicity second moment, ${f}_{2}^{\mathrm{cc}}$, and the second moment of produced (+ -) pairs, ${f}_{2}^{\ensuremath{-}\ensuremath{-}}$, are presented both with and without the diffractive-dissociation events, and are discussed in terms of the two-component model invoked to explain $\mathrm{pp}$ multiplicity distributions above 100 GeV. Single-particle inclusive distributions are presented and studied in terms of the Regge-Mueller forms of approach to scaling at asymptotic energies. Pomeron factorization is found to hold in the target-proton-associated backward center-of-mass hemisphere for inclusive particle production by incident ${\ensuremath{\pi}}^{+}$, ${K}^{+}$, and protons.

A new parametrization for single-particle inclusive distributions

A simple parametrization for the pT dependence of single-particle inclusive distributions is proposed. The parametrization works for all pT. This, together with the similarity between the various particle spectra, points towards a common dynamical mechanism for all particles and all pT. The energy dependence can also be conveniently parametrized. For large pT it extrapolates well between PS and highest ISR energies.

Two-Particle Correlations and Band Structure inp+Be→h1+h2+X

The observed band structure in $p+\mathrm{Be}\ensuremath{\rightarrow}{h}_{1}+{h}_{2}+X$ ($h=p, \overline{p}, {\ensuremath{\pi}}^{+}, {\ensuremath{\pi}}^{\ensuremath{-}}, {K}^{\ensuremath{-}}$) at 30 GeV/c can be understood from inclusive single-particle distributions and kinematical correlations. This indicates that central correlations in (${h}_{1}, {h}_{2}$) channels are similar to the already known $\ensuremath{\pi}\ensuremath{\pi}$ correlations. Because of the difference in the rise with energy of single-particle distributions in the central region, and band structure is predicted to change with energy.

S-channel unitarity and inclusive distributions in cut reggeon field theory

Unitarity constraints on generalized eikonal diagrams with pomeron interactions are shown to hold in cut reggeon field theory. A non-perturbative proof of the AGK cancellation in this class of diagrams is given for the single-particle inclusive distribution. However, the two-particle distribution turns out to be modified by pomeron interactions in a non-trivial way. An approximate calculation shows that these modifications are crucial for consistency with momentum sum rules.

Single-particle distributions and particle production ratios in the thermodynamic model

A new version of the thermodynamic model for inclusive single-particle distributions is described, which is based on the strong statistical bootstrap model. The parameters of the new model are optimized using data for π ±, K ± and p ± production at accelerator and ISR energies. Good agreement is found with data on particle production ratios.

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.

Approach to scaling in proton fragmentation studied in the reactions K +p → π±X and K −p → π±X

Data are presented on inclusive single particle distributions in the proton fragmentation region for the reactions K +p → π ±X at 8.2 and 16 GeV/ c and K −p → π ±X at 10 and 16 GeV/ c. The energy dependence is studied and compared with the dual Regge model predictions for approach to scaling. None of the existing models is in full agreement with the data. The model of Chan and his collaborators is consistent with our results under the additional assumption of equality of vector and meson coupling constants in the p π + vertex in the Mueller diagram.

Scaling versus fireball behaviour in dual resonance decay

The dual resonance model is used to calculate inclusive single particle distributions for the decay of a heavy cluster with fixed spin. In the statistical average, with equal weights and random phases for all degenerate states, the resulting spectrum provides, for a wide range of cluster masses and spins, a linearly exponential cut-off: the same behaviour as found in the statistical bootstrap model. On the other hand, specific (high mode) degenerate states are shown to yield a scaling decay spectrum, as conjectured e.g. by parton considerations for time-like photons. Consequences for hadron-hadron interactions and for e +e − annihilation are discussed.

Hydrodynamical model of electron-positron annihilation into hadrons

Landau's hydrodynamical model of multiparticle production is formulated for e +e − → hadrons at center-of-momentum energies 10 GeV and higher. An analytical solution to the problem of spherical expansion of a relativistic fluid is presented. When hadrons condense out at the last stage of expansion, fluid thermal motion is taken into account. We derive predictions for multiplicities, average secondary energies and inclusive single particle distributions for various secondary hadrons; these results are then compared to other models. Finally, we investigate the internal consistency of the model.

Landau's hydrodynamic model of particle production and electron-positron annihilation into hadrons

The hydrodynamic model of Landau is formulated in very general terms and applied to the determination of average energy of secondaries, and single-particle inclusive distributions of secondaries. Attention is focused on the relationship between various dynamical assumptions and the equation of state assumed for the fluid motion. In the regimes of scaling and approximate scaling, we solve analytically the hydrodynamic motion of the fluid for both $\mathrm{pp}\ensuremath{\rightarrow}\ensuremath{\pi}+X$ and ${e}^{+}+{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\pi}+X$. For the annihilation process we solve the hydrodynamic equations numerically and discuss the validity of the scaling approximations. Explicit comparison is made between two dynamical models, the ultrarelativistic model (ideal-gas model) and the hadronic spectrum model.

New scaling variable and early scaling in single-particle inclusive distributions for hadron-hadron collisions

We suggest that the invariant cross section for $a+b\ensuremath{\rightarrow}c+X$ should be plotted in terms of ($\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{x},{P}_{\ensuremath{\perp}}$), where $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{x}=\frac{2{E}^{*}}{\sqrt{s}}$ and ${E}^{*}$ is the energy of particle $c$ in the center-of-mass system. We have shown for processes with exotic $\mathrm{ab}\overline{c}$ [such as $p+p\ensuremath{\rightarrow}({\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}},{K}^{\ifmmode\pm\else\textpm\fi{}},\overline{p})+X$] that the invariant cross sections $\frac{E{d}^{3}\ensuremath{\sigma}}{{d}^{3}p}\ensuremath{\rightarrow}f(\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{x},{P}_{\ensuremath{\perp}})$ at ${P}_{\ensuremath{\perp}}=0.2, 0.4, \mathrm{and} 0.8$ GeV/c over an energy range of ${P}_{\mathrm{inc}}=12\ensuremath{-}1500$ GeV/c. Furthermore, scaling in terms of ($\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{x},{P}_{\ensuremath{\perp}}$) provides a natural connection between the small-${P}_{\ensuremath{\perp}}$ and large-${P}_{\ensuremath{\perp}}$ regions. Predictions on the single-particle distribution when both ${P}_{\ensuremath{\parallel}}^{*}$ and ${P}_{\ensuremath{\perp}}^{*}$ are large are also presented.

Regge-muellervs. parton model analysis of deep inelastic reactions

The Regge-Mueller expansion of single-particle inclusive distributions in deep inelastic lepton-hadron scattering is matched with the ω → ∞ limit of the parton model description of the same reaction. Relations and inequalities among couplings and fragmentation functions, which appear also in purely hadronic reactions, are obtained.

Multiplicities, topological cross sections, and single particle inclusive distributions from pp interactions at 12 and 24 GeV/c

Results on multiplicities, topological cross sections, total particle production cross sections, and correlations between charged particle and π 0 production are presented for pp interactions at 12 and 24 GeV/ c incident laboratory momentum. Inclusive production of π ±, K s 0, p, Λ, Σ ± and Λ is studied; particle spectra are shown in single and double differential form and are compared, in different kinematic regions, with data obtained at other incident momenta and with other beam particles.

Statistical and thermodynamic descriptions of hadron production in e+e− annihilation

The statistical model and the thermodynamic (statistical bootstrap) model are formulated for multihadron production in e+e− annihilation. Asymptotic results are derived for both approaches, with particular attention to critical features subject to experimental test. Quantitative predictions of multiplicities, average secondary energies and inclusive single-particle distributions are presented for storage ring centre-of-mass energies from 2 to 6 GeV.

Deep-inelastic scattering, partons and strong interaction ideas

The quark-parton model as applied to deep-inelastic lepton-hadron scattering is used as a laboratory model for the study of ideas encountered in strong interaction physics. First, two-component duality constraints are imposed on single-particle inclusive deep-inelastic distributions. In the target fragmentation region this involves a modification of the definition of the E functions introduced by Feynman. A duality relation connecting neutrino and electroproduction single-particle inclusive distributions is obtained. For ω → 1 and ω → ∞ we predict in the target fragmentation region an excess of π + over π − production for proton targets and an excess of π − over π + for neutron targets. For deuteron targets we find an excess of π − over π + for ω → 1. In our laboratory model we study the analogue of the problem of approach to Feynman scaling encountered in hadronic reactions and the related problem of exodicity criteria. We find that for large ω, in both fragmentation regions, Feynman scaling is reached from above. If ab is exotic, single particle inclusive distributions for any type of observed hadron are flat as a function of ω. For the production of fast hadrons in the fragmentation regions, even when ab is not exotic, cross sections are flat when ab c is exotic.

Experimental tests of limiting fragmentation at the ISR

We present direct tests of the hypothesis of limiting fragmentation from an experiment at the CERN Intersecting Storage Rings at centre-of-mass energies between 31 and 53 GeV. Single-particle inclusive distributions and partial multiplicity distributions are observed for the case in which the energy of one beam is fixed while varying the energy of the other beam. Within cones around the beam, limiting fragmentation is shown to be valid.