Single-particle Inclusive Cross Sections Research Articles

Threshold resummation at NNLL for single-particle production in hadronic collisions

We develop threshold resummation for single-particle inclusive cross sections in hadron-hadron collisions to the level of next-to-next-to-leading logarithm, up to full matching with two-loop hard functions. We define and calculate all one-loop soft functions for all partonic channels. This enables us to separate the hard and soft functions at one loop. Along with these results, the one-loop finite parts of jet functions are used to check that the full soft, collinear and virtual corrections are reproduced to one loop for all partonic reactions. We exhibit these NLO results explicitly. NLO expansions of the resummed cross section match the exact NLO results extremely well numerically, and two loop expansions result in substantial corrections over many kinematic configurations. Explicit results are given in Mellin moment space, and a number of options for generating resummed cross sections are discussed.

Radial scaling in inclusive jet production at hadron colliders

Inclusive jet production in p-p and pbar-p collisions shows many of the same kinematic systematics as observed in single particle inclusive production at much lower energies. In an earlier study (1974) a phenomenology, called radial scaling, was developed for the single particle inclusive cross sections that attempted to capture the essential underlying physics of point-like parton scattering and the fragmentation of partons into hadrons suppressed by the kinematic boundary. The phenomenology was successful in emphasizing the underlying systematics of the inclusive particle productions. Here we demonstrate that inclusive jet production at the LHC in high-energy p-p collisions and at the Tevatron in pbar-p inelastic scattering show similar behavior. The ATLAS inclusive jet production plotted as a function of this scaling variable is studied for sqrt(s) of 2.76, 7 and 13 TeV and is compared to pbar-p inclusive jet production at 1.96 TeV measured at the CDF and D0 at the Tevatron and p-Pb inclusive jet production at the LHC ATLAS at sqrt(sNN) = 5.02 TeV. Inclusive single particle production at FNAL fixed target and ISR energies are compared to inclusive J/Psi production at the LHC measured in ATLAS, CMS and LHCb. Striking common features of the data are discussed.

Final state interactions in single- and multiparticle inclusive cross sections for hadronic collisions

We study the role of low momentum transfer (soft) interactions between high transverse momentum heavy particles and beam remnants (spectators) in hadronic collisions. Such final state interactions are power suppressed for single-particle inclusive cross sections whenever that particle is accompanied by a recoiling high-${p}_{T}$ partner whose momentum is not fixed. An example is the single-top inclusive cross section in top-pair production. Final state soft interactions in multiparticle inclusive cross sections, including transverse momentum distributions, however, produce leading-power corrections in the absence of hard recoiling radiation. Nonperturbative corrections due to scattering from spectators are generically suppressed by powers of $\ensuremath{\Lambda}/{p}_{T}^{\ensuremath{'}}$, where $\ensuremath{\Lambda}$ is a hadronic scale and ${p}_{T}^{\ensuremath{'}}$ is the largest transverse momentum of radiation recoiling against the particles whose momenta are observed.

RG-improved single-particle inclusive cross sections and forward-backward asymmetry in $ t\bar{t} $ production at hadron colliders

We use techniques from soft-collinear effective theory (SCET) to derive renormalization-group improved predictions for single-particle inclusive (1PI) observables in top-quark pair production at hadron colliders. In particular, we study the top-quark transverse-momentum and rapidity distributions, the forward-backward asymmetry at the Tevatron, and the total cross section at NLO + NNLL order in resummed perturbation theory and at approximate NNLO in fixed order. We also perform a detailed analysis of power corrections to the leading terms in the threshold expansion of the partonic hard-scattering kernels. We conclude that, although the threshold expansion in 1PI kinematics is susceptible to numerically significant power corrections, its predictions for the total cross section are in good agreement with those obtained by integrating the top-pair invariant-mass distribution in pair invariant-mass kinematics, as long as a certain set of subleading terms appearing naturally within the SCET formalism is included.

Recoil and threshold corrections in short-distance cross sections

We identify and resum corrections associated with the kinematic recoil of the hard scattering against soft-gluon emission in single-particle inclusive cross sections. The method avoids double counting and conserves the flow of partonic energy. It reproduces threshold resummation for high-pT single-particle cross sections, when recoil is neglected, and QTresummation at low QT, when higher-order threshold logarithms are suppressed. We exhibit explicit resummed cross sections, accurate to next-to-leading logarithm, for electroweak annihilation and prompt photon inclusive cross sections.

Resummation of threshold corrections for single-particle inclusive cross sections

We derive threshold resummations for single-particle and single-jet inclusive cross sections, thus generalizing previous results at fixed invariant mass to a wider class of cross sections with phenomenological interest. We confirm the structure of our resummed expressions by comparison with explicit one-loop calculations for direct photons and heavy quarks.

Particle ratios in double-meson production by baryon's fragmentation

The double-meson inclusive reaction in the fragmentation region of incident baryons is studied with the sequential decay mechanism of excited hadrons, which has successfully explained the variety of the longitudinal-momentum dependence of the single-particle inclusive cross sections. The production ratios of two charged pions with the opposite sign to those with the same sign by incident proton are reproduced with the values of the parameters obtained previously.

Projectile fragmentation in hadron collisions

A model is formulated for projectile fragmentation in hadron collisions and is used to study the longitudinal-momentum dependence of the single-particle inclusive cross sections. The inclusive cross section consists of two parts due to the initial decay and many-particle production effects, the latter decreasing more rapidly than the former as the longitudinal momentum increases. The variety in the longitudinal-momentum dependence of the cross sections is explained naturally by the different weights of the two effects for the produced particles.

On large-pTsingle-particle inclusive cross sections and temperatures

A two-temperature thermodynamical idea is proposed for single-particle inclusive cross sections over a large range of c.m. energy $\sqrt{s}$ (23.5 to 540 GeV), and is shown to be valid at sufficiently high ${p}_{T}$ values. A possible relation to the proposed existence of hadron phase transition to quark-gluon plasma is discussed.

Short-Distance Behavior of Spontaneously Broken Quantum Chromodynamics

Light, colored scalars are shown to preserve all presently observed short-distance properties of quantum chromodynamics even when belonging to large multiplets of SU(3)/sub c/. However, light-scalar pair production by gluon fusion dominates hadronic high-p/sub T/ single-particle inclusive production cross sections at p-barp collider energies (..sqrt..s = 540 GeV) and two-jet production even at ..sqrt..sroughly-equal50--60 GeV. Embedding in a unified SU(5) theory requires many scalars to be superheavy in order to preserve asymptotic freedom below the unification mass.

Fireball analysis of large-p T single-particle inclusive cross sections

An expressionE(d3 σ/dp3)=KpT−n exp(−E/τ, wheren, K and τ are parameters to be fitted, has been used to represent the large-pT hadron invariant single-particle inclusive cross sections. In most cases the fitting is within the quoted experimental uncertainties. An interpretation of the expression in terms of fireballs is given. Scaling is seen to be violated in large-pT phenomena.

Observation of scaling deviations in the energy distribution of secondary hadrons in inelastic neutrino-proton interactions

An analysis is presented of the z distributions of secondary hadrons produced in 5600 charged current events from a BEBC neutrino-hydrogen experiment. Evidence is presented for scaling deviations in the z distributions and a breakdown of factorization in the single particle inclusive cross sections. The results are consistent with the leading order QCD predictions on the q 2 dependence of nonsinglet moments of quark fragmentation functions, yielding a value of Λ ≈ 0.6 GeV.

180° Production ofp,d, andt, andp−pCorrelation inp-Nucleus Collisions

The characteristic features of the energy distributions of the 180/sup 0/-emitted protons, deuterons, and tritons from 0.6 to 400 GeV incident energy, the extremely weak angular dependence of single-particle inclusive cross sections in the backward directions, and the existence of forward-backward pp correlation are shown to be due to fragmentation of the effective target (that is, the system of nucleons in the target nucleus along the axis of the incident proton) in proton-nucleus collisions. Correlation effects in violent processes are also briefly discussed.

Vortex String Picture and Large pT Reactions

The deviation of the observed behavior, ρ∼pT−n (n∼8) of the single particle inclusive cross section from the QCD prediction of ρ∼pT−4 may suggest that we have not yet reached the asymptotically perturbative region of QCD but nonperturbative effects of confinement remain in the hard subprocess of strong interactions. On the basis of the vortex string model as a realization of confinement, a possibility is examined to attribute the above deviation from the pT−4 rule to the radial density distribution of the vortex flux along the transverse extension l⊥, if the hard subprocess takes place only when two vortex strings overlap with each other. In a simplified treatment of scattering of two parallel vortices, the magnetic flux distribution of the Nielsen-Olesen model gives ρ∼pT−12, and the two-dimensional Yukawa type distribution gives the pT-8 behavior. When the overlap through crossover of two vortex strings is the basic interaction and has the form ̃χ(k)∼k−2 for the transferred momentum k, ρ∼pT−8 and various power behaviors are explained in accord with the quark-junction power counting rule proposed earlier. A relation of the vortex crossover to quantization of the vortex flux is discussed. Since photons and leptons interact with neither strings nor the junctions but only with quarks, the possibility proposed here allows the ordinary parton interpretation of the lepton-hadron reactions. The observed kT∼1GeV, the averaged transverse momentum of quarks, may be related to l⊥.

The transverse momentum of partons in large pT processes

An approximate method is used to investigate the effects of parton transverse momentum in large p T particle production within the framework of hard scattering models. We derive an approximate expression for the mean bias towards the trigger of each of the two participating partons and find that event one of the partons is biased more than the other, even with a 90° trigger. We treat the transverse momentum of partons and their closely related off-mass-shell behaviour as a perturbation in the equation for the single-particle inclusive cross section, and then expand in a Taylor series. We calculate the first non-zero correction term and find that to this order, the cross section is increased by parton transverse momentum effects by typically a factor of 1.7 for p T = 3 GeV/c with 〈 k T〉 = 500 MeV/c, or 1.25 for p T = 3 GeV/c with 〈 k T〉 = 300 MeV/c, and that the correction decreases rapidly with increasing p T.

Detailed quantum-chromodynamic predictions for high-pTprocesses

High-${p}_{T}$ single-particle inclusive cross section calculations are presented for the CERN ISR and ISABELLE energy ranges, taking into account all lowest-order hard-scattering subprocesses required by quantum chromodynamics (QCD). The input quark and gluon distribution and fragmentation functions were determined from analyses of deep-inelastic lepton data and were subject to various theoretical constraints such as sum rules and SU(3) symmetry. We thoroughly discuss the effects of the individual contributions from fermionic and gluonic subprocesses, as well as those effects stemming from QCD scaling violations in parton distributions and/or fragmentation functions. In particular, the inclusion of the large elastic gluon-gluon and gluon-quark scattering terms has a profound effect on both the normalization and the ${p}_{T}$ dependence of the predictions. The ${p}_{T}$ and $\ensuremath{\theta}$ dependences of single-${\ensuremath{\pi}}^{0}$ production are shown to be in good agreement with available data in the region ${p}_{T}\ensuremath{\gtrsim}4.5$ GeV/c and $\sqrt{s}\ensuremath{\gtrsim}50$ GeV. In addition, we predict and discuss various ratios for inclusive single-particle production of ${\ensuremath{\pi}}^{+}$, ${\ensuremath{\pi}}^{\ensuremath{-}}$, ${K}^{+}$, and ${K}^{\ensuremath{-}}$, which also turn out to be in excellent agreement with presently available experiments.

Calculations with the nuclear firestreak model

A model is presented which is capable of calculating simultaneously the spectra of pions, nucleons, and light nuclei from the collision of relativistic heavy ions. It is based on the nuclear thermodynamics of Mekjian and Kapusta. Maximum use is made of the conservation laws for baryon number, charge, energy, momentum, and angular momentum. Single particle inclusive cross sections were calculated and compared with experiment for a wide range of beam energies and observed fragments. Except for some conflicting normalizations and high-energy pions good agreement is found. The density at which hadrons effectively cease to interact, which is the only parameter in the model, is determined to be 0.12 hadrons/${\mathrm{fm}}^{3}$.NUCLEAR REACTIONS Relativistic heavy ions; firestreaks, hadronic thermal equilibrium; calculated differential cross sections of ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$, $p$, $d$, $t$, $^{3}\mathrm{He}$, $^{4}\mathrm{He}$; comparisons with experiment.

A comparison of models for large transverse momentum meson production

The predictions of three hard scattering models of large- p T meson production are compared with data on single-particle inclusive cross sections. The three models are: (i) the quark fusion model ( QF): q + q → M + M ; (ii) the constituent intercharge model (CIM): q + M → M + q and (iii) a model with disquarks (DQ): q + q → M + qq. The motivation for these models is discussed. We show that each model by itself has serious difficulties with the single-particle inclusive data but that the fits are greatly improved by taking natural combinations of them: a mixture of DQ and QF and of CIM and QF. Throughout, we compare our results with those of the quark-quark elastic scattering model of Field and Feynman, which is shown to have some problems of its own.

Analytic properties of the inclusive cross section in cos ? in the ladder model with an asymptotically constant total cross section

function is analytic in the variable cos 0 (0 is the production angle of the particle in the center of mass system) within an ellipse whose focuses are located at the points cos O=-+-I and whose semimajor axis is equal to xp=)'t+rnp2/Ipl "- (mp is the mass of the particle, and p is its momentum in the center of mass system). This conjecture,' which has been developed further in the papers [2,3], has made it possible to obtain several conditions on the distribution function; it itself, however, being unproven from the general principles of field theory, still needs confirmation, ha the paper [4] it was shown that the condition of analyticity just mentioned is fulfilled for the pole diagrams. In the present note we show that the conjecture on analyticity of the single-particle distribution in cos 0 is also satisfied for a less trivial model like the ladder ~c 3- model with an asymptotically constant total cross section. The single-particle inclusive cross section was computed for such a model in the paper [5] by means of the generalized optical theorem. The absorptive part of the forward scattering amplitude, which enters the integrand in the generalized optical theorem, was derived in the papers [6, 7] by solving the corresponding ladder equation. To calculate the inclusive cross section in [5] all the masses, except for the "internal" (i.e., entering the propagator) mass m, were set equal to zero. This assumption simply means the high energy approximation with respect to the masses of the colliding particles, while as far as the masses of the created particles are concerned it is dictated by the framework of our ladder model. In the paper [5] the inclusive cross section was given by a single integral of a comparatively simple elementary function. For our purpose it is not necessary to give this rather lengthy expression in full, but it is sufficient to note that it is a combination of the integrals I(n0 , I(~ ), and I (3) , where s(i-z) s(i--x) ~Ct-x)

Erratum: Analysis of radial scaling in single-particle inclusive reactions

An analysis of an extensive sample of the world's data has been performed to test the hypothesis of radial scaling. We have studied the inclusive reactions $p+p\ensuremath{\rightarrow}({\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{},0} or {K}^{\ifmmode\pm\else\textpm\fi{}} or p or \overline{p})+\mathrm{anything}$ to determine the behavior of the invariant cross section as a function of ${p}_{\ensuremath{\perp}}$, ${x}_{R}=\frac{{E}^{*}}{{{E}^{*}}_{max}}$, the radial scaling variable, and $s$. The data cover a range in ${p}_{\ensuremath{\perp}}$ from 0.25 to \ensuremath{\sim}6.0 GeV/c and a range in $\ensuremath{\surd}s$ from 3.0 to 63 GeV. For small ${x}_{R}$ and all available ${p}_{\ensuremath{\perp}}$ the single-particle inclusive cross sections for the reactions studied scale to a good approximation for all $\ensuremath{\surd}s$, even down to the kinematic threshold. For large ${x}_{R}$, the single-particle inclusive cross sections for increasing $\ensuremath{\surd}s$ show a rapid approach to the scaling limit from above. In these cases the scaling limit is always approached by $\ensuremath{\surd}s\ensuremath{\approx}10$ GeV. Thus, data for all particles to a good approximation exhibit radial scaling at all available ${p}_{\ensuremath{\perp}}$ and ${x}_{R}$ over the CERN ISR energy range. A comparison of radial scaling with Feynman scaling is given. It is shown that in the Feynman case the cross sections for small ${x}_{\ensuremath{\parallel}}$ (${x}_{\ensuremath{\parallel}}=\frac{{{p}^{*}}_{\ensuremath{\parallel}}}{{{p}^{*}}_{max}}$) approach their scaling limit from below, and that the approach to the scaling limit is slower than is exhibited for the case of small ${x}_{R}$. The systematic differences among the inclusive cross sections of various particles are discussed in the range of $\ensuremath{\surd}s$ where radial scaling has been shown to be valid. In particular, the ${p}_{\ensuremath{\perp}}$ and ${x}_{R}$ distributions of $E\frac{d\ensuremath{\sigma}}{d{p}^{3}}$ are examined.