Hadron Formation Research Articles

Experimental Studies of Hadronization and Parton Propagation in the Space-Time Domain

Over the past decade, new data have become available from DESY, Jefferson Lab, Fermilab, and RHIC that connect to parton propagation and hadron formation. Semi-inclusive DIS on nuclei, the Drell-Yan reaction, and heavy-ion collisions all bring different kinds of information on parton propagation within a medium, while the most direct information on hadron formation comes from the DIS data. Over the next decade one can hope to begin to understand these data within a unified picture. We briefly survey the most relevant data and the common elements of the physics picture, then highlight the new Jefferson Lab data from CLAS, and close with prospects for the future.

Jet-Medium Interactions with Identified Particles

Identified particles have long been of great interest at RHIC in large part because of the baryon/meson differences observed at intermediate p T and the implications for hadronization via quark coalescence. With recent high statistics data identified particles are also now central to understanding the details of the jet-medium interactions and energy loss and hadron formation at intermediate and high p T . In particular, high p T identified particle spectra along with two-particle correlations triggered with direct photons, neutral pions or electrons from heavy flavor decay with hadrons can provide information about how medium modifications to jet fragmentation depend on parton type. I will review recent results with identified particles both in heavy ion systems and the reference measurements in p+p collisions.

Renormalization group equation and QCD coupling constant in the presence of SU(3) chromo-electric field

We solve renormalization group equation in QCD in the presence of SU(3) constant chromo-electric field E^a with arbitrary color index a=1,2,...8 and find that the QCD coupling constant \alpha_s depends on two independent casimir/gauge invariants C_1=[E^aE^a] and C_2=[d_{abc}E^aE^bE^c]^2 instead of one gauge invariant C_1=[E^aE^a]. The \beta function is derived from the one-loop effective action. This coupling constant may be useful to study hadron formation from color flux tubes/strings at high energy colliders and to study quark-gluon plasma formation at RHIC and LHC.

Parton distributions at hadronization from bulk dense matter produced at the RHIC

In this paper, we present an analysis of Ω, Ξ, Λ and ϕ spectra from Au+Au collisions at GeV in terms of distributions of effective constituent quarks at hadronization. We argue that the constituent quark distribution reflects properties of the partonic degrees of freedom at hadronization. Experimental data indicate that partons may have developed a significant radial flow during the partonic evolution stage. Consistency in quark ratios derived from various hadron spectra provides clear evidence for hadron formation dynamics as suggested by quark coalescence or recombination models. The strange and up/down quark distributions when used in the AMPT model where hadrons are formed through dynamical coalescence can describe the measured transverse momenta of hyperons and ϕ mesons very well.

Transverse momentum broadening in semi-inclusive DIS on nuclei

Using a three stage model of hadron formation we calculate the change of the transverse momentum distribution of hadrons produced in semi-inclusive deep inelastic scattering (SIDIS) on nuclei. In the first stage after its interaction with the virtual photon, the struck quark propagates quasi free in the nuclear environment undergoing multiple collisions with nucleons. During this stage it can acquire transverse momentum. In the second stage a prehadron is formed which has a very small elastic cross section with the nucleons. In the third stage the prehadron turns into a hadron. For HERMES energies, prehadron elastic scatterings contribute little to p ⊥ -broadening. The acquired extra Δ p ⊥ 2 of hadrons can therefore be deduced entirely from the first stage of quasi free quark propagation with quark–nucleon collisions. We use this model to describe π-production on Ne, Kr, Xe and compare with the most recent HERMES data.

Herwig++ physics and manual

In this paper we describe \(\mathsf{Herwig++}\) version 2.2, a general-purpose Monte Carlo event generator for the simulation of hard lepton-lepton and hadron-hadron collisions. A number of important hard scattering processes are available, together with an interface via the Les Houches Accord to specialized matrix element generators for additional processes. The simulation of Beyond the Standard Model (BSM) physics includes a range of models and allows new models to be added by encoding the Feynman rules of the model. The parton-shower approach is used to simulate initial- and final-state QCD radiation, including colour coherence effects, with special emphasis on the correct description of radiation from heavy particles. The underlying event is simulated using an eikonal multiple parton-parton scattering model. The formation of hadrons from the quarks and gluons produced in the parton shower is described using the cluster hadronization model. Hadron decays are simulated using matrix elements, where possible including spin correlations and off-shell effects.

Parton distributions at hadronization from bulk dense matter produced inAu+Aucollisions atsNN=200GeV

We present an analysis of $\ensuremath{\Omega},\ensuremath{\Xi},\ensuremath{\Lambda}$, and $\ensuremath{\phi}$ spectra from $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{\mathit{NN}}}=200$ GeV in terms of distributions of effective constituent quarks at hadronization. Consistency in quark ratios derived from various hadron spectra provides clear evidence for hadron formation dynamics as suggested by quark coalescence or recombination models. We argue that the constituent quark distribution reflects properties of the effective partonic degree of freedom at hadronization. Experimental data indicate that strange quarks have a transverse-momentum distribution flatter than that of up/down quarks consistent with hydrodynamic expansion in partonic phase prior to hadronization. Our extracted parton transverse-momentum distributions at the hadronization provide a unique constraint on the partonic evolution history. After the multiphase transport model is tuned to reproduce the strange and up/down quark distributions, the model can describe the measured spectra of hyperons and $\ensuremath{\phi}$ mesons very well where hadrons are formed through dynamical coalescence.

Coalescence Models for Hadron Formation from Quark-Gluon Plasma

We review hadron formation from a deconfined quark-gluon plasma (QGP) via coalescence or recombination of quarks and gluons. We discuss the abundant experimental evidence for coalescence from the Relativistic Heavy Ion Collider (RHIC) and compare the various coalescence models advocated in the literature. We comment on the underlying assumptions and remaining challenges as well as the merits of the models. We conclude with a discussion of some recent developments in the field.

Latest HERMES results on transverse spin effects in hadron structure and formation⋆

Transverse target single-spin asymmetries in semi-inclusive deep inelastic scattering allow to study the so-called Collins and Sivers mechanisms. The first one connects the poorly known fundamental transversity distribution function, describing the transverse spin-polarization of quarks in a transversely polarized proton, to the Collins fragmentation function, describing spin-orbit correlations in the hadron formation process. The second one is sensitive to the Sivers function, which correlates the intrinsic transverse momentum of quarks with the proton’s spin orientation and is related to the orbital angular momentum of quarks. Preliminary results on azimuthal single target-spin asymmetries in semi-inclusive electro-production of pions and kaons at the HERMES experiment are presented. The full data set collected with a transversely polarized hydrogen target was analyzed providing the HERMES most precise results on the Collins and Sivers azimuthal moments.

Strange hadron yields and ratios in heavy ion collisions at RHIC energy

Recent experimental data support the presence of quark coalescence in heavy ion collisions at RHIC energies. Hadronization of quark matter and hadron formation in heavy ion collisions can be described by the coalescence process, and measured data are reproduced successfully. On the other hand, the theoretical coalescence calculations are based on a non-relativistic description. Here we investigate the robustness of the coalescence description, using different wavefunction overlap during hadron formation.

The robustness of quasiparticle coalescence in quark matter

Experimental data collected in heavy ion collisions at RHIC energies strongly support quark matter formation and the presence of quark coalescence at these energies. Hadronization of quark matter and hadron formation in heavy ion collisions can be described by the coalescence process, and measured data could have been reproduced successfully. Theoretical calculations are based on a quantum mechanical description of coalescence. Here we investigate the robustness of the coalescence description, using different wave-function overlap during hadron formation.

Possible influence of the two string events on the hadron formation in a nuclear environment

One of the basic assumptions of the string model is that as a result of a DIS in nucleus a single string arises, which then breaks into hadrons. However the pomeron exchange considered in this work, leads to the production of two strings in the one event. The hadrons produced in these events have smaller formation lengths, than those with the same energy produced in the single string events. As a consequence, they undergo more substantial absorption in the nuclear matter.

Disappearance of squeezed back-to-back correlations: a new signal of hadron freeze-out from a supercooled quark gluon plasma

We briefly discuss four different possible types of transitions from quark to hadronic matter and their characteristic signatures in terms of correlations. We also highlight the effects arising from mass modification of hadrons in hot and dense hadronic matter, as well as their quantum statistical consequences: the appearance of squeezed quantum states and the associated experimental signatures, i.e., the back-to-back correlations of particle-antiparticle pairs. We briefly review the theoretical results of these squeezed quanta, generated by in-medium modified masses, starting from the first indication of the existence of surprising particle-antiparticle correlations, and ending by considering the effects of chiral dynamics on these correlation patterns. Nevertheless, a prerequisite for such a signature is the experimental verification of its observability. Therefore, the experimental observation of back-to-back correlations in high energy heavy ion reactions would be a unique signature, proving the existence of in-medium mass modification of hadronic states. On the other hand, their disappearance at some threshold centrality or collision energy would indicate that the hadron formation mechanism would have qualitatively changed: asymptotic hadrons above such a threshold are not formed from medium modified hadrons anymore, but rather by new degrees of freedom characterizing the medium. Furthermore, the disappearance of the squeezed BBC could also serve as a signature of a sudden, non-equilibrium hadronization scenario from a supercooled quark-gluon plasma phase.

HADRON FORMATION IN HIGH ENERGY ELEMENTARY AND NUCLEAR COLLISIONS

We consider the dynamical origin of the apparent statistical equilibrium that governs the yields, and yield ratios, of all hadron and resonance species (consisting of the three light quark flavours) produced in nucleus-nucleus collisions from AGS via SPS to RHIC energies [Formula: see text]. This hadro-chemical equilibrium state is well described, overall, by the grand canonical, quasi-classical Gibbs ensemble of all corresponding hadrons and resonances. In order to pin down the stochastic elements, featured by the dynamical evolution prior to hadron formation and hadronic "chemical" (i.e. species) freeze-out, and determining the eventual equilibrium state, we concentrate on the high energy domain, [Formula: see text], where a model of primordial perturbative QCD partonic shower evolution appears plausible. For guidance concerning a hadronization model we revisit the QCD description of jet-induced hadron formation in e+e- annihilation at LEP energy. At the end of the pQCD partonic shower evolution a stage of color neutralization and flavour recombination leads to transition into non perturbative QCD clusters or strings, that decay to hadrons/resonances under phase space dominance. The combination of stochastic shower multiplication and cluster decay to the phase space defined by the hadron/resonancemass and spin spectrum results in a hadronization output featuring statistical equilibrium of the species, which is well described by the canonical Gibbs ensemble. We then assume that hadronization in A + A collisions occurs from a similar stage of singlet cluster formation. However, owing to the extreme overall energy density these clusters should overlap spatially, giving rise to extended super-cluster formation, increasing with [Formula: see text], A and collision centrality. In the limit of an extended volume decaying coherently, hadronization is free of local quantum number conservation constraints. This leads to strangeness enhancement and explains the success of a grand canonical description.

Scaling Properties of Hyperon Production inAu+AuCollisions atsNN=200 GeV

We present the scaling properties of Lambda, Xi, and Omega in midrapidity Au+Au collisions at the Brookhaven National Laboratory Relativistic Heavy Ion Collider at sqrt[s_{NN}]=200 GeV. The yield of multistrange baryons per participant nucleon increases from peripheral to central collisions more rapidly than that of Lambda, indicating an increase of the strange-quark density of the matter produced. The strange phase-space occupancy factor gamma_{s} approaches unity for the most central collisions. Moreover, the nuclear modification factors of p, Lambda, and Xi are consistent with each other for 2<p_{T}<5 GeV/c in agreement with a scenario of hadron formation from constituent quark degrees of freedom.

Hadronization in Cold Nuclear Matter

I review a recently proposed scaling analysis of hadron suppression in Deeply Inelastic Scattering on nuclear targets measured at the HERMES experiment. The analysis can distinguish 2 competing explanations for the observed suppression, namely, quark radiative energy loss with long hadron formation times, and prehadron nuclear absorption with hadronization starting inside the nucleus. Experimental data are shown to favor short formation times and prehadron absorption.

In-medium Hadrons – Properties, Interaction and Formation

In this talk various aspects of in-medium behavior of hadrons are discussed with an emphasis on observable effects. Examples for theoretical predictions of in-medium spectral functions are given and the importance of resonance-hole excitations is stressed. It is also stressed that final state interactions can have a major effect on observables and thus have to be considered as part of the theory. This is demonstrated with examples from neutrino-nucleus interactions. Finally, the possibility to access hadron formation times in high-energy photonuclear (or neutrino-induced) reactions is illustrated.

UCLA space-time area law model: A persuasive foundation for hadronization

From the studies of rates and distributions of heavy quark (c, b) mesons we have developed additional evidence that hadron formation, at least in the simplest environment of e+e- collisions, is dominantly controlled by a space-time area law (“STAL”), an approach suggested by both non-perturbative QCD and relativistic string models. From the dynamics of heavy quarks whose classical space-time world-lines deviate significantly from the light-cone, we report the exact calculation of the relevant space-time area and the derivation of a Lorentz invariant variable, zeff, which reduces to the light-cone momentum fraction z for low mass quarks. Using zeff in the exponent of our fragmentation function in place of z, we find persuasive agreement with L=0, 1 charmed and bottom meson data as well as for u, d, s L=0 states. Presuming STAL to be a valid first-order description for all these meson data, we find the scale of other possible second-order effects to be limited to ∼20% or less of the observed rates. The model favors a b-quark mass of ∼4.5 GeV.

Space-time evolution of hadronization

Beside its intrinsic interest for the insights it can give into color confinement, knowledge of the space-time evolution of hadronization is very important for correctly interpreting jet-quenching data in heavy ion collisions and extracting the properties of the produced medium. On the experimental side, the cleanest environment to study the space-time evolution of hadronization is semi-inclusive Deeply Inelastic Scattering on nuclear targets. On the theoretical side, 2 frameworks are presently competing to explain the observed attenuation of hadron production: quark energy loss (with hadron formation outside the nucleus) and nuclear absorption (with hadronization starting inside the nucleus). I discuss recent observables and ideas which will help to distinguish these 2 mechanisms and to measure the time scales of the hadronization process.

Evidence from identified particles for active quark and gluon degrees of freedom

Measurements of intermediate pT (1.5 < pT < 5.0 GeV/c) identified particle distributions in heavy-ion collisions at SPS and RHIC energies display striking dependences on the number of constituent quarks in the corresponding hadron. One finds that elliptic flow at intermediate pT follows a constituent quark scaling law as predicted by models of hadron formation through coalescence. In addition, baryon production is also found to increase with event multiplicity much faster than meson production. The rate of increase is similar for all baryons and seemingly independent of mass. This indicates that the number of constituent quarks determines the multiplicity dependence of identified hadron production at intermediate pT. We review these measurements and interpret the experimental findings.