Parton Momentum Distribution Research Articles

Momentum-kick model description of the ridge inΔφ-Δηcorrelations inppcollisions at 7 TeV

The near-side ridge structure in the $\ensuremath{\Delta}\ensuremath{\varphi}$-$\ensuremath{\Delta}\ensuremath{\eta}$ correlation observed by the CMS Collaboration for $pp$ collisions at 7 TeV at the Large Hadron Collider can be explained by the momentum kick model in which the ridge particles are medium partons that suffer a collision with the jet and acquire a momentum kick along the jet direction. Similar to the early medium parton momentum distribution obtained in previous analysis for nucleus-nucleus collisions at $\sqrt{{s}_{{}_{NN}}}=0.2$ TeV, the early medium parton momentum distribution in $pp$ collisions at 7 TeV exhibits a rapidity plateau as arising from particle production in a flux tube.

Parton transverse momentum distribution at the moment of hadronization at RHIC

We extract the transverse momentum distribution of effective partons using the spectra of Ω, Ξ, Λ and ϕ hadrons measured by the STAR Collaboration from Au + Au collisions at \( \sqrt {s_{NN} } \) = 200 GeV at RHIC. The extracted momentum distribution of strange quarks is flatter than that of up/down quarks consistent with hydrodynamics expansion in partonic phase prior to hadronization. Consistency in quark ratios derived from various hadron spectra gives clear evidence for hadron production as suggested by quark coalescence or recombination model.

Longitudinal and transverse parton momentum distributions for pion and nucleon within relativistic constituent quark models

Longitudinal and transverse quark momentum distributions for the pion and the nucleon are calculated from quark-hadron vertexes obtained by an investigat ion of electromagnetic form factors within relativistic constituent quark models. The no-helicity flip generalized parton distributions for the pion are evaluated within three different models. The relevance for the pion of the one-gluon-exchange dominance at short range for the behavior of the form factor at large momentum transfer and of the parton distributions at the end points is shown.

Jet evolution in Yang-Mills-Wong simulations

We present results for collisional energy loss and momentum broadening of high momentum partons in a hot and dense non-Abelian plasma obtained by solving the coupled system of Yang-Mills-Wong equations on a lattice in real time. Including hard elastic collisions among the particles we obtain cutoff independent results for the collisional energy loss d E / d x and the transport coefficient q ˆ . The latter is found to receive a sizable contribution from a power-law tail in the transverse momentum distribution of high-momentum partons. We further argue that the effect of instabilities on jet broadening should be accessible by experiment when employing jet cones with elliptical bases or studying correlations within the cone in full jet reconstruction methods.

Markovian Monte Carlo program EvolFMC v.2 for solving QCD evolution equations

Abstract We present the program EvolFMC v.2 that solves the evolution equations in QCD for the parton momentum distributions by means of the Monte Carlo technique based on the Markovian process. The program solves the DGLAP-type evolution as well as modified-DGLAP ones. In both cases the evolution can be performed in the LO or NLO approximation. The quarks are treated as massless. The overall technical precision of the code has been established at 5 × 10 − 4 . This way, for the first time ever, we demonstrate that with the Monte Carlo method one can solve the evolution equations with precision comparable to the other numerical methods. New version program summary Program title: EvolFMC v.2 Catalogue identifier: AEFN_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEFN_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including binary test data, etc.: 66 456 (7407 lines of C++ code) No. of bytes in distributed program, including test data, etc.: 412 752 Distribution format: tar.gz Programming language: C++ Computer: PC, Mac Operating system: Linux, Mac OS X RAM: Less than 256 MB Classification: 11.5 External routines: ROOT ( http://root.cern.ch/drupal/ ) Nature of problem: Solution of the QCD evolution equations for the parton momentum distributions of the DGLAP- and modified-DGLAP-type in the LO and NLO approximations. Solution method: Monte Carlo simulation of the Markovian process of a multiple emission of partons. Restrictions: 1. Limited to the case of massless partons. 2. Implemented in the LO and NLO approximations only. 3. Weighted events only. Unusual features: Modified-DGLAP evolutions included up to the NLO level. Additional comments: Technical precision established at 5 × 10 − 4 . Running time: For the 10 6 events at 100 GeV: DGLAP NLO: 27s; C ′ -type modified DGLAP NLO: 150s (MacBook Pro with Mac OS X v.10.5.5, 2.4 GHz Intel Core 2 Duo, gcc 4.2.4, single thread).

Momentum kick model analysis of PHENIX near-side ridge data and photon jet

We analyze PHENIX near-side ridge data for central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{\mathit{NN}}}=200$ GeV with the momentum-kick model, in which a near-side jet emerges near the surface, kicks medium partons, loses energy, and fragments into the trigger particle and fragmentation products. The kicked medium partons subsequently materialize as the observed ridge particles, which carry direct information on the early parton momentum distribution and the magnitude of the momentum kick. We find that the PHENIX ridge data can be described well by the momentum-kick model and the extracted early partons momentum distribution has a thermal-like transverse distribution and a rapidity plateau structure. We also find that the parton-parton scattering between the jet parton and the medium parton involves the exchange of a nonperturbative pomeron, for jet partons in momentum range considered in the near-side ridge measurements.

Markovian MC simulation of QCD evolution at NLO level with minimum k T

We present two Monte Carlo algorithms of the Markovian type which solve the modified QCD evolution equations at NLO level. The modifications with respect to the standard DGLAP evolution concern the argument of the strong coupling constant, α S. We first analyze the z-dependent argument and then the k T -dependent one. The evolution time variable is identified with the rapidity. The two algorithms are tested to 0.05% precision level. We find that the NLO corrections in the evolution of the parton momentum distributions with k T -dependent coupling constant are of the order of 10 to 20%, and in the small-x region even up to 30%, with respect to the LO contributions.

Deeply inelastic pions in the exclusive reactionp(e,e′π+)nabove the resonance region

A model for the $p(e,{e}^{\ensuremath{'}}{\ensuremath{\pi}}^{+})n$ reaction which combines an improved treatment of gauge invariant meson-exchange currents and hard deep-inelastic scattering (DIS) of virtual photons off nucleons is proposed. It is shown that DIS dominates and explains the transverse response at moderate and high photon virtualities ${Q}^{2}$, whereas the longitudinal response is dominated by hadronic degrees of freedom and the pion electromagnetic form factor. This leads to a combined description of the longitudinal and transverse components of the cross section in a wide range of photon virtuality ${Q}^{2}$ and momentum transfer to the target $t$ and solves the longstanding problem of the observed large transverse cross sections. The latter are shown to be sensitive to the intrinsic transverse momentum distribution of partons.

Momentum kick model description of the near-side ridge and jet quenching

In the momentum kick model, a near-side jet emerges near the surface, kicks medium partons, loses energy, and fragments into the trigger particle and fragmentation products. The kicked medium partons subsequently materialize as the observed ridge particles, which carry direct information on the magnitude of the momentum kick and the initial parton momentum distribution at the moment of jet--medium-parton collisions. The initial parton momentum distribution extracted from the STAR ridge data for central $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{\mathit{NN}}}=200$ GeV has a thermal-like transverse momentum distribution and a rapidity plateau structure with a relatively flat distribution at mid-rapidity and sharp kinematic boundaries at large rapidities. Such a rapidity plateau structure may arise from particle production in flux tubes, as color charges and anticolor charges separate at high energies. The centrality dependence of the ridge yield and the degree of jet quenching can be consistently described by the momentum kick model.

Parton Momentum Distribution at the Moment of Jet-Parton Collisions

The early parton momentum distribution is extracted by using the STAR collaboration data of ridge particles associated with a near-side jet in central A uAu collisions at . The ridge particles are identified as medium partons kicked by the jet near the surface and they carry direct information on the parton momentum distribution at the moment of jet-parton collisions. The extracted parton momentum distribution has a thermal-like transverse momentum distribution but a rapidity plateau structure with a relatively flat rapidity distribution at mid-rapidities with sharp kinematic boundaries at large rapidities that depend on the transverse momentum.

Exploring early parton momentum distribution with the ridge from the near-side jet

In a central nucleus–nucleus collision at high energies, medium partons kicked by a near-side jet acquire a momentum along the jet direction and subsequently materialize as the observed ridge particles. They carry direct information on the early parton momentum distribution which can be extracted by using the ridge data for central AuAu collisions at GeV. The extracted parton momentum distribution has a thermal-like transverse momentum distribution but a non-Gaussian, relatively flat rapidity distribution at mid-rapidity with sharp kinematic boundaries at large rapidities that depend on the transverse momentum.

Ridge structure in theΔϕ−Δηcorrelation function associated with a near-side jet

In the $\ensuremath{\Delta}\ensuremath{\phi}\text{\ensuremath{-}}\ensuremath{\Delta}\ensuremath{\eta}$ correlation associated with a near-side jet observed by the STAR Collaboration in heavy-ion collisions at the BNL Relativistic Heavy Ion Collider (RHIC), the ridge structure can be explained by the momentum kick model in which the ridge particles are identified as medium partons which suffer a collision with the jet and acquire a momentum kick along the jet direction. If this is indeed the correct mechanism, the ridge structure associated with the near-side jet may be used to probe the parton momentum distribution at the moment of the jet-parton collision, leading to the result that at that instant the parton temperature is slightly higher and the rapidity width substantially greater than corresponding quantities of their evolution product inclusive particles at the end point of the nucleus-nucleus collision.

THE NUCLEON STRUCTURE AND THE EQUATION OF STATE FOR NUCLEAR MATTER

We show the density dependent corrections to the nucleon structure function in the frame of nuclear Relativistic Mean Field (RMF) models. These corrections are connected with the modifications of the parton distribution in nuclei emerging from generalized nuclear Fermi motion and final state interactions between the nucleon and the rest of the nucleus. The medium effects concern the nucleon structure, namely the changes in the nucleon rest energy, the enhancement of sea quark contribution (simulated with "nuclear pions") and the modifications of the transverse parton momentum distribution inside Nuclear Matter (NM). The sea parton distributions are described by the modified cloud of virtual pions in order to saturate the nuclear energy-momentum sum rule. The description of theses features are in good agreement with experimental data; the EMC effect for x > 0.15 and nuclear lepton pair production data has been described essentialy without free parameters. The influence of these medium modifications to the nucleon structure function within the equation of state in RMF models of NM will be discussed.

Di-hadron correlations and parton intrinsic transverse momentum

The transverse momentum distribution of partons in the proton is studied with the help of di-hadron correlations. A simple randomization model is compared to the data.

Nonlinear screening effects in high energy hadronic interactions

Non-linear effects in hadronic interactions are treated by means of enhanced pomeron diagrams, assuming that pomeron-pomeron coupling is dominated by soft partonic processes. It is shown that the approach allows to resolve a seeming contradiction between realistic parton momentum distributions, measured in deep inelastic scattering experiments, and the energy behavior of total proton-proton cross section. Also a general consistency with both ``soft'' and ``hard'' diffraction data is demonstrated. An important feature of the proposed scheme is that the contribution of semi-hard processes to the interaction eikonal contains a significant non-factorizable part. On the other hand, the approach preserves the QCD factorization picture for inclusive high p_t jet production.

Strongly and weakly unstable anisotropic quark-gluon plasma

Using explicit solutions of the QCD transport equations, we derive an effective potential for an anisotropic quark-gluon plasma which under plausible assumptions holds beyond the Hard Loop approximation. The configurations, which are unstable in the linear response approach, are characterized by a negative quadratic term of the effective potential. The signs of higher-order terms can be either negative or positive, depending on the parton momentum distribution. In the case of a Gaussian momentum distribution, the potential is negative and unbound from below. Therefore, the modes, which are unstable for gauge fields of small amplitude, remain unstable for arbitrary large amplitudes. We also present an example of a momentum distribution which gives a negative quadratic term of the effective potential but the whole potential has a minimum and it grows for sufficiently large gauge fields. Then, the system is weakly unstable. The character of the instability is important for the dynamical evolution of the plasma system.

Hard-loop effective action for anisotropic plasmas

We generalize the hard-thermal-loop effective action of the equilibrium quark-gluon plasma to a non-equilibrium system which is space-time homogeneous but for which the parton momentum distribution is anisotropic. We show that the manifestly gauge-invariant Braaten-Pisarski form of the effective action can be straightforwardly generalized and we verify that it then generates all n-point functions following from collisionless gauge-covariant transport theory for a homogeneous anisotropic plasma. On the other hand, the Taylor-Wong form of the hard-thermal-loop effective action has a more complicated generalization to the anisotropic case. Already in the simplest case of anisotropic distribution functions, it involves an additional term that is gauge invariant by itself, but nontrivial also in the static limit.

A first measurement of the tensor structure function b1d

The Hermes experiment studies the spin structure of the nucleon using the 27.6 GeV longitudinally polarized positron beam of HERA and an internal target of pure gases. In addition to the well-known spin structure function g 1 , measured precisely with longitudinally polarized proton and deuteron targets, the use of a tensor-polarized deuteron target provides access to the tensor structure function b 1 d . The latter, measured with an unpolarized beam, quantifies the dependence of the parton momentum distribution on the nucleon spin. Hermes had a 1-month dedicated run with a tensor-polarized deuterium target during the 2000 data taking period. Here preliminary results on the tensor structure function b 1 d are presented for the kinematic range 0.002 < χ < 0.85 and 0.1 GeV 2 < Q 2 < 20 GeV 2 .

Contemporary models of high energy interactions: present status and perspectives

Modern approaches to the description of high energy hadronic and nuclear collisions are reviewed in connection with extensive air shower (EAS) physics. Special attention is devoted to the so-called semihard partonic processes which appear to dominate the interactions at very high energies. It is shown that a corresponding treatment can be developed in the framework of the Gribov–Regge approach, introducing a concept of ‘semihard Pomeron’, the latter being a t-channel iteration of the phenomenological ‘soft’ Pomeron and QCD parton ladder. A comparison is made with the QCD eikonal (mini-jet) scheme and essential differences as well as observable consequences for EAS development are analysed in detail. The role of nonlinear interaction contributions described by enhanced Pomeron diagrams is also investigated. It is demonstrated that such diagrams provide important screening corrections to the interaction mechanism and allow us to resolve a seeming contradiction between realistic parton momentum distributions and observed energy dependence of hadron–hadron cross sections. A modification of the standard scheme by correct treatment of energy–momentum sharing mechanism in hadronic collisions is also considered. Finally, we discuss possible ways to discriminate between the alternative approaches.

High-pTpion and kaon production in relativistic nuclear collisions

High-p_T pion and kaon production is studied in relativistic proton-proton, proton-nucleus, and nucleus-nucleus collisions in a wide energy range. Cross sections are calculated based on perturbative QCD, augmented by a phenomenological transverse momentum distribution of partons (``intrinsic k_T''). An energy dependent width of the transverse momentum distribution is extracted from pion and charged hadron production data in proton-proton/proton-antiproton collisions. Effects of multiscattering and shadowing in the strongly interacting medium are taken into account. Enhancement of the transverse momentum width is introduced and parameterized to explain the Cronin effect. In collisions between heavy nuclei, the model over-predicts central pion production cross sections (more significantly at higher energies), hinting at the presence of jet quenching. Predictions are made for proton-nucleus and nucleus-nucleus collisions at RHIC energies.