QCD Parton Model Research Articles

Modification of Quark-Gluon Distributions in Nuclei by Correlated Nucleon Pairs.

We extend the QCD Parton Model analysis using a factorized nuclear structure model incorporating individual nucleons and pairs of correlated nucleons. Our analysis of high-energy data from lepton deep-inelastic scattering, Drell-Yan, and W and Z boson production simultaneously extracts the universal effective distribution of quarks and gluons inside correlated nucleon pairs, and their nucleus-specific fractions. Such successful extraction of these universal distributions marks a significant advance in our understanding of nuclear structure properties connecting nucleon- and parton-level quantities.

Extracting the jet transport coefficient from hadron suppressions by confronting current NLO parton fragmentation functions

Nuclear modification factors of single hadrons and dihadrons at large transverse momentum ( $$p_{\mathrm{T}}$$ ) in high-energy heavy-ion collisions are studied in a next-to-leading-order (NLO) perturbative QCD parton model. Parton fragmentation functions (FFs) in $$A+A$$ collisions are modified due to jet energy loss which is proportional to the jet transport coefficient $$\hat{q}$$ characterizing the interaction between the parton jet and the produced medium. By confronting 6 current sets of NLO parton FFs for large $$p_{\mathrm{T}}$$ hadron productions, we extract $$\hat{q}$$ quantitatively via a global fit to data for both single hadron and dihadron suppressions and obtain $$\hat{q}/T^3 = 4.74 - 6.72$$ at $$T = 370$$ MeV in central $$Au+Au$$ collisions at $$\sqrt{s_{\mathrm{NN}}}=200$$ GeV, and $$\hat{q}/T^3 = 3.07 - 3.98$$ at $$T = 480$$ MeV in central $$Pb+Pb$$ collisions at $$\sqrt{s_{\mathrm{NN}}}=2.76$$ TeV. The numerical results show that the uncertainties for $$\hat{q}$$ extraction are brought by the different contributions of gluon-to-hadron in the six sets of FFs due to gluon energy loss being 9/4 times of quark energy loss.

γ -hadron spectra in p+Pb collisions at sNN=5.02 TeV

Under the assumption that a quark-gluon plasma droplet is produced and its evolution can be described by hydrodynamics in p + A collisions, $\gamma$-triggered hadron spectra are studied within a next-to-leading-order perturbative QCD parton model with the medium-modified parton fragmentation functions. The initial conditions and space-time evolution of the small QGP droplet are provided by the superSONIC hydrodynamic model simulations and parton energy loss in such a medium is described by the high-twist (HT) approach. The scaled jet transport coefficient $\hat{q}/T^3$ in this HT approach is extracted from single hadron suppression in central A + A collisions at the same colliding energy. Numerical results for this scenario show that $\gamma$-hadron spectra at $p_{\rm T}^\gamma=12-40$ GeV/$c$ are suppressed by 5\% $\sim$ 10\% in the most central 0 - 10\% p + Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV. The suppression becomes weaker at higher transverse momentum of the $\gamma$ trigger. As a comparison, $\gamma$-hadron suppression in Pb + Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ and 5.02 TeV is also predicted.

Extracting jet transport coefficient via single hadron and dihadron productions in high-energy heavy-ion collisions

We study the suppressions of high transverse momentum single hadron and dihadron productions in high-energy heavy-ion collisions based on the framework of a next-to-leading-order perturbative QCD parton model combined with the higher-twist energy loss formalism. Our model can provide a consistent description for the nuclear modification factors of single hadron and dihadron productions in central and non-central nucleus–nucleus collisions at RHIC and the LHC energies. We quantitatively extract the value of jet quenching parameter hat{q} via a global chi ^2 analysis, and obtain {hat{q}}/{T^3} = 4.1–4.4 at T = 378 MeV at RHIC and {hat{q}}/{T^3} = 2.6–3.3 at T = 486 MeV at the LHC, which are consistent with the results from JET Collaboration. We also provide the predictions for the nuclear modification factors of dihadron productions in Pb + Pb collisions at sqrt{s_mathrm{{NN}}} = 5.02 TeV and in Xe + Xe collisions at sqrt{s_mathrm{{NN}}} = 5.44 TeV.

Quantifying jet transport properties via large $$p_T$$ p T hadron production

Nuclear modification factor $R_{AA}$ for large $p_T$ single hadron is studied in a next-to-leading order (NLO) perturbative QCD (pQCD) parton model with medium-modified fragmentation functions (mFFs) due to jet quenching in high-energy heavy-ion collisions. The energy loss of the hard partons in the QGP is incorporated in the mFFs which utilize two most important parameters to characterize the transport properties of the hard parton jets: the jet transport parameter $\hat q_{0}$ and the mean free path $\lambda_{0}$, both at the initial time $\tau_0$. A phenomenological study of the experimental data for $R_{AA}(p_{T})$ is performed to constrain the two parameters with simultaneous $\chi^2/{\rm d.o.f}$ fits to RHIC as well as LHC data. We obtain for energetic quarks $\hat q_{0}\approx 1.1 \pm 0.2$ GeV$^2$/fm and $\lambda_{0}\approx 0.4 \pm 0.03$ fm in central $Au+Au$ collisions at $\sqrt{s_{NN}}=200$ GeV, while $\hat q_{0}\approx 1.7 \pm 0.3$ GeV$^2$/fm, and $\lambda_{0}\approx 0.5 \pm 0.05$ fm in central $Pb+Pb$ collisions at $\sqrt{s_{NN}}=2.76$ TeV. Numerical analysis shows that the best fit favors a multiple scattering picture for the energetic jets propagating through the bulk medium, with a moderate averaged number of gluon emissions. Based on the best constraints for $\lambda_{0}$ and $\tau_0$, the estimated value for the mean-squared transverse momentum broadening is moderate which implies that the hard jets go through the medium with small reflection.

Diffractive Bremsstrahlung in Hadronic Collisions

Production of heavy photons (Drell-Yan), gauge bosons, Higgs bosons, and heavy flavors, which is treated within the QCD parton model as a result of hard parton-parton collision, can be considered a bremsstrahlung process in the target rest frame. In this review, we discuss the basic features of the diffractive channels of these processes in the framework of color dipole approach. The main observation is a dramatic breakdown of diffractive QCD factorisation due to the interplay between soft and hard interactions, which dominates these processes. This observation is crucial for phenomenological studies of diffractive reactions in high energy hadronic collisions.

Six “beyond Collins and Sivers” transverse spin asymmetries at COMPASS

COMPASS is a fixed-target high energy physics experiment at the SPS at CERN \cite{Abbon:2007pq}. One of the important objectives of the experiment is the exploration of the transverse spin structure of the nucleon via spin dependent azimuthal asymmetries in single-hadron production in deep inelastic scattering of polarized leptons off transversely polarized target. For this purpose a series of measurements were made in COMPASS, using 160 GeV/c longitudinally polarized muon beam and transversely polarized $^6LiD$ (in 2002, 2003 and 2004) and $NH_3$ (in 2007 and 2010) targets. Till now main attention was focused on Collins and Sivers asymmetries and obtained results play an important role in the general understanding of the three-dimensional nature of the nucleon in terms of Transverse Momentum Dependent (TMD) Parton Distribution Functions (PDFs) and Fragmentation Functions (FFs). In addition to these two measured leading-twist effects, the SIDIS cross-section counts six more target transverse spin dependent azimuthal effects, which have their own well defined leading or higher-twist interpretation in terms of QCD parton model. So far COMPASS presented preliminary results for these asymmetries from deuteron \cite{Parsamyan:2007ju},\cite{Kotzinian:2007uv} and "proton-2007" data \cite{Parsamyan:2010se}. In this contribution we review the results obtained with the last "proton-2010" data sample.

Hadron transverse momentum distributions in muon deep inelastic scattering at 160 GeV/c

Multiplicities of charged hadrons produced in deep inelastic muon scattering off a 6LiD target have been measured as a function of the DIS variables x Bj , Q 2, W 2 and the final state hadron variables p T and z. The $p_{T}^{2}$ distributions are fitted with a single exponential function at low values of $p_{T}^{2}$ to determine the dependence of $\langle p_{T}^{2} \rangle$ on x Bj , Q 2, W 2 and z. The z-dependence of $\langle p_{T}^{2} \rangle$ is shown to be a potential tool to extract the average intrinsic transverse momentum squared of partons, $\langle k_{\perp}^{2} \rangle$ , as a function of x Bj and Q 2 in a leading order QCD parton model.

Suppression of high pT hadrons in Pb + Pb collisions at 2.76 TeV

The nuclear modification factor RAA(pT) for large pT hadrons in central Pb + Pb collisions at TeV/n is calculated within the next-to-leading order perturbative QCD parton model with medium-modified fragmentation functions and agree well with the new data. The jet transport parameter that controls medium modification is assumed to be proportional to the initial parton density and the coefficient is fixed by the RHIC data. The charged hadron multiplicity dNch/dη = 1584 ± 80 in central Pb + Pb collisions from the ALICE experiment at the LHC is used to determine both the jet transport parameter and the initial condition for (3+1)D ideal hydrodynamic evolution of the bulk matter that is employed for the calculation of RAA(pT).

Suppression of high-pThadrons in Pb+Pb collisions at energies available at the CERN Large Hadron Collider

Nuclear modification factor $R_{AA}(p_{T})$ for large transverse momentum pion spectra in $Pb+Pb$ collisions at $\sqrt{s}=2.76$ TeV is predicted within the NLO perturbative QCD parton model. Effect of jet quenching is incorporated through medium modified fragmentation functions within the higher-twist approach. The jet transport parameter that controls medium modification is proportional to the initial parton density and the coefficient is fixed by the RHIC data on suppression of large $p_{T}$ hadron spectra. Data on charged hadron multiplicity $dN_{ch}/d\eta=1584 \pm 80$ in central $Pb+Pb$ collisions from the ALICE Experiment at the LHC are used to constrain the initial parton density both for determining the jet transport parameter and the 3+1D ideal hydrodynamic evolution of the bulk matter that is employed for the calculation of $R_{PbPb}(p_{T})$ for neutral pions.

Polarized and unpolarized Drell-Yan angular distribution in the helicity formalism

We present a decomposition of the hadronic tensor for a general polarized Drell-Yan process AB --> l^+ l^- X in terms of helicity structure functions using the helicity axes of the dilepton rest frame as a basis. Next, we consider a QCD parton model and in the framework of a generalized QCD factorization scheme, which applies when the dilepton invariant mass M is much larger than the transverse component of the photon momentum, q_T, in the hadronic center of mass frame. In this approximation we compute the angular distribution of the unpolarized Drell Yan cross section and of the Sivers effect, in single polarized Drell-Yan scattering, by taking into account the transverse motion of partons inside the initial hadrons, k_\perp. Interesting and simple results are found in the kinematical region of k_\perp similar to q_T << M, to first order in a q_T / M expansion. Finally, explicit analytical expressions, convenient for phenomenological studies, are obtained assuming a factorized Gaussian dependence on intrinsic momenta for the unpolarized and Sivers distribution functions, in analogy to those obtained for semi-inclusive deep inelastic scattering.

General helicity formalism for semi-inclusive deep inelastic scattering

We study polarized and unpolarized semi-inclusive deep inelastic scattering processes, $\ensuremath{\ell}({S}_{\ensuremath{\ell}})+p(S)\ensuremath{\rightarrow}{\ensuremath{\ell}}^{\ensuremath{'}}hX$, within a QCD parton model motivated by a generalized QCD factorization scheme. We take into account all transverse motions, of partons inside the initial proton and of hadrons inside the fragmenting partons and use the helicity formalism. The elementary interactions are computed at leading order with noncollinear exact kinematics, which introduces phases in the expressions of their helicity amplitudes. Several transverse momentum dependent distribution and fragmentation functions appear and contribute to the cross sections and to spin asymmetries. Our results agree with those obtained with different formalisms, showing the consistency of our approach. The full expression for single and double spin asymmetries ${A}_{{S}_{\ensuremath{\ell}}S}$ is derived. Simplified, explicit analytical expressions, convenient for phenomenological studies, are obtained assuming a factorized Gaussian dependence on intrinsic momenta for transverse momentum dependent functions.

Transverse spin dependent azimuthal asymmetries at COMPASS

In the semi-inclusive deep inelastic scattering of polarized leptons on a transversely polarized target eight target transverse spin-dependent azimuthal modulations are allowed. In the QCD parton model half of these asymmetries can be interpreted within the leading order approach and the other four are twist-three contributions. The first two leading twist asymmetries extracted by HERMES and COMPASS experiments are related: one to the transversity distribution and the Collins effect, the other to the Sivers distribution function. These results triggered a lot of interest in the past few years and allowed the first extractions of the transversity and the Sivers distribution functions of nucleon. The remaining six asymmetries were obtained by the COMPASS experiment using a 160 GeV/c longitudinally polarized muon beam and transversely polarized deuteron and proton targets. Here we review preliminary results from COMPASS proton data of 2007.

Shadowing effects in direct photon and hadron production in heavy-ion collisions

Nuclear shadowing effects are checked in the production of direct photons and neutral pions in heavy-ion collisions at RHIC/LHC energy within a next-to-leading order perturbative QCD parton model. The transverse momentum dependence of the nuclear modification factors is presented in p + A and A + A collisions to distinguish different parameterizations for nuclear shadowing effects. Our numerical results show that in central A + A collisions the nuclear modification factor for direct photons is more sensitive to shadowing effects than the factor for pion hadrons, and it is a powerful observable to discriminate different parameterizations for parton distributions.

Bulk matter evolution and extraction of jet transport parameters in heavy-ion collisions at energies available at the BNL Relativistic Heavy Ion Collider (RHIC)

Within the picture of jet quenching induced by multiple parton scattering and gluon bremsstrahlung, medium modification of parton fragmentation functions and therefore the suppression of large transverse-momentum hadron spectra are controlled by both the value and the space-time profile of the jet transport parameter along the jet propagation path. Experimental data on single-hadron suppression in high-energy heavy-ion collisions at the Relativistic Heavy Ion Collider energy are analyzed within the higher-twist (HT) approach to the medium-modified fragmentation functions and the next-to-leading order perturbative QCD parton model. Assuming that the jet transport parameter $\mathrm{q\ifmmode \hat{}\else \^{}\fi{}}$ is proportional to the particle number density in both quark gluon plasma (QGP) and hadronic phase, experimental data on jet quenching in deeply inelastic scattering off nuclear targets can provide guidance on ${\mathrm{q\ifmmode \hat{}\else \^{}\fi{}}}_{h}$ in the hot hadronic matter. One can then study the dependence of the extracted initial value of jet-quenching parameter ${\mathrm{q\ifmmode \hat{}\else \^{}\fi{}}}_{0}$ at initial time ${\ensuremath{\tau}}_{0}$ on the bulk medium evolution. Effects of transverse expansion, radial flow, phase transition, and nonequilibrium evolution are examined. The extracted values are found to vary from ${\mathrm{q\ifmmode \hat{}\else \^{}\fi{}}}_{0}{\ensuremath{\tau}}_{0}=0.54$ GeV${}^{2}$ in the ($1+3$)d ideal hydrodynamic model to 0.96 GeV${}^{2}$ in a cascade model, with the main differences coming from the initial nonequilibrium evolution and the later hadronic evolution. The overall contribution to jet quenching from the hadronic phase, about $22%--44$$%$, is found to be significant. Therefore, a realistic description of the early nonequilibrium parton evolution and later hadronic interaction will be critical for accurate extraction of the jet transport parameter in the strongly interacting QGP phase in high-energy heavy-ion collisions.

Gamma-Jet Tomography of Quark-Gluon Plasma in High-Energy Nuclear Collisions

Within the next-to-leading order (NLO) perturbative QCD (pQCD) parton model, suppression of away-side hadron spectra associated with a high p T photon due to parton energy loss is shown to provide a complete tomographic picture of the dense matter formed in high-energy heavy-ion collisions at RHIC. Dictated by the shape of the γ-triggered jet spectrum in NLO pQCD, hadron spectra at large z T = p T h / p T γ ≳ 1 are more susceptible to parton energy loss and therefore are dominated by surface emission of γ-triggered jets, whereas small z T hadrons mainly come from fragmentation of jets with reduced energy from volume emission. These lead to different centrality dependence of the hadron suppression in different regions of z T .

Tomography of High-Energy Nuclear Collisions with Photon-Hadron Correlations

Within the next-to-leading order (NLO) perturbative QCD (PQCD) parton model, suppression of away-side hadron spectra associated with a high pT photon due to parton energy loss is studied in high-energy heavy-ion collisions. Because of the sharp falloff of the gamma-jet spectrum in momentum imbalance pTjet-pTgamma>0 in NLO PQCD, hadron spectra at large zT=pTh/pTgamma greater than approximately 1 are more susceptible to parton energy loss and therefore are dominated by surface emission of gamma-associated jets with almost no energy loss, whereas small zT hadrons mainly come from the volume emission of jets with reduced energy. These lead to different centrality dependence of the gamma-hadron suppression for different values of zT. Therefore, a complete measurement of the suppression of gamma-triggered hadron spectra allows a true tomographic study of the quark-gluon plasma in high-energy heavy-ion collisions.

Multiparton correlations and “exclusive” cross sections

In addition to the inclusive cross sections discussed within the QCD-parton model, in the regime of multiple parton interactions, different and more exclusive cross sections become experimentally viable and may be suitably measured. Indeed, in its study of double parton collisions, the quantity measured by CDF was an "exclusive" rather than an inclusive cross section. The non perturbative input to the "exclusive" cross sections is different with respect to the non perturbative input of the inclusive cross sections and involves correlation terms of the hadron structure already at the level of single parton collisions. The matter is discussed in details keeping explicitly into account the effects of double and of triple parton collisions.

Surface versus volume emissions in photon–hadron correlations

High-p T photon–hadron correlations are studied within the next-to-leading order (NLO) perturbative QCD parton model with modified parton-jet fragmentation functions due to jet quenching in high-energy A+A collisions. In central A+A collisions, the away-side hadrons with large z T=p T /p T are controlled mainly by the surface emission of the gamma-jet events, while a small z T region will be volume emission bias. In other words, gamma jets for a small-z T region probe the dense matter deeper than those gamma jets for a large-z T region, so the small-z T gamma jets are found to be slightly more sensitive to the properties of the dense matter than the large-z T gamma jets.

Azimuthal asymmetry of pions inppandpAcollisions

We investigate the azimuthal asymmetry v{sub 2} of produced pions in pp and pA collisions at both the Relativistic Heavy Ion Collider and CERN SPS energies. In our approach, based on the perturbative QCD parton model and the light-cone QCD-dipole formalism, the azimuthal asymmetry results from a correlation between the color-dipole orientation and the impact parameter of the collision. We introduce the color-dipole orientation within an improved Born approximation and the saturation model which satisfies available deep inelastic scattering data, showing that the azimuthal asymmetry of partons and pions is very sensitive to the choice of the model, and that it is reduced in the saturation model. We find that v{sub 2} of quarks and gluons in parton-nucleus collisions have very different patterns. The azimuthal asymmetry of gluons in gluon-nucleus collisions can be negative at small transverse momentum, and can change sign and become positive at high transverse momentum. The azimuthal asymmetry of quarks in quark-nucleus collisions is positive at all values of transverse momentum. We find that the azimuthal anisotropy v{sub 2} of produced pions in both pp and pA collisions is positive, albeit rather small.