Quark Distribution Functions Research Articles

Extraction of quark transversity distribution and Collins fragmentation functions with QCD evolution

We study the transverse momentum dependent (TMD) evolution of the Collins azimuthal asymmetries in $e^+e^-$ annihilations and semi-inclusive hadron production in deep inelastic scattering (SIDIS) processes. All the relevant coefficients are calculated up to the next-to-leading logarithmic (NLL) order accuracy. By applying the TMD evolution at the approximate NLL order in the Collins-Soper-Sterman (CSS) formalism, we extract transversity distributions for $u$ and $d$ quarks and Collins fragmentation functions from current experimental data by a global analysis of the Collins asymmetries in back-to-back di-hadron productions in $e^+e^-$ annihilations measured by BELLE and BABAR Collaborations and SIDIS data from HERMES, COMPASS, and JLab HALL A experiments. The impact of the evolution effects and the relevant theoretical uncertainties are discussed. We further discuss the TMD interpretation for our results, and illustrate the unpolarized quark distribution, transversity distribution, unpolarized quark fragmentation and Collins fragmentation functions depending on the transverse momentum and the hard momentum scale. We make detailed predictions for future experiments and discuss their impact.

Quark and gluon distribution functions in a viscous quark-gluon plasma medium and dilepton production viaqq¯annihilation

Viscous modifications to the thermal distributions of quark-antiquarks and gluons have been studied in a quasi-particle description of the quark-gluon-plasma medium created in relativistic heavy ion collision experiments. The model is described in terms of quasi-partons that encode the hot QCD medium effects in their respective effective fugacities. Both shear and bulk viscosities have been taken in to account in the analysis and the modifications to thermal distributions have been obtained by modifying the the energy momentum tensor in view of the non-trivial dispersion relations for the gluons and quarks. As an implication, dilepton production rate in the $q \bar{q}$ annihilation process has been investigated. Significant modifications have been observed in the dilepton production rate in the presence of interactions encoded in the QCD equation of state.

Effective model for the QCD phase transitions at finite baryon density

We introduce an effective quark-meson-nucleon model for the QCD phase transitions at finite baryon density. The nucleon and the quark degrees of freedom are described within a unified framework of a chiral linear sigma model. The deconfinement transition is modeled through a simple modification of the distribution functions of nucleons and quarks, where an additional auxiliary field, the bag field, is introduced. The bag field plays a key role in converting between the nucleon and the quark degrees of freedom. The model predicts that the chiral and the deconfinement phase transitions are always separated. Depending on the model parameters, the chiral transition occurs in the baryon density range of $(1.5-15.5)n_0$, while the deconfinement transition occurs above $5 n_0$, where $n_0$ is the saturation density.

Quark flavor distribution functions for the octet baryons in the chiral quark constituent model

The quark flavor distribution functions of the octet baryons ($N$, $\mathrm{\ensuremath{\Sigma}}$, $\mathrm{\ensuremath{\Xi}}$, and $\mathrm{\ensuremath{\Lambda}}$) have been calculated in the chiral constituent quark model. In particular, the valence and sea quark flavor distribution functions of the scalar density matrix elements of octet baryons have been computed explicitly. The implications of chiral symmetry breaking and SU(3) symmetry breaking have been discussed in detail for the sea quark asymmetries, a fraction of a particular quark (antiquark) present in a baryon, flavor structure functions and the Gottfried integral. The meson-baryon sigma terms ${\ensuremath{\sigma}}_{\ensuremath{\pi}B}$, ${\ensuremath{\sigma}}_{KB}$, and ${\ensuremath{\sigma}}_{\ensuremath{\eta}B}$ for the case of $N$, $\mathrm{\ensuremath{\Sigma}}$, and $\mathrm{\ensuremath{\Xi}}$ baryons have also been calculated. The results have been compared with the recent available experimental observations for the case of $N$, and how the future experiments for $\mathrm{\ensuremath{\Sigma}}$, $\mathrm{\ensuremath{\Xi}}$, and $\mathrm{\ensuremath{\Lambda}}$ can provide important constraints to describe the role of nonvalence (sea) degrees of freedom has been discussed.

Electron structure: Shape, size, and generalized parton distributions in QED

The shape of the electron is studied using lowest-order perturbation theory. Quantities used to probe the structure of the proton---form factors, generalized parton distributions, transverse densities, Wigner distributions and the angular momentum content---are computed for the electron-photon component of the electron wave function. The influence of longitudinally polarized photons, demanded by the need for infrared regularization via a nonzero photon mass, is included. The appropriate value of the photon mass depends on experimental conditions, and consequently the size of the electron (as defined by the slope of its Dirac form factor) bound in a hydrogen atom is found to be about four times larger than when the electron is in a continuum scattering state. The shape of the electron, as determined from the transverse density and generalized parton distributions, is shown not to be round, and the continuum electron is shown to be far less round than the bound electron. An electron distribution function (analogous to the quark distribution function) is defined, and that of the bound electron is shown to be suppressed compared to that of the continuum electron. If the relative transverse momentum of the virtual electron and photon is large compared with the electron mass, the virtual electron and photon each carry nearly the total angular momentum of the physical electron ($1/2$), with the orbital angular momentum being nearly ($\ensuremath{-}1/2$). Including the nonzero photon mass leads to the suppression of end-point contributions to form factors. Implications for proton structure and color transparency are discussed.

Uncertainties of Drell-Yan production cross section in pp collisions at the LHC

The results of calculations of uncertainties of the Drell-Yan production cross section at the energy √s = 13 TeV are presented. Systematic errors related to uncertainties in the quark and gluon distribution functions, the choice of the QCD factorization scale, and the QCD running coupling constant are considered.

The Glasma, photons and the implications of anisotropy

We introduce distribution functions for quarks and gluons in the Glasma and discuss how they satisfy various relationships of statistical physics. We use these distributions to compute photon production in the early stages of heavy ion collisions. Photon rates satisfy geometric scaling, that is, the emission rate per unit area scales as a function of the saturation momenta divided by the transverse momentum of the photon. Photon distributions from the Glasma are steeper than those computed in the Thermalized Quark Gluon Plasma (TQGP). Both the delayed equilibration of the Glasma and a possible anisotropy in the pressure lead to slower expansion and mean times of photon emission of fixed energy are increased. This delayed emission might allow for larger photon elliptic flow.

The quark beam function at two loops

In differential measurements at a hadron collider, collinear initial-state radiation is described by process-independent beam functions. They are the field-theoretic analog of initial-state parton showers. Depending on the measured observable they are differential in the virtuality and/or transverse momentum of the colliding partons in addition to the usual longitudinal momentum fraction. Perturbatively, the beam functions can be calculated by matching them onto standard quark and gluon parton distribution functions. We calculate the inclusive virtuality-dependent quark beam function at NNLO, which is relevant for any observables probing the virtuality of the incoming partons, including N-jettiness and beam thrust. For such observables, our results are an important ingredient in the resummation of large logarithms at N3LL order, and provide all contributions enhanced by collinear t-channel singularities at NNLO for quark-initiated processes in analytic form. We perform the calculation in both Feynman and axial gauge and use two different methods to evaluate the discontinuity of the two-loop Feynman diagrams, providing nontrivial checks of the calculation. As part of our results we reproduce the known two-loop QCD splitting functions and confirm at two loops that the virtuality-dependent beam and final-state jet functions have the same anomalous dimension.

Nuclear dependencies of azimuthal asymmetries in the Drell-Yan process

We study nuclear dependences of azimuthal asymmetries in the Drell-Yan lepton pair production in nucleon-nucleus collisions with polarized nucleons.We use the "maximal two-gluon correlation approximation", so that we can relate the transverse momentum dependent quark distribution in a nucleus to that in a nucleon by a convolution with a Gaussian broadening.We use the Gaussian ansatz for the transverse momentum dependence of such quark distribution functions,and obtain the numerical results for the nuclear dependences.These results show that the averaged azimuthal asymmetries are suppressed.

Charge asymmetry of weak boson production at the LHC and the charm content of the proton

We investigate the production of the weak bosons $W^+$, $W^-$ and $Z$ at the LHC as a function of their rapidity, reconstructed {\it experimentally} from their leptonic decay. We show that the measurements provide a powerful tool for constraining the parton distribution functions, as was already the case for the lower energy $p\bar{p}$ collider data. We study the charge asymmetry determining the $u$ and $d$ distribution functions using the reconstructed $W^+$, $W^-$ rapidities. We also show how the ratio of the $W$ and $Z$ boson rapidity distributions directly probes the charm quark distribution function of the proton.

Charge symmetry breaking from a chiral extrapolation of moments of quark distribution functions

We present a determination, from lattice QCD, of charge symmetry violation in the spin-independent and spin-dependent parton distribution functions of the nucleon. This is done by chirally extrapolating recent QCDSF/UKQCD Collaboration lattice simulations of the first several Mellin moments of the parton distribution functions of octet baryons to the physical point. We find small chiral corrections for the polarized moments, while the corrections are quantitatively significant in the unpolarized case.

Hadron Structure Function in Flux Tube Model

The quark distribution functions of the meson (q-q̅ system) and the nucleon (both q-diquark system and symmetric Y shape system) are calculated using the yo-yo mode of the classical string model. The valence quark distributions of the proton are consistent with intermediate value of q-diquark and symmetric Y shape calculation. Using the Weizsäcker-Williams approximation, the gluon distribution function is obtained from the Poynting vector of the flux tube which has the same energy-momentum relation as the string.

Probing the nucleon structure with SIDIS at Jefferson Lab.

In recent years, measurements of azimuthal moments of polarized hadronic cross sections in hard processes have emerged as a powerful tool to probe nucleon structure. Many experiments worldwide are currently trying to pin down various effects related to nucleon structure through Semi-Inclusive Deep-Inelastic Scattering (SIDIS). Azimuthal distributions of final-state particles in semi-inclusive deep inelastic scattering, in particular, are sensitive to the orbital motion of quarks and play an important role in the study of Transverse Momentum Dependent parton distribution functions (TMDs) of quarks in the nucleon. The CLAS spectrometer, installed in Hall-B at Jefferson Lab, has collected semi-inclusive data using the CEBAF 6 GeV polarized electron beam on polarized solid NH3 and ND3 targets. An overview of these measurements is presented.

Effective nucleon mass and thermodynamics in the quark-meson coupling model

In this work, we study the quark energy spectrum in an MIT bag using the quark-meson coupling model. In particular, thermal distribution functions of quarks at finite temperature are explicitly incorporated into the calculations. It is found that when temperature is less than 50 MeV, the probability for a quark to occupy an exciting state is very rare and negligible, therefore the corresponding contributions to the thermodynamic potential undermean-field theory are strongly suppressed. In this context, if one calculates other physical quantities derived from thermodynamic potential, effects due to quark distribution functions are also likely to be unimportant. DOI: 10.1103/PhysRevC.86.068201

Charm Production in Association with an Electroweak Gauge Boson at the LHC

The production of charm quark jets in association with electroweak gauge bosons at the LHC can be used as a tool to constrain quark parton distribution functions (PDFs). Motivated by recent measurements at the Tevatron and LHC, we calculate cross sections for W/Z+c, comparing these to W/Z+jet, for various PDF sets. The cross-section differences can be understood in terms of the different underlying PDFs, with the strange quark distribution being particularly important for W+c production. We suggest measurements of appropriately defined ratios and comment on how these measurements at the LHC can be used to extract information on the strange and charm content of the proton at high Q(2) scales.

Parton energy loss in cold nuclei

Within the generalized high-twist factorization formalism, we express the contribution from multiple parton scattering and induced gluon radiation to the DY dilepton spectra in terms of nuclear modified e ective beam quark distribution function. We show that beam quark energy loss is characterized by jet transport parameter ˆ q, which is related to the local gluon density of the medium. Using the value of ˆ q determined from the deeply inelastic scattering (DIS) data, we evaluate the nuclear modification factor in the Drell-Yan process in p+A collisions. E ects of parton energy loss in the DY spectra are found negligible in the Fermilab experimental data at Elab = 800 GeV relative to parton shadowing while the predicted suppression of the DY spectra are significant at Elab = 120 GeV.

Fragmentation and quark distribution functions for the pion and kaon with explicit flavor-SU(3)-symmetry breaking

We investigate the unpolarized pion and kaon fragmentation functions, employing the nonlocal chiral-quark model, which manifests the nonlocal interactions between the quarks and pseudoscalar mesons, considering the explicit flavor-SU(3)-symmetry breaking in terms of the current-quark masses. Moreover, we study the quark-distribution functions, derived from the fragmentation ones with the Drell-Yan-Levi relation. Numerical results are evaluated to higher Q^2 by the DGLAP evolution and compared with the empirical data. The ratios between the relevant valance quark-distribution functions are also discussed. It turns out that the present results are in relatively good agreement with available data and other theoretical estimations.

Transverse-momentum-dependent fragmentation and quark distribution functions from the Nambu–Jona-Lasinio–jet model

Using the model of Nambu and Jona-Lasinio to provide a microscopic description of both the structure of the nucleon and of the quark to hadron elementary fragmentation functions, we investigate the transverse momentum dependence of the unpolarized quark distributions in the nucleon and of the quark to pion and kaon fragmentation functions. The transverse momentum dependence of the fragmentation functions is determined within a Monte Carlo framework, with the notable result that the average $P_\perp^2$ of the produced kaons is significantly larger than that of the pions. We also find that $<P_\perp^2>$ has a sizable $z$ dependence, in contrast with the naive Gaussian ansatz for the fragmentation functions. Diquark correlations in the nucleon give rise to a non-trivial flavor dependence in the unpolarized transverse momentum dependent quark distribution functions. The $<k_T^2>$ of the quarks in the nucleon are also found to have a sizable $x$ dependence. Finally, these results are used as input to a Monte Carlo event generator for semi-inclusive deep inelastic scattering (SIDIS), which is used to determine the average transverse momentum squared of the produced hadrons measured in SIDIS, namely $<P_T^2>$. Again we find that the average $P_T^2$ of the produced kaons in SIDIS is significantly larger than that of the pions and in each case $\la P_T^2 \ra$ has a sizable $z$ dependence.

Quark distributions and gluon contents of η and η′

Using the QCD sum rule, we calculate valance quark distribution functions of η and η′ in a chiral limit. Extrapolating the calculated quark distribution functions at both end regions, their first two moments have been calculated and compared with those of other hadrons.

Single jet and prompt-photon inclusive production with multi-Regge kinematics: From Tevatron to LHC

We study single jet and prompt-photon inclusive hadroproduction with multi-Regge kinematics invoking the hypothesis of parton Reggeization in t-channel exchanges at high energy. In this approach, the leading contributions are due to the fusion of two Reggeized gluons into a Yang-Mills gluon and the annihilation of a Reggeized quark-antiquark pair into a photon, respectively. Adopting the Kimber-Martin-Ryskin and Bluemlein prescription to derive unintegrated gluon and quark distribution functions of the proton from their collinear counterparts, for which we use the Martin-Roberts-Stirling-Thorne set, we evaluate cross section distributions in transverse momentum (p_T) and rapidity. Without adjusting any free parameters, we find good agreement with measurements by the CDF and D0 Collaborations at the Tevatron and by the ATLAS Collaboration at the LHC in the region 2p_T/sqrt{S} < 0.1, where sqrt{S} is the hadronic c.m. energy.