Nucleon Parton Distributions Research Articles

Hadron pair production in semi-inclusive electron positron annihilation process at twist-4

Fragmentation functions are important quantities in describing the hadronization process in high energy reactions. They can induce various azimuthal modulations which can be measured to reveal correlations between transverse momenta and polarizations. Without introducing initial state uncertainties, electron positron annihilation process is known as an ideal process to investigate the fragmentation functions. In this paper, therefore, we calculate the hadron pair production in the semi-inclusive electron positron annihilation process e^+ + e^- rightarrow h_1+h_2 + {bar{q}} +X at twist-4 to study dihadron fragmentation functions. Here {bar{q}} denotes an antiquark that corresponds to a jet of hadrons in experiments. Together with single hadron fragmentation functions, dihadron fragmentation functions can provide additional ways to extract nucleon parton distribution functions from the semi-inclusive deeply inelastic scattering experiments with two detected final state hadrons. We calculate the differential cross section of the hadron pair production semi-inclusive electron positron annihilation process at twist-4 level. The calculation is carried out by using the collinear expansion method. We also calculate azimuthal asymmetries in terms of dihadron fragmentation functions. Contributions from four-quark correlator are also taken into account. Both the electromagnetic and weak interactions are considered in this paper.

QCD factorization for chiral-odd parton quasi- and pseudo-distributions

We study chiral-odd quark-antiquark correlation functions suitable for lattice calculations of twist-three nucleon parton distribution functions hL(x) and e(x), and also the twist-two transversity distribution δq(x). The corresponding factorized expressions are derived in terms of the twist-two and twist-three collinear distributions to one-loop accuracy. The results are presented both in position space, as the factorization theorem for Ioffe-time distributions, and in momentum space, for quasi- and pseudo-distributions. We demonstrate that the twist-two part of the hL quasi(pseudo)-distribution can be separated from the twist-three part by virtue of an exact Jaffe-Ji-like relation.

QCD factorization for twist-three axial-vector parton quasidistributions

The transverse component of the axial-vector correlation function of quark fields is a natural starting object for lattice calculations of twist-3 nucleon parton distribution functions. In this work we derive the corresponding factorization expression in terms of twist-2 and twist-3 collinear distributions to one-loop accuracy. The results are presented both in position space, as the factorization theorem for Ioffe-time distributions, and in momentum space, for the axial-vector quasi- and pseudodistributions.

Neural-network analysis of Parton Distribution Functions from Ioffe-time pseudodistributions

We extract two nonsinglet nucleon Parton Distribution Functions from lattice QCD data for reduced Ioffe-time pseudodistributions. We perform such analysis within the NNPDF framework, considering data coming from different lattice ensembles and dis- cussing in detail the treatment of the different source of systematics involved in the fit. We introduce a recipe for taking care of systematics and use it to perform our extraction of light-cone PDFs.

Parton Distributions in Nucleons and Nuclei

We review the current status of parton distribution function (PDF) determinations for unpolarized and longitudinally polarized protons and for unpolarized nuclei, which are probed by high-energy hadronic scattering in perturbative quantum chromodynamics (QCD). We present the established theoretical framework, the experimental information, and the methodological aspects inherent to any modern PDF extraction. Furthermore, we summarize the present knowledge of PDFs and discuss their limitations in both accuracy and precision relevant to advancing our understanding of QCD proton substructure and pursuing our quest for precision in the Standard Model and beyond. In this respect, we highlight various achievements, discuss contemporary issues in PDF analyses, and outline future directions of progress.

Parton distribution functions from Ioffe time pseudo-distributions

In this paper, we present a detailed study of the unpolarized nucleon parton distribution function (PDF) employing the approach of parton pseudo-distribution func- tions. We perform a systematic analysis using three lattice ensembles at two volumes, with lattice spacings a = 0.127 fm and a = 0.094 fm, for a pion mass of roughly 400 MeV. With two lattice spacings and two volumes, both continuum limit and infinite volume ex- trapolation systematic errors of the PDF are considered. In addition to the x dependence of the PDF, we compute their first two moments and compare them with the pertinent phenomenological determinations.

Charting the coming synergy between lattice QCD and high-energy phenomenology

Building upon the PDFSense framework developed in Ref. [1], we perform a comprehensive analysis of the sensitivity of present and future high-energy data to a number of quantities commonly evaluated in lattice gauge theory, with a particular focus on the integrated Mellin moments of nucleon parton distribution functions (PDFs), such as $\langle x \rangle_{u^+ - d^+}$ and $\langle x \rangle_{g}$, as well as $x$-dependent quark quasi-distributions -- in particular, that of the isovector combination. Our results demonstrate the potential for lattice calculations and phenomenological quark distributions informed by high-energy experimental data to cooperatively improve the picture of the nucleon's collinear structure. This will increasingly be the case as computational resources for lattice calculations further expand, and QCD global analyses continue to grow in sophistication. Our sensitivity analysis suggests that a future lepton-hadron collider would be especially instrumental in providing phenomenological constraints to lattice observables.

Nucleon resonance contributions to unpolarized inclusive electron scattering

The first CLAS12 experiments will provide high-precision data on inclusive electron scattering observables at a photon virtuality $Q^2$ ranging from 0.05 GeV$^2$ to 12 GeV$^2$ and center-of-mass energies $W$ up to 4 GeV. In view of this endeavour, we present the modeling of the resonant contributions to the inclusive electron scattering observables. As input, we use the existing CLAS electrocoupling results obtained from exclusive meson electroproduction data off protons, and evaluate for the first time the resonant contributions based on the experimental results on the nucleon resonance electroexcitation. The uncertainties are given by the data and duly propagated through a Monte Carlo approach. In this way, we obtain estimates for the resonant contributions, important for insight into the nucleon parton distributions in the resonance region and for the studies of quark-hadron duality.

Nucleon parton distributions from hadronic quantum fluctuations

A physical model is presented for the nonperturbative parton distributions in the nucleon. This is based on quantum fluctuations of the nucleon into baryon-meson pairs convoluted with Gaussian momentum distributions of partons in hadrons. The hadronic fluctuations, here developed in terms of hadronic chiral perturbation theory, occur with high probability and generate sea quarks as well as dynamical effects also for valence quarks and gluons. The resulting parton momentum distributions $f(x,{Q}_{0}^{2})$ at low momentum transfers are evolved with conventional Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equations from perturbative QCD to larger scales. This provides parton density functions $f(x,{Q}^{2})$ for the gluon and all quark flavors with only five physics-motivated parameters. By tuning these parameters, experimental data on deep-inelastic structure functions can be reproduced and interpreted. The contribution to sea quarks from hadronic fluctuations explains the observed asymmetry between $\overline{u}$ and $\overline{d}$ in the proton. The strange-quark sea is strongly suppressed at low ${Q}^{2}$, as observed.

Low Q2 boundary conditions for DGLAP equations dictated by quantum statistical mechanics

We discuss the role of quantum statistical mechanics in the description of the parton distribution functions in the proton. It provides the low Q2 boundary conditions for DGLAP equations in terms of Fermi–Dirac and Bose–Einstein functions of the fractional momentum variable x. The successful comparison with experimental data on both the unpolarised and polarised deep inelastic structure functions is reviewed. We argue that the statistical approach for the nucleon parton distributions functions has the nice feature that the free model parameters are fixed from data with high statistics and small systematic uncertainties, providing a strong constraint on the information not supplied by the experiments.

Nucleon and nuclear structure functions with nonperturbative and higher order perturbative QCD effects

We have studied the nucleon structure functions $F_{iN}^{EM} (x,Q^2);~i=1,2$, by including contributions due to the higher order perturbative QCD effect up to NNLO and the non-perturbative effects due to the kinematical and dynamical higher twist (HT) effects. The numerical results for $F_{iN}^{EM}(x,Q^2)$ are obtained using Martin, Motylinski, Harland-Lang, Thorne (MMHT) 2014 NLO and NNLO nucleon parton distribution functions (PDFs). The dynamical HT correction has been included following the renormalon approach as well as the phenomenological approach and the kinematical HT effect is incorporated using the works of Schienbein et al. These nucleon structure functions have been used as an input to calculate the nuclear structure functions $F_{iA}^{EM} (x,Q^2)$. In a nucleus, the nuclear corrections arise because of the Fermi motion, binding energy, nucleon correlations, mesonic contribution, shadowing and antishadowing effects. These nuclear corrections are taken into account in the numerical calculations to obtain the nuclear structure functions $F_{iA}^{EM} (x,Q^2)$, for the various nuclear targets like $^{12}C$, $^{27}Al$, $^{56}Fe$, $^{64}Cu$, $^{118}Sn$, $^{197}Au$ and $^{208}Pb$ which are of experimental interest. The effect of isoscalarity correction for nonisoscalar nuclear targets has also been studied. The results for the $F_{iA}^{EM} (x,Q^2)$ are compared with nCTEQ nuclear PDFs parameterization as well as with the experimental results from JLab, SLAC and NMC in the kinematic region of $0.1 \le x \le 0.8$ for several nuclei.

Parton distributions from nonlocal chiral SU(3) effective theory: Splitting functions

We present a new formulation of pseudoscalar meson loop corrections to nucleon parton distributions within a nonlocal covariant chiral effective field theory, including contributions from SU(3) octet and decuplet baryons. The nonlocal Lagrangian, constrained by requirements of local gauge invariance and Lorentz-invariant ultraviolet regularization, generates additional interactions associated with gauge links. We use these to compute the full set of proton $\to$ meson + baryon splitting functions, which in general contain on-shell and off-shell contributions, in addition to $\delta$-function terms at zero momentum, along with nonlocal contributions associated with the finite size of the proton. We illustrate the shapes of the various local and nonlocal functions numerically using a simple example of a dipole regulator.

Semi-inclusive production of two back-to-back hadron pairs in e+e− annihilation revisited

The cross section for back-to-back hadron pair production in $e^+e^-$ annihilation provides access to the dihadron fragmentation functions (DiFF) needed to extract nucleon parton distribution functions from the semi-inclusive deep inelastic scattering (SIDIS) experiments with two detected final state hadrons. Particular attention is given to the so-called interference DiFF (IFF), which makes it possible to extract the transversity parton distribution of the nucleon in the collinear framework. However, previously unnoticed discrepancies were recently highlighted between the definitions of the IFFs appearing in the collinear kinematics when reconstructed from DiFFs entering the unintegrated fully differential cross sections of SIDIS and $e^+e^-$ annihilation processes. In this work, to clarify this problem we rederive the fully differential cross section for $e^+e^-$ annihilation at the leading-twist approximation. We find a mistake in the definition of the kinematics in the original expression that systematically affects a subset of terms and that leads to two significant consequences. First, the discrepancy between the IFF definitions in the cross sections for SIDIS and $e^+e^-$ annihilation is resolved. Second, the previously derived azimuthal asymmetry for accessing the helicity dependent DiFF $G_1^\perp$ in $e^+e^-$ annihilation vanishes, which explains the nonobservation of this asymmetry in the recent experimental searches by the ${\tt BELLE}$ Collaboration. We discuss the recently proposed alternative option to extract $G_1^\perp$.

Transverse-momentum-dependent fragmentation functions in e+e- annihilation

Fragmentation functions are non-perturbative functions used to describe the formation of colorless, observable hadrons starting from a colored, partonic initial state. The knowledge of these functions are based on the experimental data, and a good parameterization of the fragmentation processes can shed light on the confining aspect of QCD, and are also a key ingredient in accessing nucleon parton distribution functions in semi-inclusive deep inelastic scattering and proton-proton collisions. In the last decade, a strong interest has risen about the transverse-momentum-dependent (TMD) fragmentation functions, which can be used as tools to probe the 3D-structure of nucleons, and to investigate the Q2 evolution of TMD objects. In this review we will summarize the existing light-quarks fragmentation related measurements from the BaBar, Belle, and BESIII e + e - experiments; in particular, we will focus on the polarized TMD Collins fragmentation functions, emerging from correlations between the transverse polarization of the fragmenting parton and the direction of the resulting hadrons.

Centrality, rapidity, and transverse momentum dependence of isolated prompt photon production in lead-lead collisions atsNN=2.76TeV measured with the ATLAS detector

Prompt photon production in $\sqrt{s_{\mathrm{NN}}} = 2.76$ TeV Pb+Pb collisions has been measured by the ATLAS experiment at the Large Hadron Collider using data collected in 2011 with an integrated luminosity of 0.14 nb$^{-1}$. Inclusive photon yields, scaled by the mean nuclear thickness function, are presented as a function of collision centrality and transverse momentum in two pseudorapidity intervals, $|\eta| < 1.37$ and $1.52 < |\eta| < 2.37$. The scaled yields in the two pseudorapidity intervals, as well as the ratios of the forward yields to those at midrapidity, are compared to the expectations from next-to-leading order perturbative QCD calculations from JETPHOX. The measured cross sections agree well with the predictions for proton-proton collisions within statistical and systematic uncertainties. Both the yields and ratios are also compared to two other pQCD calculations, one which uses the isospin content appropriate to colliding lead nuclei, and another which includes the EPS09 nuclear modifications to the nucleon parton distribution functions.

Consistency check of charged hadron multiplicities and fragmentation functions in SIDIS

We derived the conditions on certain combinations of integrals of the fragmentation functions of pion using HERMES data of the sum for the charged pion multiplicities from semi-inclusive deep-inelastic scattering (SIDIS) off the deuteron target. In our derivation the nucleon parton distribution functions (PDFs) are assumed to be isospin SU(2) symmetric. Similar conditions have also been obtained for the fragmentation functions (FFs) of kaon by the sum of charged kaon multiplicities as well. We have chosen several FFs to study the impact of those conditions we have derived. Among those FFs, only that produced in the nonlocal chiral-quark model (NL$\chi$QM) constantly satisfy the conditions. Furthermore, the ratios of the strange PDFs $S(x)$ and the nonstrange PDFs $Q(x,Q^2)$ extracted from the charged pion and kaon multiplicities differ from each other significantly. Finally, we demonstrate that the HERMES pion multiplicity data is unlikely to be compatible with the two widely-used PDFs, namely CTEQ6M and NNPDF3.0.

Research on parton distributions in nucleon

We present the parton distributions at leading order(LO) coming from GJR,MSTW and CTEQ parton sets and compare them at different momentum scales.Obvious differences exist in their gluon and sea quark distributions at small x region.Itindicates that people have not known the nucleon parton distributions very well.We analysze the influence of higher twist effects,i.e.,the shadowing effects and anti-shadowing effects,on parton distributions.Because of the shadowing effects,the twist-4 gluon and sea quark distributions are smaller than the twist-2 distributions at small and middle x region,while,the anti-shadowing effects make the twist-4 gluon and sea quark distributions larger than the twist-2 distributions at x≥2 region.Finally,we present a detailed analysis of how the proton's momentum is shared among various parton flavors at different Q~2 for different parton sets.With the numerical calculation,we show that the MD-DGLAP equations are momentum conservation.

Next-to-next-to-leading-order nucleon parton distributions from a light-cone quark model dressed with its virtual meson cloud

A detailed study of nucleon parton distribution functions is performed within a radiative Next-to-Next-to Leading Order (NNLO) parton model whose low-scale input is rigidly described by wave functions which include quarks and dressing meson-cloud. The light-front Hamiltonian dynamics fixes the three-quark wave functions and the meson cloud is introduced by means of high-order Fock component in time-ordered perturbation theory in the infinite momentum frame. Non-strange as well as strange mesons-baryon fluctuations are considered ($\pi$, $\rho$, $\omega$, $K$ and $K^*$, together with $N$, $\Delta$, $\Lambda$ and $\Sigma$) and the effects on strange and non-strange parton distributions investigated showing the large effects due to (non-strange) sea asymmetries and the delicate balance of the strange asymmetry. The non-strange and the strange components, the valence as well as the gluon distributions are compared with available experimental data confirming the need of both non-perturbative degrees of freedom and perturbative (NNLO) radiative effects.

RECENT PROGRESS ON NUCLEON STRUCTURE WITH LATTICE QCD

I review recent progress made in the calculation of nucleon structure in lattice QCD. Due to space limitations, I will focus on a few specific topics: systematic control of lattice-QCD matrix elements, probing TeV-physics with the aid of nucleon tensor and scalar charges, and Bjorken-x dependence of nucleon parton distribution functions.

Event-by-event gluon multiplicity, energy density, and eccentricities in ultrarelativistic heavy-ion collisions

The event-by-event multiplicity distribution, the energy densities and energy density weighted eccentricity moments ${\ensuremath{\epsilon}}_{n}$ (up to $n=6$) at early times in heavy-ion collisions at both the BNL Relativistic Heavy Ion Collider (RHIC) ($\sqrt{s}=200\phantom{\rule{0.16em}{0ex}}\mathrm{GeV}$) and the CERN Large Hardron Collider (LHC) ($\sqrt{s}=2.76\phantom{\rule{0.16em}{0ex}}\mathrm{TeV}$) are computed in the IP-Glasma model. This framework combines the impact parameter dependent saturation model (IP-Sat) for nucleon parton distributions (constrained by HERA deeply inelastic scattering data) with an event-by-event classical Yang-Mills description of early-time gluon fields in heavy-ion collisions. The model produces multiplicity distributions that are convolutions of negative binomial distributions without further assumptions or parameters. In the limit of large dense systems, the $n$-particle gluon distribution predicted by the Glasma-flux tube model is demonstrated to be nonperturbatively robust. In the general case, the effect of additional geometrical fluctuations is quantified. The eccentricity moments are compared to the MC-KLN model; a noteworthy feature is that fluctuation dominated odd moments are consistently larger than in the MC-KLN model.