Integrated and Unintegrated Parton Distributions

We compare the twist-2 and twist-4 parton distributions both in integrated and unintegrated parton distributions. We find that when x decreases the difference between the twist-2 and twist-4 patton distributions become obvious except for the valence quark distributions. We hope the future experiments may distinguish whether the twist-4 correction is needed or not and select a reasonable unintegrated parton distribution model

QCD Predictions for Spin Dependence of Parton Distributions

We introduce the polarized valon distributions to describe the spin dependence of parton distributions.The polarized valon distributions in the proton and polarized parton distributions inside the valon can help to obtain polarized parton distribution in a proton. In order to be able to obtain the spin contribution of sea quarks, we need to improve the valon model We employ the Bernstein polynomial averages to obtain the unknown parameters which exist in our calculations. Our results for the polarized proton structure function, xg1p, are in good agreement with the experimental data for some values of Q2.

Revealing pion and kaon structure via generalised parton distributions

Clear windows onto emergent hadron mass(EHM)and modulations thereof by Higgs boson interactions are provided by observable measures of pion and kaon structure,many of which are accessible via generalised parton distributions(GPDs).Beginning with algebraic GPD Ansätze,constrained entirely by hadron-scaleπand K valence-parton distribution functions(DFs),in whose forms both EHM and Higgs boson influences are manifest,numerous illustrations are provided.They include the properties of electromagnetic form factors,impact parameter space GPDs,gravitational form factors and associated pressure profiles,and the character and consequences of allorders evolution.The analyses predict that mass-squared gravitational form factors are stiffer than electromagnetic form factors;reveal that K pressure profiles are tighter than profiles,with both mesons sustaining near-core pressures at magnitudes similar to that expected at the core of neutron stars;deliver parameter-free predictions for and K valence,glue,and sea GPDs at the resolving scale l=2GeV;and predict that at this scale the fraction of meson mass-squared carried by glue and sea combined matches that lodged with the valence degrees-of-freedom,with a similar statement holding for mass-squared radii.

Regularization dependence of pion generalized parton distributions

Pion generalized parton distributions are calculated within the framework of the Nambu-Jona-Lasinio model using different regularization schemes,including the proper time regularization scheme,the three-dimensional(3D)momentum cutoff scheme,the four-dimensional momentum cutoff scheme,and the Pauli-Villars regularization scheme.Furthermore,we check the theoretical constraints of pion generalized parton distributions required by the symmetries of quantum chromodynamics in different regularization schemes.The diagrams of pion parton distribution functions are plotted,in addition,we evaluate the Mellin moments of generalized parton distributions,which are related to the electromagnetic and gravitational form factors of pion.Pion generalized parton distributions are continuous but not differential at x=±ξ,when considering the effect of the contact contribution term,generalized parton distributions become not continuous at x=±ξin all the four regularization schemes.Generalized parton distributions in impact parameter space are considered,the width distribution of u quark in the pion and the meansquared<b_(⊥)^(2)>πu are calculated.The light-front transverse-spin distributions are studied when quark polarized in the light-front-transverse+x direction,the transverse-spin density is no longer symmetric around(bx=0,by=0),the peaks shift to(bx=0,by>0),we compare the average transverse shift<b_(⊥)^(y)>1u and<b_(⊥)^(y)>2u in different regularization schemes.The light-cone energy radius rE,LC and the light-cone charge radius rc,LC are also evaluated,we found that in the proper time regularization scheme the values of these quantities were the largest,in the 3 D momentum cutoff scheme they were the smallest.

Drawing insights from pion parton distributions

A symmetry-preserving continuum approach to the two valence-body bound-state problem is used to calculate the valence, glue and sea distributions within the pion; unifying them with, inter alia, electromagnetic pion elastic and transition form factors. The analysis reveals the following momentum fractions at the scale ζ2:= 2GeV :〈xvalence〉 = 0.48（3）, 〈xglue〉 = 0.41（2）, 〈xsea〉 = 0.11（2）;and despite hardening induced by the emergent phenomenon of dynamical chiral symmetry breaking, the valence-quark distribution function, qπ（x）, exhibits the x ≈ 1 behaviour predicted by quantum chromodynamics（QCD）. After evolution to o ζ = 5.2 GeV, the prediction for qπ（x） matches that obtained using lattice-regularised QCD. This confluence should both stimulate improved analyses of existing data and aid in planning efforts to obtain new data on the pion distribution functions.

A New Research about Pion Parton Distribution Function

A new fit of the pion parton distribution functions is provided. Only valence quark distributions are used at a low evolution scale and are evolved with the modified Dokshitzer- Gribov-Lipatov-Altarelli-Parisi equation which is briefly introduced in this work, and the sea quark and gluon distributions are only generated by the quantum chromodynamics processes. We find that the patton distributions can explain the pion-nucleon experiments data well, and it can also be compared with the data from the leading neutron data of experiments at HERA. The momentum distributions among the partons are discussed and our results are consistent with some models.

Reconstructing parton distribution function based on maximum entropy method

A new method based on the maximum entropy principle for reconstructing the parton distribution function(PDF)from moments is proposed.Unlike traditional methods,the new method does not require any artificial assumptions.For the case of moments with errors,we introduce Gaussian functions to soften the constraints of moments.Through a series of tests,the effectiveness and reconstruction efficiency of this new method are evaluated comprehensively,demonstrating that this method is reasonable and can achieve high-quality reconstruction with at least the first six moments as input.Finally,we select a set of lattice quantum chromodynamics(QCD)results regarding moments as input and provide reasonable reconstruction results for the pion.

Systematic studies on the nuclear parton distribution with photon and hadron productions in nuclear collisions at the LHC

A systematic study on the impact of widely-used nuclear-modified parton distribution function(nPDF)parameterizations on the production of direct photons and charged hadrons is performed by employing a next-toleading order Monte Carlo event generator JETPHOX in hadronic collisions at LHC energies.The nuclear modification factors of photon and charged hadron productions are studied in three types of collision systems,i.e.,small(p+p and p+Pb),medium(O+O),and large(Pb+Pb),in a wide rapidity acceptance.The results illustrate that the direct photon production process is a sensitive probe to decipher the difference of the nPDF parameterization implementations,which provides new insights for the experimental measurements to refine the nuclear modifications of the parton distributions.To provide a benchmark for searching for quark gluon plasma in the upcoming small system measurements at LHC energies,we carry out detailed studies on the cold nuclear matter effect in(O+O)collisions.Our outcomes show that the cold nuclear matter effects are negligible for the charged hadron production in(O+O)collisions,which can be used as a baseline to subtract the initial state contribution.

Searching for a_(0)(980)-meson parton distribution function

In this paper,we calculate the scalar a_(0)(980)-meson leading-twist wave function by using the light-cone harmonic oscillator model(LCHO),where the model parameters are determined by fitting theξ-moments■of its light-cone distribution amplitudes.Then,the a_(0)(980)-meson leading-twist light-cone distribution amplitudes with three different scalesζ=(1.0,2.0,5.2)Ge V are given.After constructing the relationship between the a_(0)(980)-meson leading-twist parton distribution functions/valence quark distribution function and its LCHO wave function,we exhibit the■(x,ζ)and■(x,ζ)with different scales.Furthermore,we also calculate the Mellin moments of the a_(0)(980)-meson’s valence quark distribution function■with n=(1,2,3),i.e.■=0.027,■=0.018 and■=0.013.Finally,the scale evolution for the ratio of the Mellin moments x■are presented.

Uncertainty of parton distribution functions due to physical observables in a global analysis

The recent measurement of the differential γ ＋ c-jet cross section, performed at the Tevatron collider in Run II by the D0 collaboration, is studied in a next-to-leading order（NLO） global QCD analysis to assess its impact on the proton parton distribution functions（PDFs）. We show that these data lead to a significant change in the gluon and charm quark distributions. We demonstrate also that there is an inconsistency between the new high precision HERA I＋II combined data and Tevatron measurement. Moreover, in this study we investigate the impact of older EMC measurements of charm structure function F_c^2 on the PDFs and compare the results with those from the analysis of Tevatron data. We show that both of them have the same impact on the PDFs, and thus can be recognized as the same evidence for the inefficiency of perturbative QCD in dealing with charm production in some kinematic regions.

Parton distribution functions and nuclear EMC effect in a statistical model

A new and simple statistical approach is performed to calculate the parton distribution functions （PDFs） of the nucleon in terms of light-front kinematic variables.Analytic expressions of x-dependent PDFs are obtained in the whole x region.And thereafter,we treat the temperature T as a parameter of the atomic number A to explain the nuclear EMC effect in the region x ∈ [0.2,0.7].We give the predictions of PDF ratios,and they are very different from those by other models,thus experiments aiming at measuring PDF ratios are suggested to provide a discrimination of different models.

Drell-Yan nuclear modification due to nuclear effects of nPDFs and initial-state parton energy loss

By globally analyzing nuclear Drell-Yan data including all incident energies,the nuclear effects of nuclear parton distribution functions(nPDFs)and initial-state parton energy loss are investigated.Based on the Landau-Pomeranchuk-Migdal(LPM)regime,the calculations are carried out by means of analytic parametrizations of quenching weights derived from the Baier-Dokshitzer-Mueller-Peigné-Schiff(BDMPS)formalism and using the new EPPS16 nPDFs.It is found that the results are in good agreement with the data and the role of the energy loss effect in the suppression of Drell-Yan ratios is prominent,especially for low-mass Drell-Yan measurements.Thenuclear effects of nPDFs become more obvious with increasing nuclear mass number A,the same as the energy loss effect.By a global fit,the transport coefficient extracted is q=0.26±0.04 GeV^(2)/fm.In addition,to avoid diminishing the QCD NLO correction to the data form of Drell-Yan ratios,separate calculations of the Compton differentialcross section ratios RFe(W)/C(xF)at 120 GeV are performed,which provides a feasible way to better distinguish the gluon energy loss in Compton scattering.It is found that the role of the initial-state gluon energy loss in the suppression of Compton scattering ratios is not very important and disappears with the increase of xF.

Pion parton distribution function in light-front holographic QCD

The valence-quark distribution function of the pion has been of interest for decades;particularly,the profile it should adopt when x→1(the large-x behavior)has been the subject of a long-standing debate.In the light-front holographic QCD(LFHQCD)approach,this behavior is controlled by the so-called reparametrization function,wτ(x),which is not fully determined from first principles.We show that,owing to the flexibility of wτ(x),the large-x profile u^π(x)∼(1−x)^2 can be contained within the LFHQCD formalism.This is in contrast to a previous LFHQCD study(Guy F.de Teramond et al.,Phys.Rev.Lett.,120(18),2018)in which u^π(x)∼(1−x)^1 was found instead.Given our observations,augmented by perturbative QCD and recent lattice QCD results,we state that the large-x exponent of“2”cannot be excluded.

Study of transversity GPDs from pseudoscalar mesons production at EIC of China

The exclusive η and π^(0)electroproduction is studied in the handbag approach based on the generalized parton distributions(GPDs)factorization.Predictions of π^(0)and η mesons are calculated for future electron-ion collider in China(EicC)energy ranges,using obtained cross sections we extract information on the transversity GPDs contributions to these processes.

Recent results from the HERMES experiment

Results are presented from the Hermes experiment which uses semi-inclusive deep inelastic lepton scattering to study the flavor structure of the nucleon.Data have been accumulated for pion and kaon double spin asymmetries,single-spin azimuthal asymmetries for meson electroproduction,deep virtual Compton scattering （DVCS）,and meson multiplicities.These results provide information on the properties of the strange sea in the proton,constraints on transverse momentum dependent quark parton distributions,and demonstrate the promise of DVCS for isolating the total angular momentum carried by the quarks in the proton.

Parity violation in electron scattering

By comparing the cross Sections for left- and right-handed electrons scattered from various unpolarized nuclear targets, the small parity-violating asymmetry can be measured. These asymmetry data probe a wide variety of important topies, including searches for new fundamental interactions and important features of nuclear structure that cannot be studied with other probes. A special feature of these experiments is that the results are interpreted with remarkably few theoretical uncertainties, which justifies pushing the experiments to the highest possible precision. To measure the small asymmetries accurately, a number of novel experimental techniques have been developed.

Exclusive π^(0) production at EIC of China within handbag approach

Exclusive π^(0) electroproduction is analyzed within the handbag approach based on Generalized Parton Distribution(GPDs)factorization.We consider the leading-twist contribution together with the transversity effects.It is shown that the transversity GPDs H_(T) and E_(T) are essential in the description of the π^(0) cross section.Predictions for the future Electron-Ion Collider of China(EicC)energy range are provided.It is found that transversity dominanceσ_(T)>>σ_(L),observed at low energies,is valid up to the EicC energy range.

Exclusive meson production at HERMES

The exclusive electroproduction of pseudoscalar and vector mesons was studied with the HERMES spectrometer at the DESY laboratory by scattering 27.6 GeV positron and electron beams off a transversely polarized hydrogen target.The results are compared to calculations based on generalized parton distributions,some of which are sensitive to the contribution of the total angular momentum of the quarks to the proton spin.

Electron-ion collider in China

Lepton scattering is an established ideal tool for studying inner structure of small particles such as nucleons as well as nuclei.As a future high energy nuclear physics project,an Electron-ion collider in China(EicC)has been proposed.It will be constructed based on an upgraded heavy-ion accelerator,High Intensity heavy-ion Accelerator Facility(HIAF)which is currently under construction,together with a new electron ring.The proposed collider will provide highly polarized electrons(with a po-larization of 80%)and protons(with a polarization of 70%)with variable center of mass energies from 15 to 20 GeV and the luminosity of(2–3)×1033 cm^(−2)·s^(−1).Polarized deuterons and Helium-3,as well as unpolarized ion beams from Carbon to Uranium,will be also available at the EicC.The main foci of the EicC will be precision measurements of the structure of the nucleon in the sea quark region,including 3D tomography of nucleon;the partonic structure of nuclei and the parton interaction with the nuclear environment;the exotic states,especially those with heavy flavor quark contents.In addition,issues fundamental to understanding the origin of mass could be addressed by measurements of heavy quarkonia near-threshold production at the EicC.In order to achieve the above-mentioned physics goals,a hermetical detector system will be constructed with cutting-edge technologies.This document is the result of collective contributions and valuable inputs from experts across the globe.The EicC physics program complements the ongoing scientific programs at the Jefferson Laboratory and the future EIC project in the United States.The success of this project will also advance both nuclear and particle physics as well as accelerator and detector technology in China.

Collective Perspective on Advances in Dyson–Schwinger Equation QCD

We survey contemporary studies of hadrons and strongly interacting quarks using QCD's Dyson-Schwinger equations, addressing the following aspects: confinement and dynamical chiral symmetry breaking; the hadron spectrum; hadron elastic and transition form factors, from small-to large-Q2; parton distribution functions; the physics of hadrons containing one or more heavy quarks; and properties of the quark gluon plasma.