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.

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.

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.

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.

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.

Tackling the kaon structure function at EicC

Measuring the kaon structure beyond proton and pion structures is a prominent topic in hadron physics,as it is one way to understand the nature of the Nambu-Goldstone boson of QCD and observe the interplay between the EHM and HB mechanisms for hadron mass generation.In this study,we present a simulation of the leading A baryon tagged deep inelastic scattering experiment at EicC(Electron-ion collider in China),which is engaged to unveil the internal structure of kaon via the Sullivan process.According to our simulation results,the suggested experiment will cover the kinematical domain of 0.05≤xK≤0.85 and Q^(2)up to 50 GeV^(2),with the acceptable statistical uncertainties.In the relatively low-Q^(2) region(<10 GeV^(2)),the Monte-Carlo simulation shows a good statistical precision(<5%)for the measurement of the kaon structure function F2K.In the high-Q^(2) region(up to 50 GeV^(2)),the statistical uncertainty of F_(2)^(K) is also acceptable(<10%)for the data at xK<0.8.To perform such an experiment at an electron-ion collider,a high-performance zero-degree calorimeter is suggested.The magnitude of the background process and the assumed detector capabilities are also discussed and illustrated in the paper.

Reduction of PDF uncertainty in the measurement of the weak mixing angle at the ATLAS experiment

We investigate the parton distribution function(PDF)uncertainty in the measurement of the effective weak mixing angle sin2θ^(l)_(eff)at the CERN Large Hadron Collider(LHC).The PDF-induced uncertainty is large in proton-proton collisions at the LHC due to the dilution effect.The measurement of the Drell-Yan forward-backward asymmetry(ApB)at the LHC can be used to reduce the PDF uncertainty in the sin2θ^(l)_(eff)measurement.However,when including the full mass range of lepton pairs in the AFB data analysis,the correlation between the PDF updating procedure and the sin2θ^(l)_(eff) extraction leads to a sizable bias in the obtained sin2θ^(l)_(eff)value.From our studies,we find that the bias can be significantly reduced by removing Drell-Yan events with invariant mass around the Z-pole region,while most of the sensitivity in reducing the PDF uncertainty remains.Furthermore,the lepton charge asymmetry in the^boson events as a function of the rapidity of the charged leptons,A±(ηl),is known to be another observable which can be used to reduce the PDF uncertainty in the sin2θ^(l)_(eff)measurement.The constraint from A±(ηl)is complementary to that from AFB,and thus no bias affects the sin2θ^(l)_(eff)extraction.The studies are performed using the error PDF Updating Method Package(ePump),which is based on Hessian updating methods.In this article,the CT14HERA2 PDF set is used as an example.

Three-dimensional imaging of the nucleon and semi-inclusive high-energy reactions

We present a short overview of studies of the transverse-momentum-dependent parton distribution functions of the nucleon. The aim of such studies is to provide three-dimensional imaging of the nucleon and a comprehensive description of semi-inclusive high-energy reactions. By summarizing what we have done in constructing the theoretical framework for inclusive deep inelastic lepton-nucleon scattering and one-dimensional imaging of the nucleon, we try to sketch out an outline of what we need to do to construct such a comprehensive theoretical framework for semi-inclusive processes in terms of three-dimensional gauge-invariant patton distributions. Next, we present an overview of what we have already achieved, with an emphasis on the theoretical framework for semi-inclusive reactions in leading-order perturbative quantum chromodynamics but with leading and higher twist contributions. We summarize in particular the results for the differential cross section and azimuthal spin asymmetries in terms of the gauge-invariant transverse-momentum-dependent parton distribution functions. We also briefly summarize the available experimental results on semi-inclusive reactions and the parameterizations of transverse-momentum-dependent parton distributions extracted from them and present an outlook for future studies.