Empirical Determination of the Pion Mass Distribution

Existing pion+nucleus Drell-Yan and electron+pion scattering data are used to develop ensembles of modelindependent representations of the pion generalized parton distribution(GPD).Therewith,one arrives at a datadriven prediction for the pion mass distribution form factor,θ_(2)^(π).Compared with the pion elastic electromagnetic form factor,θ_(2)^(π)is harder:the ratio of the radii derived from these two form factors is r_(π)^(θ2)/r_(π)= 0.79(3).Our datadriven predictions for the pion GPD,related form factors and distributions should serve as valuable constraints on theories of pion structure.

All-Orders Evolution of Parton Distributions:Principle,Practice,and Predictions

Parton distribution functions(PDFs)are defining expressions of hadron structure.Exploiting the role of effective charges in quantum chromodynamics,an algebraic scheme is described which,given any hadron’s valence parton PDFs at the hadron scale,delivers predictions for all its PDFs(unpolarized and polarized)at any higher scale.The scheme delivers results that are largely independent of both the value of the hadron scale and the pointwise form of the charge;and,inter alia,enables derivation of a model-independent identity that relates the strength of the proton’s gluon helicity PDF,ΔG_(p)ζ,to that of the analogous singlet polarized quark PDF and valence quark momentum fraction.Using available data fits and theory predictions,the identity yieldsΔG_(p)(ζC=√3 GeV)=1.48(10).It furthermore entails that the measurable quark helicity contribution to the proton spin is a_(op)^(ζC)=0.32(3),thereby reconciling contemporary experiment and theory.

Valence Quark Ratio in the Proton

Beginning with precise data on the ratio of structure functions in deep inelastic scattering(DIS)from ^3He and ^3H,collected on the domain 0.19≤xB≤0.83,where xBis the Bjorken scaling variable,we employ a robust method for extrapolating such data to arrive at a model-independent result for the xB=1 value of the ratio of neutron and proton structure functions.Combining this with information obtained in analyses of DIS from nuclei,corrected for target-structure dependence,we arrive at a prediction for the proton valence-quark ratio:d_(v)/u_(v)|_(xB→1)=0.230(57).Requiring consistency with this result presents a challenge to many descriptions of proton structure.

Pauli Radius of the Proton

Using a procedure based on interpolation via continued fractions supplemented by statistical sampling,we analyze proton magnetic form factor data obtained via electron+proton scattering on Q^(2)∈[0.027,0.55]GeV^(2)with the goal of determining the proton magnetic radius.The approach avoids assumptions about the function form used for data interpolation and ensuing extrapolation onto Q^(2)■0 for extraction of the form factor slope.In this way,we find r_(M)=0.817(27)fm.Regarding the difference between proton electric and magnetic radii calculated in this way,extant data are seen to be compatible with the possibility that the slopes of the proton Dirac and Pauli form factors,F1,2(Q^(2)),are not truly independent observables;to wit,the difference F_(1)’(0)-F_(2)’(0)/κp=[1+Kp]/[4 m_(p)^(2)],viz.,the proton Foldy term.

Dyson-Schwinger Equations of Chiral Chemical Potential

We discuss the chiral phase transition of quantum chromodynamics （QCD） with a chiral chemical potential μ5 as an additional scale. Within the framework of Dyson-Schwinger equations, we focus particularly on the behavior of the widely accepted as well as interesting critical end point （CEP）, using a separable gluon propagator and a Gaussian gluon propagator. We find that there may be no CEP5 in the T-μ5 plane, and the phase transition in the T μ5 plane might be totally crossover. Our results have apparent consistency with the Lattice QCD calculation. On the other hand, our study may also provide some useful hints to some other studies related to μ5.

Discussion of Various Susceptibilities within Thermal and Dense Quantum Chromodynamics

It is commonly accepted that the system undergoes a crossover at high temperature and low chemical potential beyond the chiral limit case, and the properties of the crossover region are important for researchers to understand the nature of strong interacting matters of quantum chromodynamics （QCD）. Since at present there is no exact order of parameters of the phase transitions beyond the chiral limit, QCD susceptibilities are widely used as indicators. In this work various susceptibilities are discussed in the framework of Dyson-Schwinger equations. The results show that different kinds of susceptibilities give the same critical end point, which is the bifurcation point of the crossover region and the first order phase transition line of QCD. Nevertheless, different pseudo- critical points are found in the temperature axis. We think that defining a critical band is more suitable in the crossover region.

A Model-Independent Discussion of Quark Number Density and Quark Condensate at Zero Temperature and Finite Quark Chemical Potential

Generally speaking, the quark propagator is dependent on the quark chemical potential in the dense quantum chromodynamics （QCD）. By means of the generating functional method, we prove that the quark propagator actually depends on p4 ＋ iμ from the first principle of QCD. The relation between quark number density and quark condensate is discussed by analyzing their singularities. It is concluded that the quark number density has some singularities at certain # when T = 0, and the variations of the quark number density as well as the quark condensate are located at the same point. In other words, at a certain # the quark number density turns to nonzero, while the quark condensate begins to decrease from its vacuum value.

中国极化电子离子对撞机计划

轻子散射实验是探索核子与原子核结构的理想工具。中国电子离子对撞机(Electron Ion Collider in China,EicC)建议书设想在已开建的强流重离子加速器装置(High Intensity heavy ion Accelerator Facility,HIAF)的基础上,升级质子束流为20 GeV的极化束流,并建造2.8~5 GeV极化电子束流,从而实现质心系能量为15~20 GeV的双极化电子-离子对撞。EicC设计的亮度为(2~4)×10^33cm^-2·s^-1,质子束流极化率达到70%,电子束流极化率达到80%。该装置除了能提供极化轻离子束流(例如:氦-3)外,也可产生非极化重离子束流(碳-12~铀-238)。EicC将聚焦核子海夸克部分子结构、原子核物质结构与性质、奇特强子态三个方面的物理研究。高亮度、高精度的对撞机有助于精确地测量核子结构函数并对核子进行三维成像,揭示强相互作用的动力学规律;原子核部分子分布包括核子短程关联以及原子核介质效应同样是该提案的重要科学目标;EicC能区接近重味夸克产生阈值,在研究重味强子谱方面拥有低背景的独特优势,有助于发现研究新的奇特强子态。质子质量起源问题也可以通过重味矢量介子的产生来研究。为了完成上述物理目标,我们将利用最先进的探测器技术建造接近全立体角覆盖的EicC对撞机谱仪。在准备EicC白皮书的过程中,我们得到世界各国专家的支持。EicC的物理与已有的实验和美国即将建设的EIC中的物理项目相互补充。EicC的建成及运行有望引领前沿的中高能核物理研究,使我国在加速器和探测器先进技术等领域实现跨越式发展,为我国核物理与强子物理以及相关科学领域提供大型综合实验平台与人才培养基地。

Hadron and light nucleus radii from electron scattering

Conceptually,radii are amongst the simplest Poincaré-invariant properties that can be associated with hadrons and light nuclei.Accurate values of these quantities are necessary so that one may judge the character of putative solutions to the strong interaction problem within the Standard Model.However,limiting their ability to serve in this role,recent measurements and new analyses of older data have revealed uncertainties and imprecisions in the radii of the proton,pion,kaon,and deuteron.In the context of radius measurement using electron+hadron elastic scattering,the past decade has shown that reliable extraction requires minimisation of bias associated with practitioner-dependent choices of data fitting functions.Different answers to that challenge have been offered;and this perspective describes the statistical Schlessinger point method(SPM),in unifying applications to proton,pion,kaon,and deuteron radii.Grounded in analytic function theory,independent of assumptions about underlying dynamics,free from practitioner-induced bias,and applicable in the same form to diverse systems and observables,the SPM returns an objective expression of the information contained in any data under consideration.Its robust nature and versatility make it suitable for use in many branches of experiment and theory.

Effective charge from lattice QCD

Using lattice configurations for quantum chromodynamics(QCD)generated with three domain-wall fermions at a physical pion mass,we obtain a parameter-free prediction of QCD’s renormalisation-group-invariant process-independent effective charge,α^(k2).Owing to the dynamical breaking of scale invariance,evident in the emergence of a gluon mass-scale,m0=0.43(1)GeV,this coupling saturates at infrared momenta:α^(0)/π=0.97(4).Amongst other things:α^(k2)is almost identical to the process-dependent(PD)effective charge defined via the Bjorken sum rule;and also that PD charge which,employed in the one-loop evolution equations,delivers agreement between pion parton distribution functions computed at the hadronic scale and experiment.The diversity of unifying roles played byα^(k^2)suggests that it is a strong candidate for that object which represents the interaction strength in QCD at any given momentum scale;and its properties support a conclusion that QCD is a mathematically well-defined quantum field theory in four dimensions.

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.