Parton distribution functions(DFs)have long been recognized as key measures of hadron structure.Today,theoretical prediction of such DFs is becoming possible using diverse methods for continuum and lattice analyses of...Parton distribution functions(DFs)have long been recognized as key measures of hadron structure.Today,theoretical prediction of such DFs is becoming possible using diverse methods for continuum and lattice analyses of strong interaction(QCD)matrix elements.Recent developments include a demonstration that continuum and lattice analyses yield mutually consistent results for all pion DFs,with behavior on the far valence domain of light-front momentum fraction that matches QCD expectations.Theory is also delivering an understanding of the distributions of proton mass and spin amongst its constituents,which varies,of course,with the resolving scale of the measuring probe.Aspects of the pion DF and proton spin developments are sketched herein,along with some novel perspectives on gluon and quark orbital angular momentum.展开更多
A novel method for constructing a kernel for the meson bound-state problem is described.It produces a closed form that is symmetry-consistent(discrete and continuous)with the gap equation defined by any admissible glu...A novel method for constructing a kernel for the meson bound-state problem is described.It produces a closed form that is symmetry-consistent(discrete and continuous)with the gap equation defined by any admissible gluon-quark vertex,Γ.Applicable even when the diagrammatic content ofΓis unknown,the scheme can foster new synergies between continuum and lattice approaches to strong interactions.The framework is illustrated by showing that the presence of a dressed-quark anomalous magnetic moment inΓ,an emergent feature of strong interactions,can remedy many defects of widely used meson bound-state kernels,including the mass splittings between vector and axial-vector mesons and the level ordering of pseudoscalar and vector meson radial excitations.展开更多
Modern and anticipated facilities will deliver data that promises to reveal the innermost workings of quantum chromodynamics(QCD).In order to fulfill that promise,phenomenology and theory must reach a new level,limiti...Modern and anticipated facilities will deliver data that promises to reveal the innermost workings of quantum chromodynamics(QCD).In order to fulfill that promise,phenomenology and theory must reach a new level,limiting and overcoming model-dependence,so that clean lines can be drawn to connect the data with QCD itself.Progress in that direction,made using continuum methods for the hadron bound-state problem,is sketched herein.展开更多
Understanding why the scale of emergent hadron mass is obvious in the proton but hidden in the pion may rest on mapping the distribution functions(DFs)of all partons within the pion and comparing them with those in th...Understanding why the scale of emergent hadron mass is obvious in the proton but hidden in the pion may rest on mapping the distribution functions(DFs)of all partons within the pion and comparing them with those in the proton;and since glue provides binding in quantum chromodynamics,the glue DF could play a special role.Producing reliable predictions for the proton’s DFs is difficult because the proton is a three-valence-body bound-state problem.As sketched herein,the situation for the pion,a two-valence-body problem,is much better,with continuum and lattice predictions for the valence-quark and glue DFs in agreement.This beginning of theory alignment is timely because experimental facilities now either in operation or planning promise to realize the longstanding goal of providing pion targets,thereby enabling precision experimental tests of rigorous theory predictions concerning Nature’s most fundamental Nambu-Goldstone bosons.展开更多
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)wi...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.展开更多
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 datadrive...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.展开更多
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 par...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.展开更多
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 meth...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.展开更多
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 e...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.展开更多
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-ind...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.展开更多
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...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.展开更多
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 distri...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.展开更多
基金National Natural Science Foundation of China(Grant No.12135007).
文摘Parton distribution functions(DFs)have long been recognized as key measures of hadron structure.Today,theoretical prediction of such DFs is becoming possible using diverse methods for continuum and lattice analyses of strong interaction(QCD)matrix elements.Recent developments include a demonstration that continuum and lattice analyses yield mutually consistent results for all pion DFs,with behavior on the far valence domain of light-front momentum fraction that matches QCD expectations.Theory is also delivering an understanding of the distributions of proton mass and spin amongst its constituents,which varies,of course,with the resolving scale of the measuring probe.Aspects of the pion DF and proton spin developments are sketched herein,along with some novel perspectives on gluon and quark orbital angular momentum.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11805024 and 11947406).
文摘A novel method for constructing a kernel for the meson bound-state problem is described.It produces a closed form that is symmetry-consistent(discrete and continuous)with the gap equation defined by any admissible gluon-quark vertex,Γ.Applicable even when the diagrammatic content ofΓis unknown,the scheme can foster new synergies between continuum and lattice approaches to strong interactions.The framework is illustrated by showing that the presence of a dressed-quark anomalous magnetic moment inΓ,an emergent feature of strong interactions,can remedy many defects of widely used meson bound-state kernels,including the mass splittings between vector and axial-vector mesons and the level ordering of pseudoscalar and vector meson radial excitations.
基金the National Natural Science Foundation of China(Grant Nos.11805024 and 11947406)Jiangsu Province Hundred Talents Plan for Professionals。
文摘Modern and anticipated facilities will deliver data that promises to reveal the innermost workings of quantum chromodynamics(QCD).In order to fulfill that promise,phenomenology and theory must reach a new level,limiting and overcoming model-dependence,so that clean lines can be drawn to connect the data with QCD itself.Progress in that direction,made using continuum methods for the hadron bound-state problem,is sketched herein.
文摘Understanding why the scale of emergent hadron mass is obvious in the proton but hidden in the pion may rest on mapping the distribution functions(DFs)of all partons within the pion and comparing them with those in the proton;and since glue provides binding in quantum chromodynamics,the glue DF could play a special role.Producing reliable predictions for the proton’s DFs is difficult because the proton is a three-valence-body bound-state problem.As sketched herein,the situation for the pion,a two-valence-body problem,is much better,with continuum and lattice predictions for the valence-quark and glue DFs in agreement.This beginning of theory alignment is timely because experimental facilities now either in operation or planning promise to realize the longstanding goal of providing pion targets,thereby enabling precision experimental tests of rigorous theory predictions concerning Nature’s most fundamental Nambu-Goldstone bosons.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12135007 and 11805097)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20180323)STRONG-2020,“the strong interaction at the frontier of knowledge:fundamental research and applications”which received funding from the European Union’s Horizon 2020 Research and Innovation Programme(Grant No.824093)。
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.12135007 and 12233002)the Natural Science Foundation of Jiangsu Province (Grant No.BK20220122)+1 种基金Spanish Ministry of Science and Innovation (MICINN Grant No.PID2019-107844GB-C22)Junta de Andalucía (Grant No.P18-FR-5057)。
文摘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.
基金supported by the National Natural Science Foundation of China(Grant No.12135007)Nanjing University of Posts and Telecommunications Science Foundation(Grant No.NY221100)+2 种基金the Natural Science Foundation of Jiangsu Province(Grant No.BK20220122)Spanish Ministry of Science and Innovation(MICINN Grant No.PID2019-107844GBC22)Junta de Andalucía(Grant No.P18-FR-5057)。
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.12135007 and 11805097)the Alexander von Humboldt Foundation+1 种基金and STRONG-2020“The strong interaction at the frontier of knowledge:fundamental research and applications”which received funding from the European Union’s Horizon 2020 research and innovation programme(Grant No.824093)。
文摘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.
基金Supported by the Chinese Government’s Thousand Talents Plan for Young ProfessionalsJiangsu Province Hundred Talents Plan for ProfessionalsForschungszentrum Jülich GmbH
文摘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.
文摘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.
基金Supported by the National Natural Science Foundation of China(12135007)Natural Science Foundation of Jiangsu Province(BK20220122)STRONG-2020"The strong interaction at the frontier of knowledge:fundamental research and applications"which received funding from the European Union's Horizon 2020 research and innovation programme(824093)。
文摘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.
基金Supported by National Natural Science Foundation of China(12135007,11805097)Jiangsu Provincial Natural Science Foundation of China(BK20180323)+2 种基金Spanish Ministry of Science and Innovation(MICINN)(PID2019-107844GB-C22)Junta de Andalucía(P18-FR-5057,UHU-1264517)University of Huelva(EPIT-2019)。
文摘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.
