34 pages, 5 figures, 2 tables; invited review submitted to Annual Review of Nuclear and Particle Science, Vol.70 (2020); version accepted for publication; various references updated; improved discussion on implications for astroparticle physics
发表信息：
Annual Review of Nuclear and Particle Science, Vol.70 (2020)
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 advance our understanding of QCD proton substructure and pursue 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.
This contribution to CIPANP 2012 highlights what we have learned about the asymmetric parton distributions of the nucleon over the past 20 years. These distributions include the transverse momentum dependent parton distributions describing spin-orbit correlations, but also their generalized parton and Wigner distribution analogues. Besides quark distributions, also gluon distributions are discussed, in particular the distribution of linearly polarized gluons inside unpolarized nucleons and its applications, such as at LHC in Higgs production and at a future Electron-Ion Collider in heavy quark…
The present understanding of the spin structure of the nucleon is briefly reviewed. The main focus is on parton helicity distributions, orbital angular momentum of partons as defined through generalized parton distributions, as well as single spin asymmetries and time-reversal odd correlation functions.
We present a new leading and next-to-leading QCD analysis of the world data on inclusive polarized deep inelastic scattering. A new set of polarized parton densities is extracted from the data and the sensitivity of the results to the newly incorporated SLAC/E155 proton data is discussed.
A Comment on the recently published reevaluation of the polarization-averaged parton distribution of strange quarks in the nucleon using final data on the multiplicities of charged kaons in semi-inclusive deep-inelastic scattering is reviewed. Important features of the comparison of one-dimensional projections of the multidimensional HERMES data are pointed out. A test of the leading-order extraction of xS(x) using the difference between charged-kaon multiplicities is repeated. The results are consistent with leading-order predictions within the uncertainties in the input data, and do not inva…
We propose a new method to determine at what transverse momenta particle production in high-energy pp collisions is governed by hard parton-parton processes. Using information on the transverse spatial distribution of partons obtained from hard exclusive processes in ep/gamma p scattering, we evaluate the impact parameter distribution of pp collisions with a hard parton-parton process as a function of p_T of the produced parton (jet). We find that the average pp impact parameters in such events depend very weakly on p_T in the range 2 < p_T < few 100 GeV, while they are much smaller than those…
Generalized parton distributions have been introduced in recent years as a suitable theoretical tool to study the structure of the nucleon. Unifying the concepts of parton distributions and hadronic form factors, they provide a comprehensive framework for describing the quark and gluon structure of the nucleon. In this review their formal properties and modeling are discussed, summarizing the most recent developments in the phenomenological description of these functions. The status of available data is also presented.
The HERMES collaboration in Phys. Rev. D89 (2014) 097101 extracted information about the strange quark density in the nucleon. One of the main results is an observation that the shape of the extracted density is very different from the shapes of the strange quark density from global QCD fits and also from that of the light antiquarks. In this paper systematic studies on the HERMES published multiplicity of pion and kaon data are presented. It is shown that the conclusions concerning the strange quark distribution in the nucleon reached in Phys. Rev. D89 (2014) 097101 are at the moment prematur…
We study the parton distribution of nucleon and nuclear EMC effect in a statistical model. We find when we choose the parameters appropriately, the predictions given by pure statistical laws can fit the experimental data well in most range of $x$, this reveal statistical law play an important role in the parton distribution of nucleon.
We demonstrate that perturbative QCD leads to positive 3D parton--parton correlations inside nucleon explaining a factor two enhancement of the cross section of multi-parton interactions observed at Tevatron at $x_i\ge 0.01$ as compared to the predictions of the independent parton approximation. We also find that though perturbative correlations decrease with $x$ decreasing, the nonperturbative mechanism kicks in and should generate correlation which, at $x$ below $10^{-3}$, is comparable in magnitude with the perturbative one for $x\sim 0.01$.
The consequences of a flavor broken SU(3)_f dynamical parton model are studied in the context of the elastic scattering of supersymmetric dark matter off nucleons. It is shown that the predictions of this model differ considerably from those of the commonly applied `standard' parton model. Some notable properties of the dynamical parton model are finally presented and discussed.
The comparative analysis of different sets of the parton distribution functions (PDFs), based on the description of the whole sets of experimental data of electromagnetic form factors of the proton and neutron, is made in the framework of the model of t-dependence of the generalized parton distributions (GPDs) with minimum free parameters and some extending variants of the model. In some cases, a large difference in the description of electromagnetic form factors of nucleons with using the different sets of PDF are found out. The different variants of the flavor dependence of the up and down q…
We reply to the Comment of Brodsky and Gardner on our paper "New limits on intrinsic charm in the nucleon from global analysis of parton distributions" [Phys. Rev. Lett. 114, 082002 (2015)]. We address a number of incorrect claims made about our fitting methodology, and elaborate how global QCD analysis of all available high-energy data provides no evidence for a large intrinsic charm component of the nucleon.
In this high-$x$ region, both the flavour content and structure of the nucleon parton distribution functions remains relatively poorly known. New LHCb measurements of Z and charm jet associated production could indicate a valence-like intrinsic-charm component in the proton wave function, and measurements of Z production in pPb collisions provide new constraints on the partonic structure of nucleons bound inside nuclei. Here we will discuss these new LHCb measurements and comparisons with state-of-the-art parton distribution function calculations.
Dimuon production has been studied in a series of fixed-target experiments at Fermilab during the last two decades. Highlights from these experiments, together with recent results from the Fermilab E866 experiment, are presented. Future prospects for studying the parton distributions in the nucleons and nuclei using dimuon production are also discussed.
We have performed several fits to find the ratio $R=σ_{L}/σ_{T}$ in different phenomenological models. Our fits seem to leave no room for possible admixture of scalar partons inside the nucleon.
We discuss the general formalism for the calculation in light-front quark models of the fully unintegrated, off-diagonal quark-quark correlator of the nucleon, parametrized in terms of generalized transverse momentum dependent parton distributions (GTMDs). By taking specific limits or projections, these GTMDs yield various transverse-momentum dependent and generalized parton distributions, thus providing a unified framework to simultaneously model different observables. The corresponding distributions in impact-parameter space are the Wigner functions which provide multidimensional images of t…
We review the status of our understanding of nucleon structure based on the modelling of different kinds of parton distributions. We use the concept of generalized transverse momentum dependent parton distributions and Wigner distributions, which combine the features of transverse-momentum dependent parton distributions and generalized parton distributions. We revisit various quark models which account for different aspects of these parton distributions. We then identify applications of these distributions to gain a simple interpretation of key properties of the quark and gluon dynamics in the…
We present an exploratory study using generalized parton distributions of several observables related to transverse degrees of freedom in hadronic structure -- the nucleon transverse momentum, the transverse radius, or impact parameter, and the momentum transfer, $t$, dependence of the longitudinal variable $x$ -- in both nucleons and nuclei.
We suggest the measurement of exclusive electroproduction of lepton pairs as a tool to study inter-parton correlations in the nucleon via generalized parton distributions in the kinematical region where this process is light-cone dominated. We demonstrate how the single beam-spin asymmetry allows to perform such kind of analysis and give a number of predictions for several experimental setups. We comment on other observables which allow for a clean separation of different species of generalized parton distributions.
A model independent prediction is given for the nucleon spin contents, based only upon a reasonable theoretical postulate on the isosinglet anomalous gravitomagnetic moment of the nucleon.
The parton content of the nucleon is explored within a meson-cloud model developed to derive light-cone wave functions for the physical nucleon. The model is here applied to study electromagnetic form factors, distribution amplitudes and nucleon-to-meson transition distribution amplitudes.
Generalized parton distributions (GPDs) have become a standard QCD tool for analyzing and parametrizing the non perturbative parton structure of hadron targets. GPDs might be viewed as non-diagonal overlaps of light-cone wave functions and offer the opportunity to study the partonic content of the nucleon from a new perspective, allowing one to study the interplay between longitudinal and transverse partonic degrees of freedom. In particular, we will review some of the new information encoded in the GPDs through the definition of impact-parameter dependent parton distributions and form factors…
We argue that generalized parton distributions (GPDs), accessible in hard exclusive processes, carry information about the spatial distribution of forces experienced by quarks and gluons inside hadrons. This way the measurements of hard exclusive processes open a possibility for direct "measurements" of strong forces in different parts of nucleons and nuclei. Also such studies open a venue for addressing questions of the properties of the quark (gluon) matter inside hadrons and nuclei. We give a simple example of relations between GPDs and properties of "nuclear matter" in finite nuclei.
Using ideas from Light Front Holography, we discuss the calculation of the nucleon helicity-independent generalized parton distributions of quarks in the zero skewness case.
We study the generalized parton distributions, including the helicity-flip ones, using Nambu-Jona-Lasinio model based on a relativistic Faddeev approach with `static approximation'. Sum rules relating the generalized parton distributions to nucleon electromagnetic form factors are satisfied. Moreover, quark-antiquark contributions in the region $-ξ<x<ξ$ are non-vanishing. Our results are qualitatively similar to those calculated with Radyushkin's double distribution ansatz using forward parton distribution functions calculated in the NJL model as inputs.
We present the general formalism required to derive generalized parton distributions within a convolution model where the bare nucleon is dressed by its virtual meson cloud. In the one-meson approximation the Fock states of the physical nucleon are expanded in a series involving a bare nucleon and two-particle, meson-baryon, states. The baryon is assumed here to be either a nucleon or a $Δ$ described within the constituent quark model in terms of three valence quarks; correspondingly, the meson, assumed to be a pion, is described as a quark-antiquark pair. Explicit expressions for the unpolari…
We present first results from our analysis of the most general quark-quark correlator of the nucleon, which can be parameterized in terms of so-called generalized transverse momentum dependent parton distributions. These results include the first complete parameterization of the nucleon GPDs and TMDs to all twists as well as new results on possible nontrivial relations between them.
We discuss the relations between Generalized Parton Distributions (GPDs) and nucleon resonances. We first briefly introduce the concept of "transition" GPDs. Then we discuss a straightforward application to the modelization of the N-$Δ$ magnetic transition form factor. Finally, we discuss the experimental aspects of the subject and present first preliminary experimental investigations in this field.
The current status of global QCD analysis of parton distribution functions of the nucleon is reviewed. Recent progress made in determining various features of the parton structure of the nucleon, as well as outstanding open questions are discussed. These include: the small-$x$ and large-$x$ behavior of the partons, particularly the gluon; the differentiation of $u$ and $d$ quarks; the strangeness sea ($s+\bar{s}$), the strangeness asymmetry ($s-\bar{s}$); and the heavy quark distributions $c$ and $b$. Important issues about assessing the uncertainties of parton distributions and their physical…
We evaluate the differential cross section for the electroproduction of lepton pairs off a polarized nucleon target in the generalized Bjorken region to leading power accuracy in hard momentum. We discuss the importance of this process for phenomenology of generalized parton distributions. A special attention is given to the sensitivity of physical observables, i.e., diverse asymmetries, to their dependence on scaling variables that allows to map directly the functional two-dimensional surface of generalized parton distributions.
A new generation of (unpolarized) dynamical parton distribution functions of the nucleon is determined. After introducing basic elements of perturbative QCD, the dynamical model is discussed and compared with the approach to parton distributions used by most other groups ("standard"). Parton distributions sets (with uncertainties) at different orders (LO, NLO, NNLO), using different factorization schemes (\overline{MS}, DIS) and different treatments of heavy quark masses (FFNS, VFNS) are extracted and compared. The astrophysical implications of the dynamical predictions are outlined before foc…
Continuing with our analysis of parton distributions in the nucleon, we extend our light-front quark model in order to obtain both the helicity independent and helicity dependent parton distributions, analytically matching the results of global fits at the initial scale $μ\sim 1$ GeV, and which also contain the correct Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution. We also calculate the transverse parton, Wigner and Husimi distributions from a unified point of view, using our light-front wave functions and expressing them in terms of the parton distributions $q_v(x)$ and $δq_v(x)$. Our …
Deepening our knowledge of the partonic content of nucleons and nuclei represents a central endeavour of modern high-energy and nuclear physics, with ramifications in related disciplines such as astroparticle physics. There are two main scientific drivers motivating these investigations of the partonic structure of hadrons. On the one hand, addressing fundamental open issues in our understanding in the strong interactions such as the origin of the nucleon mass, spin, and transverse structure; the presence of heavy quarks in the nucleon wave function; and the possible onset of novel gluon-domin…
In the following, the subject of Deep Virtual Compton Scattering on the nucleon and its relation to the recently introduced concept of Generalized Parton Distributions are briefly reviewed. The general theoretical framework and the links between theory and experiment will be outlined and the recently published data which look promising for the development of this field will be discussed. Finally, the experimental prospectives of the domain will be presented.
The nucleon distribution amplitudes and the nucleon-to-pion transition distribution amplitudes are investigated at leading twist within the frame of a light-cone quark model. The distribution amplitudes probe the three-quark component of the nucleon light-cone wave function, while higher order components in the Fock-space expansion of the nucleon state are essential to describe the nucleon-to-pion transition distribution amplitudes. Adopting a meson-cloud model of the nucleon the nucleon-to-pion transition distribution amplitudes are calculated for the first time.
We discuss the links between Generalized Parton Distributions (GPDs) and elastic nucleon form factors. These links, in the form of sum rules, represent powerful constraints on parametrizations of GPDs. A Regge parametrization for GPDs at small momentum transfer, is extended to the large momentum transfer region and it is found to describe the basic features of proton and neutron electromagnetic form factor data. This parametrization is used to estimate the quark contribution to the nucleon spin.
Reports on our latest extractions of parton distribution functions of the nucleon are given. First an overview of the recent JR14 upgrade of our unpolarized PDFs, including NNLO determinations of the strong coupling constant and a discussion of the role of the input scale in parton distribution analysis. In the second part of the talk recent results on the determination of spin-dependent PDFs from the JAM collaboration are reported, including a careful treatment of hadronic and nuclear corrections, as well as reports on the impact of present and future data in our understanding of the spin of …
We incorporate the perturbative evolution effects in the generalized parton distributions (GPDs) calculated in effective light-front quark model for the nucleon. The perturbative effects enters into formalism through the evolution of GPDs according to the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-like (DGLAP) equation. We obtain the evolved GPDs in the momentum space and transverse impact parameter space. We observe that combining the light front quark model with the perturbative evolution effects, give the effective model for studying the phenomenological GPDs
We study the small-$x$ evolution equation for the gluon generalized parton distribution (GPD) $E_g$ of the nucleon. It is shown that $E_g$ at vanishing skewness exhibits the Regge behavior identical to the BFKL Pomeron, despite its association with nucleon helicity-flip processes. We also consider the effect of gluon saturation and demonstrate that $E_g$ gets saturated in the same way as its helicity-nonflip counterpart $H_g$. Our result has a direct impact on the modeling of $E_g$ as well as the small-$x$ contribution to nucleon spin sum rules.
The proton's transverse polarization structure is examined in terms of the Lorentz-covariant Pauli-Lubanski vector in QCD. We find that there are contributions from leading, subleading, and next-to-subleading partonic contributions in the light-front system of coordinates. The subleading and next-to-subleading contributions are related to the leading one through Lorentz symmetry. And the leading contribution obeys a simple partonic angular momentum sum rule that gives a clear physical interpretation to a relation known previously.
It is known that some of the deeply-virtual-Compton-scattering observables, for instance, the beam-charge asymmetry in the hard electroproduction of real photons on the nucleon, are extremely sensitive to the magnitude of D-term appearing in the parameterization of the generalized parton distributions. We report a theoretical analysis of both the isoscalar and isovector parts of the nucleon D-term within the framework of the chiral quark soliton model, without recourse to the derivative expansion type approximation used in previous works.
We discuss some recent developments concerning the nucleon's helicity parton distribution functions: New preliminary data from jet production at RHIC suggest for the first time a non-vanishing polarization of gluons in the nucleon. SIDIS measurements at COMPASS provide better constraints on the strange and light sea quark helicity distributions. Single-longitudinal spin asymmetries in W-boson production have been observed at RHIC and will ultimately give new insights into the light quark and anti-quark helicity structure of the nucleon.
Examining the structure functions of nucleons by introducing new Ansatz and their consequences on parton distribution functions in higher approximation
In this letter, we investigate the nucleon quasi-parton distribution functions in the chiral quark soliton model. We derive a set of sum-rules depending on the velocity of the nucleon and on the Dirac matrix defining the distribution functions. We present numerical results for the isosinglet unpolarized distribution, in which we find that the anti-quark distribution breaks the positivity condition at nucleon velocities $v\approx 0.99\;(P_N\approx 7.0 M_N)$ and smaller. We found that, for the isosinglet unpolarized case, a large nucleon momentum is required for the quasi-parton distribution to …
We discuss building models for nucleon generalized parton distributions (GPDs) H and E that are based on the formalism of double distributions (DDs). We found that the usual "DD+D-term" construction should be amended by an extra term, ξE^1_+(x,ξ) built from the α/βmoment of the DD e(β,α) that generates GPD E(x,ξ). Unlike the D-term, this function has support in the whole -1 \leq x \leq 1 region, and in general does not vanish at the border points |x|=ξ.
The cross section for ultra-high energy neutrino-nucleon scattering is very sensitive to the parton distributions at very small values of Bjorken x ($x \leq 10^{-4})$. We numerically investigate the effects of modifying the behavior of the gluon distribution function at very small $x$ in the DGLAP evolution equation. We then use the Color Glass Condensate formalism to calculate the neutrino-nucleon cross section at ultra-high energies and compare the result with those based on modification of DGLAP evolution equation.
We study how unintegrated parton distributions in nuclei can be calculated from the corresponding integrated partons using the EPS09 parametrization. The role of nuclear effects is presented in terms of the ratio $R^A=\text{uPDF}^A/A\cdot \text{PDF}^N$ for both large and small $x$ domains.
It is well established that the nucleon form factors can be related to Generalized Parton Distributions (GPDs) through sum-rules. On the other hand, GPDs can be expressed in terms of Parton Distribution Functions (PDFs) according to Diehl's model. In this work, we use this model to calculate polarized GPDs for quarks ($\widetilde{H}_q$) using the available polarized PDFs obtained from the experimental data, and then study the axial form factor of nucleon. We determine parameters of the model using standard $χ^2$ analysis of experimental data. It is shown that some parameters should be readjust…
We review recent progress in calculating the twist--2 parton distribution functions at a low normalization point in the large--$N_c$ limit, where the nucleon can be described as a soliton of the effective chiral lagrangian. This field-theoretic approach preserves all general requirements on the distribution functions (positivity, normalization etc.). In particular, it allows to calculate the polarized and unpolarized antiquark distributions at the low normalization point.
We predict a strong enhancement of multijet production in proton-nucleus collisions at collider energies, as compared to a naive expectation of a cross section $\propto A$. The study of the process would allow to measure, for the first time, the double parton distribution functions in a nucleon in a model independent way and hence to study both the longitudinal and the transverse correlations of partons.
We complete the analysis of twist-two generalized parton distributions of the nucleon in one-loop order of heavy-baryon chiral perturbation theory. Extending our previous study of the chiral-even isosinglet sector, we give results for chiral-even isotriplet distributions and for the chiral-odd sector. We also calculate the one-loop corrections for the chiral-odd generalized parton distributions of the pion.
We present recent progress on the study of the deep inelastic structure of nuclei that improves our current understanding of the mechanisms of nuclear modifications of parton distribution functions.
We present a phenomenological unpolarized Parton Distribution Functions for diquarks based on a soft-wall light front AdS/QCD quark-diquark nucleon model. From a probed model consistent with the Drewll-Yan-West relation and quark counting rule, we have performed a fit of some free parameters using known phenomenological quark PDF data. The model considers the entire set of possible diquarks within the nucleon valence, in the present work we focus on the spin-0 $ud_0$, spin-1 $ud_1$ and spin-1 $uu_1$ diquarks into the valence of protons. The diquark PDFs obtained are able to used in proton-prot…
An up-to-date global QCD analysis of high energy lepton-hadron and hadron-hadron interactions is performed to better determine the gluon and quark parton distributions in the nucleon. Improved experimental data on inclusive jet production, in conjunction with precise deep inelastic scattering data, place good constraints on the gluon over a wide range of x; while new data on asymmetries in Drell-Yan processes contribute to better determine the d/u ratio. Comparisons with results of other recent global analyses are made, and the differences are described. Open issues and the general problem of …
