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Authors
Wolfram Schroers
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I review the current status of lattice calculations for two selected observables related to nucleon structure: the second moment of the unpolarized parton distribution, <x> (u-d), and the first moment of the polarized parton distribution, the non-singlet axial coupling gA. The major challenge is the requirement to extract them sufficiently close to the chiral limit. In the former case, there still remains a puzzling disagreement between lattice data and experiment. For the latter quantity, however, we may be close to obtaining its value from the lattice in the immediate future.
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We present the first Monte Carlo based global QCD analysis of spin-averaged and spin-dependent parton distribution functions (PDFs) that includes nucleon isovector matrix elements in coordinate space from lattice QCD. We investigate the degree of universality of the extracted PDFs when the lattice and experimental data are treated under the same conditions within the Bayesian likelihood analysis. For the unpolarized sector, we find rather weak constraints from the current lattice data on the phenomenological PDFs, and difficulties in describing the lattice matrix elements at large spatial distances. In contrast, for the polarized PDFs we find good agreement between experiment and lattice data, with the latter providing significant constraints on the spin-dependent isovector quark and antiquark distributions.
The strong force which binds hadrons is described by the theory of Quantum Chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the Parton Distribution Functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the opportunity to additionally explore the transverse structure of hadrons which is described by Generalized Parton Distributions (GPDs) and Transverse Momentum Dependent Parton Distribution Functions (TMD PDFs). In our previous review, we compared and contrasted the two main approaches used to determine the collinear PDFs: the first based on perturbative QCD factorization theorems, and the second based on lattice QCD calculations. In the present report, we provide an update of recent progress on the collinear PDFs, and also expand the scope to encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state of the various calculations, and consider what new data might be available in the near future. We also examine how a shared effort can foster dialog between the PDF and Lattice QCD communities, and yield improvements for these generalized PDFs.
In the framework of quantum chromodynamics (QCD), parton distribution functions (PDFs) quantify how the momentum and spin of a hadron are divided among its quark and gluon constituents. Two main approaches exist to determine PDFs. The first approach, based on QCD factorization theorems, realizes a QCD analysis of a suitable set of hard-scattering measurements, often using a variety of hadronic observables. The second approach, based on first-principle operator definitions of PDFs, uses lattice QCD to compute directly some PDF-related quantities, such as their moments. Motivated by recent progress in both approaches, in this document we present an overview of lattice-QCD and global-analysis techniques used to determine unpolarized and polarized proton PDFs and their moments. We provide benchmark numbers to validate present and future lattice-QCD calculations and we illustrate how they could be used to reduce the PDF uncertainties in current unpolarized and polarized global analyses. This document represents a first step towards establishing a common language between the two communities, to foster dialogue and to further improve our knowledge of PDFs.
We derive one-loop matching relations for the Ioffe-time distributions related to the pion distribution amplitude (DA) and generalized parton distributions (GPDs). They are obtained from a universal expression for the one-loop correction in an operator form, and will be used in the ongoing lattice calculations of the pion DA and GPDs based on the parton pseudo-distributions approach.
The path-integral formulation of the hadronic tensor W_{mu u} of deep inelastic scattering is reviewed. It is shown that there are 3 gauge invariant and topologically distinct contributions. The separation of the connected sea partons from those of the disconnected sea can be achieved with a combination of the global fit of the parton distribution function (PDF), the semi-inclusive DIS data on the strange PDF and the lattice calculation of the ratio of the strange to $u/d$ momentum fraction in the disconnected insertion. We shall discuss numerical issues associated with lattice calculation of the hadronic tensor involving a four-point function, such as large hadron momenta and improved maximum entropy method to obtain the spectral density from the hadronic tensor in Euclidean time. We also draw a comparison between the large momentum approach to the parton distribution function (PDF) and the hadronic tensor approach.
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