Session RE: Mini-Symposium: Lattice QCD for PDFs

Light-cone PDFs using Lattice QCD: an overview of results, successes and challenges

Lattice QCD is a theoretical non-perturbative approach for the study of QCD dynamics numerically from first principles. The lattice formulation is widely used for hadron structure calculations and is becoming a reliable tool, striving for control of various sources of systematic uncertainties. Parton distribution functions (PDFs) have a central role in understanding hadron structure, and have been calculated in lattice QCD mainly via their Mellin moments. In this talk we will present results for alternative new methods to access PDFs, that is, quasi-PDFs, pseudo-PDFs and good lattice cross sections. The main focus of the talk is to demonstrate the successes and challenges in these approaches and the need of a careful investigation of systematic uncertainties. Lattice data will be compared against results from global fits of PDFs. Of particular importance are the lattice results on the transversity PDFs, which are not well-constrained experimentally. This presents a major success for the emerging field of direct calculations of distribution functions using lattice QCD.   

Gluon PDF Calculation from Lattice QCD Using Pseudo-PDF Technique

In this talk, I report on our calculation of the unpolarized gluon parton distribution function (PDF) in the nucleon using Pseudo-PDF technique. The computation is done on a $32^3 \times 64$ isotropic lattice with a pion mass of 380 MeV and lattice spacing, a = 0.098 fm using 2+1 flavor of Clover-Wilson fermion. This is the first application of the distillation method for constructing the nucleon interpolating fields for gluonic matrix elements. The bare matrix elements are calculated using the summation method. In order to reduce the statistical fluctuations, the gluonic operators are smeared using gradient flow. The systematic effects introduced by this smearing are studied as a function of the flow-time and the renormalized matrix elements are extracted by taking the small flow-time limit. Finally the lattice matrix elements are factorized to the $\overline{MS}$ scheme PDF, at the small z-separation limit, using NLO matching formula.   

Valence PDF of pion from fine lattices using quasi- and pseudo-PDF frameworks

We present numerical results on valence PDF of pion from our lattice computations at two fine lattice spacings of 0.04 and 0.06 fm. We employ both quasi- as well as pseudo-PDF methods to place a tighter constraint on the PDF as determined through corresponding perturbative matching. We will also present some preliminary analysis of pion GPD on the same lattice emsembles.   

Pion Valence Quark Distribution from Hadronic Lattice Cross Sections

It has been shown that a class of matrix elements of two spatially-separated currents, which are computable directly in Lattice QCD, can be factorized into parton distribution functions with calculable hard coefficients [Phys. Rev. Lett. 120 (2018) no. 2, 022003]; in the same manner as the parton distribution functions are extracted from the hadronic cross sections measured in an experiment. In this presentation, we present the progress towards solving the large-$x$ behavior of pion valence quark distribution using Lattice QCD calculation from spatially separated current-current correlations in the coordinate space. Results are presented on several lattice ensembles, thereby addressing finite-volume, discretization and quark mass effects in the extracted distributions.   

On the inverse problem of obtaining parton distribution functions from lattice QCD

Computations of parton distribution functions (PDFs) of hadrons form first principles represent an important challenge for lattice QCD. Recent theoretical developments, have identified a class of hadronic matrix elements that in principle provide access to the desired PDFs. However, accessing the PDFs requires solving an ill-defined inverse problem. In this talk I will discuss methods that allow us to address that problem and compare several of the available options.   

Machine Learning for Quasi-PDF Matrix Elements

The large‐momentum effective theory (LaMET) framework has been widely used to calculate the Bjorken‐$x$ dependence of PDFs in lattice‐QCD hadron-structure calculations. However, achieving sufficient precision for large-momentum hadrons can be computationally expensive on super-fine lattice ensembles and their lattice artifacts are seldom addressed. In this talk, we will report on-going progress on the study of systematics in quasi-PDFs using multiple lattice spacings and volumes. Then, we apply machine learning algorithms to a few selected quasi-PDF matrix elements and determine how much it can help the PDF determination.   

Confronting lattice parton densities within global QCD analysis

Recent progress in lattice QCD simulations of parton quasi-distributions is paving the way towards the study of the momentum dependence of PDFs from first principles. We present the first combined global QCD analysis of inclusive deep-inelastic scattering, Drell-Yan and other high-energy scattering data with recent results from lattice calculation of the $u-d$ PDF in the proton. We examine how the lattice results match with phenomenological determinations of PDF parameters, and determine which regions of parton fraction in the lattice data induce constraints on the $\bar d-\bar u$ PDF asymmetry in the proton.   

From Qubits to Quarks: Parton Physics on a Quantum Computer

Quantum computers provide a unique way of computing real-time correlators from first principles, a task not yet achievable on classical computers due to the sign problem. The determination of parton distribution functions on the euclidean lattice is obstructed by an inability to properly calculate real-time correlators. This is a match made in heaven: a lattice field theory simulation on a quantum computer may provide access to PDFs. In this talk we outline recent progress on simulating field theories on a quantum computer, and show how this progress may be leveraged to obtain PDFs.