We will present new results of the proton unpolarized and helicity GPDs, within lattice QCD. Their x-dependence is extracted using the quasi-distribution method, which requires matrix elements of moving hadrons coupled with non-local operators. We use momentum boost up to 1.67 GeV, and momentum transfer squared up to 1 GeV^2. The calculation is performed on an Nf=2+1+1 ensemble of twisted mass...

I present the derivation of the factorization theorem for the quasi-transverse-momentum-dependent (quasi-TMD) operator, within the soft collinear effective field theory framework. The factorized expression is built from the physical TMD distribution, and a nonperturbative lattice related factor. The lattice related functions cancel in appropriately constructed ratios. These ratios could be...

Transverse-momentum-dependent parton distribution functions (TMDPDFs) provide a unique probe of the three-dimensional spin structure of hadrons. We construct spin-dependent quasi-TMDPDFs that are amenable to lattice QCD calculations and that can be used to determine spin-dependent TMDPDFs. We calculate the short-distance coefficients connecting spin-dependent TMDPDFs and quasi-TMDPDFs at...

Recently, a hybrid scheme was proposed by the author and company to renormalize the quasi light-front correlations in the LaMET calculation of the PDFs. The hybrid scheme reduces the systematic uncertainty in the renormalization at distances where the leading-twist expansion or perturbation theory is expected to fail, so that one can have a better-controlled Fourier transform to the momentum...

We present the first next-to-next-to-leading order (NNLO) calculation of quark quasi parton distribution functions (PDFs) in the large momentum effective theory. The nontrivial factorization at this order is established explicitly and the full analytic matching coefficients between the quasi distribution and the lightcone distribution are derived for the first time. We demonstrate...

I explore the explicit relationship between the LaMET and pseudo-PDF approaches to collinear hadron structure in the context of a scalar theory, and demonstrate explicitly their equivalence at one loop in perturbation theory. Scalar field theory removes complications associated with gauge theories that enable complete calculations of all quantities, such as the Ioffe-time distribution at...

In large-momentum effective theory (LaMET), the quasi light-front correlations calculated on lattice contain both linear and logarithmic divergences in the lattice spacing, and thus need to be properly renormalized. The commonly used renormalization strategy in the literature has the problem of introducing extra non-perturbative effects at large distance. In this talk, I present a hybrid...

Quark correlation functions in position space are calculable in lattice QCD and factorizable into parton distribution functions with matching coefficients perturbatively calculable to all orders in QCD, which provides a way to extract PDFs from lattice QCD calculation. We present for the first time complete next-to-next-to-leading-order calculation of valence-quark matching coefficients. We...

Even since the quasi parton distribution function (PDF) was proposed within the large-momentum effective theory (LaMET) framework, its renormalization under lattice regularization has been a central challenge due to the existence of linear divergences. Previous theoretical studies have shown that the quasi-PDF operator is multiplicatively renormalizable and the linear divergence comes from the...

We present how partonic structure of hadrons can be extracted from matrix elements of two spatially-separated currents, which are computable directly in lattice QCD and can be factorized into parton distribution functions with calculable hard coefficients. We demonstrate the recently derived one-loop matching coefficient has a well-controlled behavior in Ioffe-time, for example, in a specific...

In this presentation, we focus on the pseudo-PDF method of calculating parton distributions. We use a Euclidean space matrix element, called the Ioffe-time pseudo distribution, and Short Distance Factorization, which allows data from all momenta to contribute in the analysis, to obtain parton distributions. We present the latest lattice results from the HadStruc collaboration, discuss several...

We present the first lattice QCD computation of the light quarks and strange helicity PDFs. We used a $N_f=2+1+1$ lattice ensemble generated by the Extended Twisted Mass collaboration (ETMC), with pion mass $M_\pi\approx 250\;{\rm GeV}$, $M_\pi L \approx 3.8$ and lattice spacing $a= 0.0938(2)(3)\;\;{\rm fm}$. Momentum smearing is employed in order to improve the signal-to-noise ratio,...

We propose to study the hadronic tensor with lattice QCD, which works in all the energy ranges (from elastic scattering to inelastic scattering and on to deep inelastic scattering) and is related to many important physical problems. A challenge of this approach in the study of PDFs is to access high momentum and energy transfers, and numerical tests show that small lattice spacings are...

We will present results on the spin decomposition and the momentum distribution among quarks and gluons in the proton. Techniques for lattice QCD simulations at the physical pion mass applied for the computation of sea-quark and gluon contributions will be presented. We will discuss several challenges and perspectives for future developments.

The transverse-momentum-dependent (TMD) soft function is a key ingredient in QCD factorization of Drell-Yan and other processes with relatively small transverse momentum. We present a lattice QCD study of this function at moderately large rapidity on a 2+1 flavor CLS dynamic ensemble with $a=0.098$ fm. We extract the rapidity-independent (or intrinsic) part of the soft function through a...

The perturbative procedure of matching within Large Momentum Effective Theory connects the quasi-parton distributions to the light-cone distributions that enter physical processes. This procedure has demonstrated success in the extraction of the twist-2 PDFs from lattice QCD. We explore the formalism of matching, for the first time, for the twist-3 PDFs $g_T(x)$, $e(x)$ and $h_L(x)$. We make...

We present a lattice exploration of the isovector flavor combination of the nucleon's twist-3 helicity PDF g_T(x), using twisted mass clover fermions. We employ the quasi-distribution approach at three values of the nucleon boost up to 1.7 GeV to connect the lattice-extracted matrix elements, renormalized in the RI/MOM scheme, to light-cone distributions, applying the matching procedure that...

I present the lattice calculation and results for the nonpertrubative Collins-Soper (CS) kernel, which describes the energy-dependence of the transverse momentum-dependent parton distribution functions (TMDPDFs). The CS kernel is extracted from the ratios of the quasi-TMD taken at different momenta.

The analysis is done with dynamical fermions for different polarization cases of quasi-TMD...

We present the results that are necessary in the ongoing lattice calculations of the gluon parton distribution functions (PDFs) within the pseudo-PDF approach. We give a classification of possible two-gluon correlator functions and identify those that contain the invariant amplitude determining the gluon PDF in the light-cone $z^2 \to 0$ limit. One-loop calculations have been performed in the...

The parton distribution functions (PDFs) provide process-independent information about the quarks and gluons inside hadrons. Although the gluon PDF can be obtained from a global fit to experimental data, it is not constrained well in the large-$x$ region. Theoretical gluon-PDF studies are much fewer than those of the quark PDFs. In this work, we present the first lattice-QCD results that...