Many present lattice QCD approaches to calculate the parton distribution functions (PDFs) rely on a factorization formula or effective theory expansion of certain Euclidean matrix elements in boosted hadron states. In the quasi- and pseudo-PDF methods, the matching coefficient in the factorization or expansion formula includes large logarithms near the threshold, which arise from the subtle...
Nucleon transversity distribution is an essential quantity that reveals the nucleon's transverse spin structure. It also provides crucial inputs for understanding high-energy collision experiments involving transversely polarized nucleons. As a chiral-odd quantity, it's difficult to measure experimentally. Thus, ab initio lattice QCD calculations play an important complementary role. We report...
I describe the structure of the nucleon obtained within the pseudo-PDF framework. In particular I present recent calculations of the unpolarized, helicity and transversity distributions. We employ the distillation framework which allows a more complete sampling of the lattice and, together with momentum smearing, enables us to extend the range of Ioffe time accessible to our computation. ...
We present recent work on the calculation of the unpolarized isovector quark parton distribution function (PDF) of the nucleon at the physical point from lattice QCD utilizing a next-to-next-to-leading order (NNLO) matching. The main observables for these calculations are equal-time spatially-separated matrix elements of a boosted nucleon. There are two main strategies one can employ to obtain...
I will discuss the matching of quasi-PDF and quasi-GPD for the hybrid scheme. The IR renormalon ambiguity of the quasi-PDF in this scheme is also discussed.
In the large-momentum expansion for parton distribution functions (PDFs), the natural physics scale is the longitudinal momentum ($p_z$) of the quarks (or gluons) in a large-momentum hadron. We show how to expose this scale dependence through resumming logarithms of the type $\ln^n p_z/\mu$ in the matching coefficient, where $\mu$ is a fixed renormalization scale. The result enhances the...
The light-cone distribution amplitude (LCDA) of the pion carries information about the parton momentum distribution and is an important theoretical input into various predictions of exclusive measurements at high energy, including the pion electromagnetic form factor. This talk presents progress towards a lattice calculation of the fourth Mellin moment of the LCDA using the heavy quark...
Calculating the $x$-dependence of pion distribution amplitude (DA) using the large-momentum effective theory has entered the era where the systematics need to be controlled. We demonstrate the necessity of a proper renormalization and a corresponding perturbative matching to achieve power accuracy ~$O(\Lambda_{QCD}/xP_z)$. By resumming the leading renormalon in the perturbative series, we are...
The electromagnetic form factor, especially its asymptotic behavior for large momentum transfer (Q^2), of pion and kaon provides crucial insight into the partonic structure of a Nambu-Goldstone boson in the strong interaction. Studies of the electromagnetic form factor of pion and kaon up to Q^2 ~ 6 GeV^2 are underway at the ongoing JLab12 experiment, and its measurements in an extended range...
As is well known, it is difficult to compute quantities defined on the light-front in a lattice approach, since the light-front dynamics is strictly in the Minkowski space, while the lattice formulation is in the Euclidean space. I will introduce a method to connect the light-front dynamics (LFD) to the ordinary instant form dynamics (IFD), which is called the interpolation method. By having...
In this work, we present the first ab-initio numerical results of unpolarized proton's isovector transverse-momentum-dependent parton distribution functions (TMDPDFs), which are essential for exploring the inner pictures of nucleon, as well as for predicting the observables in multi-scale, non-inclusive high energy processes such as semi-inclusive deep-inelastic scattering and Drell-Yan...
We present a first calculation of the unpolarized proton's
isovector transverse-momentum-dependent parton distribution functions (TMDPDFs) from lattice QCD, which are essential to predict observables of multi-scale, semi-inclusive processes in the standard model. We use a $N_f=2+1+1$ MILC ensemble with valence clover fermions on a highly improved staggered quark sea (HISQ), and compute the...
According to large momentum effective theory (LaMET), the parton observables can be extracted from lattice calculations of quasi-observables through a perturbative matching relation. In this talk, I present a unified framework for the perturbative factorization connecting Euclidean correlations to light-cone correlations. We derive the flavor singlet and non-singlet matching kernel for the...
Traditionally, lattice QCD computations of GPDs have been carried out in a frame, where the transferred momentum is symmetrically distributed between the incoming and outgoing hadrons. However, such frames are inconvenient for lattice QCD calculations since each value of the momentum transfer requires a separate calculation, increasing the computational cost. In a recent work...
Historically, GPDs have been defined in the symmetric frame, where the momentum transfer between the initial and final hadron state is equally distributed to the two states.
Such a setup is computationally very costly for their frame-dependent counterparts in lattice QCD, such as the quasi-GPDs. In this work we present a calculation of the pion GPD using the methodology proposed recently in...
I will present the recent calculations of gluonic matrix elements related to the nucleon's unpolarized and helicity gluon PDF. Gluon matrix elements are notoriously noisy. By leveraging the tools of distillation and summed GEVP, HadStruc has reach a necessary precision to compare results to phenomenological determinations of gluon structure. Recently, doubt has been given to the applicability...
We present the first physical-continuum limit $x$-dependent nucleon gluon distribution from lattice QCD using the pseudo-PDF approach, on lattice ensembles with $2+1+1$ flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration. We use clover fermions for the valence action on three lattice spacings $a \approx 0.9$, 0.12 and 0.15~fm and three pion masses $M_\pi \approx...
We present results of the x-dependence of the unpolarized gluon PDF for the proton. We use an Nf = 2 + 1 + 1 ensemble of maximally twisted mass fermions with clover improvement and the Iwasaki improved gluon action. The quark masses are tuned so that the pion mass is 260 MeV. We use a 32^3 × 64 lattice size with a lattice spacing a = 0.093 fm giving a spatial extent of 3 fm. We employ the...
In this work, we present the first results on the gluon parton distribution of the kaon from lattice quantum chromodynamics.
We carry out the lattice calculation at pion mass around 310~MeV and two lattice spacings, 0.15 and 0.12~fm, using $2+1+1$-flavor HISQ ensembles generated by MILC Collaboration. The kaon correlators are calculated using clover fermions and momentum-smearing sources with...
In large-momentum effective theory (LaMET), the transverse-momentum-dependent (TMD) light-front wave functions and soft functions can be extracted from the simulation of a four-quark form factor and equal-time correlation functions. In this work, using expansion by regions we provide a one-loop proof of TMD factorization of the form factor. For the one-loop validation, we also present a...
To calculate the transverse-momentum-dependent parton distribution functions (TMDPDFs) from lattice QCD, an important goal yet to be realized, it is crucial to establish a viable nonperturbative renormalization approach for linear divergences in the corresponding Euclidean quasi-TMDPDF correlators in large-momentum effective theory. We perform a first systematic study of the renormalization...
Soft function plays an important role in TMD factorization. We present a lattice QCD calculation for the rapidity-independent (or intrinsic) part of soft function at one-loop accuracy with a coherent normalization in large-momentum effective theory. The calculation is performed on CLS dynamic ensemble with a=0.098 fm and MILC ensemble with a=0.12 fm. Our results based on two ensembles are...
We present a state-of-the-art lattice QCD calculation of transverse momentum dependent wave function (TMDWF) of pion in large-momentum effective theory. The calculation is performed at clover fermion action ensembles with lattice spacing a=0.12fm generated by MILC Collaboration with and CLS ensembles with lattice spacing a=0.098fm. On each of the two ensembles we calculated three momentum up to...
