Since the parton model was introduced by Feynman more than fifty years ago, we have learned much about partonic structure of proton through a large body high-energy experimental data and dedicated global fits. However, calculating observables such as distribution function (PDFs) from fundamental theory strong interactions, QCD, has made limited progress. Recently, authors advocated formalism, large-momentum effective (LaMET), which one can extract physics properties travelling at moderate...

A bstract In this work, we report a lattice calculation of x -dependent valence pion generalized parton distributions (GPDs) at zero skewness with multiple values the momentum transfer − t . The calculations are based on an N f = 2 + 1 gauge ensemble highly improved staggered quarks Wilson-Clover fermion. spacing is 0.04 fm, and mass tuned to be 300 MeV. We determine Lorentz-invariant amplitudes quasi-GPD matrix elements for both symmetric asymmetric momenta transfers similar show...

We derive one-loop matching condition for non-singlet quark distributions in transverse-momentum cut-off scheme, including unpolarized, helicity and transversity distributions. The is between the quasi-distribution defined by static correlation at finite nucleon momentum light-cone distribution measurable experiments. result useful extracting latter from former a lattice QCD calculation.

In a large-momentum nucleon state, the matrix element of gauge-invariant Euclidean Wilson line operator accessible from lattice QCD can be related to standard light-cone parton distribution function through effective theory (LaMET) expansion. This relation is given by factorization formula with nontrivial matching coefficient. Using product expansion we derive quasiparton in LaMET, and show that more recently discussed pseudoparton approach also obeys an equivalent formula. Explicit results...

In the large-momentum effective field theory approach to parton physics, matrix elements of nonlocal operators quark and gluon fields, linked by straight Wilson lines in a spatial direction, are calculated lattice quantum chromodynamics as function hadron momentum. Using heavy-quark formalism, we show multiplicative renormalization these at all orders perturbation theory, both dimensional regularizations. The result provides theoretical basis for extracting properties through properly...

We present lattice results for the isovector unpolarized parton distribution with nonperturbative regularization-invariant momentum-subtraction scheme (RI/MOM) renormalization on lattice. In framework of large-momentum effective field theory (LaMET), full Bjorken-$x$ dependence a momentum-dependent quasidistribution is calculated and matched to ordinary light cone at one-loop order, power corrections included. The important step RI/MOM that connects continuum matrix elements detailed in this...

We present the first direct lattice-QCD calculation of Bjorken-$x$ dependence valence quark distribution pion. Using large-momentum effective theory (LaMET), we calculate boosted pion state with long Wilson link operators. After implementing one-loop matching and meson mass corrections, our result at $m_\pi \approx 310$ MeV is in agreement those extracted from experimental data as well Dyson-Schwinger equation small $x$ region, but a sizeable discrepancy large region. This provides nice...

The quasiparton distribution is a spatial correlation of quarks or gluons along the $z$ direction in moving nucleon which enables direct lattice calculations parton functions. It can be defined with nonperturbative renormalization regularization independent momentum subtraction scheme (RI/MOM), then perturbatively related to collinear $\overline{\mathrm{MS}}$ scheme. Here we carry out matching from RI/MOM for quasi-PDF PDF, determining non-singlet quark coefficient at next-to-leading order...

At small transverse momentum $q_T$, transverse-momentum dependent parton distribution functions (TMDPDFs) arise as genuinely nonperturbative objects that describe Drell-Yan like processes in hadron collisions well semi-inclusive deep-inelastic scattering. TMDPDFs naturally depend on the momentum, and associated evolution is determined by Collins-Soper equation. For $q_T \sim \Lambda_\mathrm{QCD}$ corresponding kernel (or anomalous dimension) must be an independent ingredient order to relate...

Large-Momentum Effective Theory (or LaMET) advocated by the present authors provides a direct approach to simulate parton physics in Eulidean lattice QCD theory. Recently, there has been much interest this theory literature, with some questioning its validity and effectiveness. Here we provide discussions aiming at further exposition of approach. In particular, explain why it does not have usual power divergence problem calculations for moments distributions. We show that although Ioffe-time...

We present a state-of-the-art calculation of the isovector quark-helicity Bjorken-x distribution in proton using lattice-QCD ensembles at physical pion mass. compute quasidistributions momenta P_{z}∈{2.2,2.6,3.0} GeV on lattice and match them systematically to parton large-momentum effective theory. reach an unprecedented precision through high statistics simulations, matrix elements, control excited-state contamination. The resulting with combined statistical systematic errors is agreement...

The Collins-Soper kernel relates transverse momentum-dependent parton distribution functions (TMDPDFs) at different energy scales. For small momentum $q_T\sim \Lambda_\text{QCD}$, this is non-perturbative and can only be determined with controlled uncertainties through experiment or first-principles calculations. This work presents the first exploratory determination of using lattice formulation Quantum Chromodynamics. In a quenched calculation, $N_f=0$ scales in range 250 MeV $< q_T < 2$...

We present a high-statistics lattice QCD determination of the valence parton distribution function (PDF) pion, with mass 300 MeV, using two very fine spacings $\mathrm{a}=0.06\text{ }\text{ }\mathrm{fm}$ and 0.04 fm. reconstruct $x$-dependent PDF, as well infer first few even moments PDF leading-twist 1-loop perturbative matching framework. Our analyses use both RI-MOM ratio-based schemes to renormalize equal-time bilocal quark-bilinear matrix elements pions boosted up 2.4 GeV momenta....

In large-momentum effective theory (LaMET), calculating parton physics starts from coordinate-space-$z$ correlation functions $\tilde h(z, a,P^z)$ in a hadron of momentum $P^z$ lattice QCD. Such involve both linear and logarithmic divergences spacing $a$, thus need to be properly renormalized. We introduce hybrid renormalization procedure match these correlations those the continuum $\overline{\rm MS}$ scheme, without introducing extra non-perturbative effects at large $z$. analyze effect...

We report the first lattice QCD calculation of pion valence quark distribution with next-to-next-to-leading order perturbative matching correction, which is done using two fine lattices spacings a=0.04 and 0.06 fm mass m_{π}=300 MeV, at boost momentum as large 2.42 GeV. As a crucial step to control systematics, we renormalize quasidistribution in recently proposed hybrid scheme, features Wilson-line subtraction distances coordinate space, develop procedure match it MS[over ¯] scheme....

Traditionally, lattice QCD computations of generalized parton distributions (GPDs) have been carried out in a symmetric frame, where the transferred momentum is symmetrically distributed between incoming and outgoing hadrons. However, such frames are inconvenient since they require separate calculation for each value transfer, increasing significantly computational cost. In this work, by focusing on quasi-distribution approach, we lay foundation faster more effective calculations GPDs...

For the first time, we present a lattice QCD determination of Mellin moments unpolarized generalized parton distributions (GPDs) proton from an analysis quasi-GPD matrix elements within short-distance factorization framework. We perform our calculation on $N_f$=2+1+1 twisted mass fermions ensemble with clover improvement at spacing $a=0.093$ fm and pion $m_\pi=260$ MeV. Focusing zero-skewness case, iso-vector iso-scalar quasi-GPDs are calculated $\gamma_0$ definition, as well recently...

Recently, we made significant advancements in improving the computational efficiency of lattice QCD calculations for generalized parton distributions (GPDs). This progress was achieved by adopting matrix elements asymmetric frames, deviating from computationally-expensive symmetric frame typically used, and allowing freedom choice distribution momentum transfer between initial final states. A crucial aspect this approach involves adoption a Lorentz covariant parametrization elements,...

We present a direct lattice QCD calculation of the $x$-dependence pion distribution amplitude (DA), which is performed using quasi-DA in large momentum effective theory on domain-wall fermion ensemble at physical quark masses and spacing $a\approx 0.084$ fm. The bare quais-DA matrix elements are renormalized hybrid scheme matched to $\overline{\rm MS}$ with subtraction leading renormalon Wilson-line mass. For first time, we include threshold resummation perturbative matching onto light-cone...

We present a general analysis of the orbital angular momentum (OAM) distribution gluons $L_g(x)$ inside nucleon with particular emphasis on small-$x$ region. derive novel operator representation in terms Wilson lines and argue that it is approximately proportional to gluon helicity $L_g(x) \approx -2\Delta G(x)$ at small-$x$. also compute longitudinal single spin asymmetry exclusive diffractive dijet production lepton-nucleon scattering next-to-eikonal approximation show direct probe...

We present the first lattice-QCD calculation of kaon distribution amplitude using large-momentum effective theory (LaMET) approach. The momentum-smearing technique has been implemented to improve signals at large meson momenta. subtract power divergence due Wilson line high precision multiple lattice spacings. structure clearly shows an asymmetry around x=1/2, a clear sign its skewness. Our result also prefers broader than asymptotic form. study leading SU(3) flavor symmetry breaking...

We report the first lattice QCD calculation of glue spin in nucleon. The is carried out with valence overlap fermions on 2+1 flavor domain-wall fermion gauge configurations four spacings and volumes including an ensemble physical values for quark masses. S_{G} Coulomb modified minimal subtraction (MS[over ¯]) scheme obtained one-loop perturbative matching. find results fairly insensitive to spacing also that proton momentum dependence range 0≤|p[over →]|<1.5 GeV very mild, we determine it...

We present a detailed Lattice QCD study of the unpolarized isovector quark Parton Distribution Function (PDF) using large-momentum effective theory framework. choose quasi-PDF defined by spatial correlator which is free from mixing with other operators same dimension. In lattice simulation, we use Gaussian-momentum-smeared source at $M_\pi=356$ MeV and $P_z \in \{1.8,2.3\}$ GeV. To control systematics associated excited states, explore {five different source-sink separations}. The...

Within the framework of large momentum effective theory (LaMET), genenaralized parton distributions (GPDs) can be extracted from lattice calculations quasi-GPDs through a perturbative matching relation, up to power corrections that are suppressed by hadron momentum. In this paper, we focus on isovector quark GPDs, including unpolarized, longitudinally and transversely polarized cases, present one-loop connects renormalized in regularization-independent subtraction (RI/MOM) scheme GPDs MS...