Related papers: Note on lattice regularization and equal-time corr…
Ioffe-time distributions, which are functions of the Ioffe-time $\nu$, are the Fourier transforms of parton distribution functions with respect to the momentum fraction variable $x$. These distributions can be obtained from suitable equal…
We study the correlation functions between the dynamical variables and between their conjugate momenta at sites of a harmonic lattice in the $d$-dimensional Euclidean space. We show that at the thermodynamic limit, they can be expressed in…
We propose a modified definition for a quasi-parton distribution function (QPDF) with an equal-time correlator in the large momentum limit, whose two pieces of space-like Wilson links are oriented in orthogonal directions. It is explicitly…
We consider linear and obstacle problems driven by a nonlocal integral operator, for which nonlocal interactions are restricted to a ball of finite radius. These type of operators are used to model anomalous diffusion and, for a special…
Generalized parton distributions describe the correlations between the longitudinal momentum and the transverse position of quarks and gluons in a nucleon. They can be constrained by measuring photon leptoproduction observables, arising…
Parton distribution functions (PDFs) are nonperturbative objects defined by nonlocal light-cone correlations. They cannot be computed directly from Quantum Chromodynamics (QCD). Using a standard lattice QCD approach, it is possible to…
We give out a simple way to connect the parton distribution functions defined in Minkowskian space and the nonperturbative QCD methods grounded in Euclidean space (e.g., lattice QCD(LQCD), Dyson-Schwinger (DS) equations, functional…
We present results for the $x$ dependence of the unpolarized, helicity, and transversity isovector quark distributions in the proton using lattice QCD, employing the method of quasi-distributions proposed by Ji in 2013. Compared to a…
Continuum limits of Laplace operators on general lattices are considered, and it is shown that these operators converge to elliptic operators on the Euclidean space in the sense of the generalized norm resolvent convergence. We then study…
A unified classification and analysis is presented of two dimensional Dirac operators of QCD-like theories in the continuum as well as in a naive lattice discretization. Thereby we consider the quenched theory in the strong coupling limit.…
The idea of ``dynamically'' generated parton distribution functions, based on regular initial conditions at low momentum scale, is reanalyzed with particular emphasize paid to its compatibility with the factorization mechanism. Basic…
The three well-known forms of relativistic dynamics are unitarily equivalent and the problem of constructing the current operators can be solved in any form. However the notion of the impulse approximation is reasonable only in the point…
Parton distribution functions are key quantities for us to understand the hadronic structures in high-energy scattering, but they are difficult to calculate from lattice QCD. Recent years have seen fast development of the large-momentum…
We consider a class of first-order partial differential operators, acting on the space of ultradifferentiable periodic functions, and we describe their range by using the following conditions on the coefficients of the operators: the…
We report on an exact calculation of lattice correlation functions on a finite four-dimensional lattice with either Euclidean or Minkowskian signature. The lattice correlation functions are calculated by the method of differential…
We present a general scheme to derive lattice differential operators from the discrete velocities and associated Maxwell-Boltzmann distributions used in lattice hydrodynamics. Such discretizations offer built-in isotropy and recursive…
Calculation of moments of generalized parton distributions in lattice QCD requires more powerful techniques than those previously used to calculate moments of structure functions. Hence, we present a novel approach that exploits the full…
We consider the problem of the continuation with respect to a small parameter $\epsilon$ of spatially localised and time periodic solutions in 1-dimensional dNLS lattices, where $\epsilon$ represents the strength of the interaction among…
The recent lattice QCD calculations of the neutron and proton electric dipole moments (EDMs) and the CP-violating $\pi {\rm NN}$ coupling constant due to the $\theta$ term are reviewed. Progress towards nucleon EDM calculations, including…
We present the unpolarized and helicity parton distribution functions calculated within lattice QCD simulations using physical values of the light quark mass. Non-perturbative renormalization is employed and the lattice data are converted…