29 research outputs found
Quasi Distribution Amplitude of Heavy Quarkonia
The recently-proposed quasi distributions point out a promising direction for
lattice QCD to investigate the light-cone correlators, such as parton
distribution functions (PDF) and distribution amplitudes (DA), directly in the
-space. Owing to its excessive simplicity, the heavy quarkonium can serve as
an ideal theoretical laboratory to ascertain certain features of quasi-DA. In
the framework of non-relativistic QCD (NRQCD) factorization, we compute the
order- correction to both light-cone distribution amplitudes (LCDA)
and quasi-DA associated with the lowest-lying quarkonia, with the transverse
momentum UV cutoff interpreted as the renormalization scale. We confirm
analytically that the quasi-DA of a quarkonium does reduce to the respective
LCDA in the infinite-momentum limit. We also observe that, provided that the
momentum of a charmonium reaches about 2-3 times its mass, the quasi-DAs
already converge to the LCDAs to a decent level. These results might provide
some useful guidance for the future lattice study of the quasi distributions.Comment: 32 pages, 5 Figures, 1 tabl
Solving the Bars-Green equation for moving mesons in two-dimensional QCD
The two-dimensional QCD in the large limit, generally referred to as the
't Hooft model, is numerically investigated in the axial gauge in a
comprehensive manner. The corresponding Bethe-Salpeter equation for a bound
pair, originally derived by Bars and Green in 1978, was first
numerically tackled by Li and collaborators in late 1980s, yet only for the
{\it stationary} mesons. In this paper, we make further progress by numerically
solving the Bars-Green equation for {\it moving} mesons, ranging from the
chiral pion to charmonium. By choosing several different quark masses, we
computed the corresponding quark condensates, meson spectra and their decay
constants for a variety of meson momenta, and found satisfactory agreement with
their counterparts obtained using light-cone gauge, thus numerically verified
the gauge and Poincar\'{e} invariance of the 't Hooft model. Moreover, we have
explicitly confirmed that, as the meson gets more and more boosted, the large
component of the Bars-Green wave function indeed approaches the corresponding
't Hooft light-cone wave function, while the small component of the wave
function rapidly fades away.Comment: v2, 25 pages, 12 figures, and 1 table; Some figures updated,
references added, typo corrrected; to appear in JHE
Reconstructing parton densities at large fractional momenta
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
compute moments of PDFs, which are matrix elements of local operators.
Recently, an alternative approach has been proposed, based on the introduction
of quasi-parton distribution functions (quasi-PDFs), which are matrix elements
of equal-time spatial correlations and hence calculable on lattice. Quasi-PDFs
approach standard PDFs in the limit of very large longitudinal proton momenta
. This limit is not attainable in lattice simulations, and quasi-PDFs fail
to reproduce PDFs at high fractional longitudinal momenta. In this paper, we
propose a method to improve the reconstruction of PDFs by combining information
from quasi-PDFs and from the Mellin moments of regular PDFs. We test our method
using the diquark spectator model for up and down valence distributions of both
unpolarized and helicity PDFs. In the future, the method can be used to produce
PDFs entirely based on lattice QCD results.Comment: 12 pages, 7 double-panel figures in pdf, RevTeX4-
One-Loop Matching for Parton Distributions: Non-Singlet Case
We derive one-loop matching condition for non-singlet quark distributions in
transverse-momentum cut-off scheme, including unpolarized, helicity and
transversity distributions. The matching is between the quasi-distribution
defined by static correlation at finite nucleon momentum and the light-cone
distribution measurable in experiments. The result is useful for extracting the
latter from the former in a lattice QCD calculation.Comment: 10 pages, 1 figur
Probing Parton Orbital Angular Momentum in Longitudinally Polarized Nucleon
While the total orbital angular momentum (OAM) of a definite quark flavor in
a longitudinally-polarized nucleon can be obtained through a sum rule involving
twist-two generalized parton distribution (GPDs), its distribution as a
function of parton momentum in light-front coordinates is more complicated to
define and measure because it involves intrinsically twist-three effects. In
this paper, we consider two different parton OAM distributions. The first is
manifestly gauge invariant, and its moments are local operators and calculable
in lattice QCD. We show that it can potentially be measured through twist-three
GPDs. The second is the much-debated canonical OAM distribution natural in
free-field theory and light-cone gauge. We show the latter in light-cone gauge
can also be related to twist-three GPDs as well as quantum phase-space Wigner
distributions, both being measurable in high-energy experiments.Comment: 14 pages, no figur