75 research outputs found
Quasi-PDFs and pseudo-PDFs
We discuss the physical nature of quasi-PDFs, especially the reasons for the
strong nonperturbative evolution pattern which they reveal in actual lattice
gauge calculations. We argue that quasi-PDFs may be treated as hybrids of PDFs
and the rest-frame momentum distributions of partons. The latter is also
responsible for the transverse momentum dependence of TMDs. The resulting
convolution structure of quasi-PDFs necessitates using large probing momenta
GeV to get reasonably close to the PDF limit. To deconvolute
the rest-frame distribution effects, we propose to use a method based directly
on the coordinate representation. We treat matrix elements as
distributions depending on the Ioffe-time and the distance parameter . The rest-frame spatial distribution is
given by . Using the reduced Ioffe function we divide out
the rest frame effects,including the notorious link renormalization factors.
The -dependence remains intact and determines the shape of PDFs in the
small region. The residual dependence of the is governed by perturbative evolution. The Fourier transform of produces pseudo-PDFs that generalize the
light-front PDFs onto spacelike intervals. On the basis of these findings we
propose a new method for extraction of PDFs from lattice calculations.Comment: 11 pages, Talk at QCD Evolution 2017 Worksho
Structure of parton quasi-distributions and their moments
We discuss the structure of the parton quasi-distributions (quasi-PDFs) outside the "canonical" support region of the usual
parton distribution functions (PDFs). Writing the moments of
in terms of the combined -moments of the transverse
momentum distribution (TMD) , we establish a connection
between the large- behavior of and large- behavior
of . In particular, we show that the hard
tail of TMDs in QCD results in a slowly decreasing behavior of
quasi-PDFs for large that produces infinite moments of .
We also relate the terms with the -singulariies of the
Ioffe-time pseudo-distributions . Converting the
operator product expansion for into a matching
relation between the quasi-PDF and the light-cone PDF ,
we demonstrate that there is no contradiction between the infinite values of
the moments of and finite values of the moments of .Comment: 9 pages, version to appear in Physics Letters
Deeply Virtual Compton Scattering: Facing Nonforward Distributions
Applications of perturbative QCD to deeply virtual Compton scattering process
require a generalization of usual parton distributions for the case when
long-distance information is accumulated in nonforward matrix elements of quark
and gluon operators. We discuss two types of functions parametrizing such
matrix elements: double distributions F(x,y;t) and nonforward distribution
functions \cal F_\zeta (X;t) and also their relation to usual parton densities
f(x).Comment: 4 pages, to be published in the Proceedings of the International
Conference on Deep Inelastic Scattering, Chicago, April 1997, AI
Asymmetric Parton Distributions
Applications of perturbative QCD to hard exclusive electroproduction
processes in the Bjorken limit at small invariant momentum transfer t bring in
a new type of parton distributions which have hybrid properties, resembling
both the parton distribution functions and the distribution amplitudes. Their
t-dependence is analogous to that of hadronic form factors. We discuss general
properties of these new parton distributions, their relation to usual parton
densities and the evolution equations which they satisfy.Comment: 4 pages, to be published in the Proceedings of the International
Conference on Deep Inelastic Scattering, Chicago, April 1997, AI
Pion Wave Function from QCD Sum Rules with Nonlocal Condensates
We investigate a model QCD sum rule for the pion wave function
based on the non-diagonal correlator whose perturbative
spectral density vanishes and , the theoretical side of the sum
rule, consists of condensate contributions only. We study the dependence of
on the Borel parameter and observe that has a
humpy form, with the humps becoming more and more pronounced when
increases. We demonstrate that this phenomenon reflects just the oscillatory
nature of the higher states wave functions, while the lowest state wave
function extracted from our QCD sum rule analysis,has no
humps, is rather narrow and its shape is close to the asymptotic form
.Comment: Talk at the Workshop "Continuous Advances in QCD", 11 pages +
appended uuencoded ps file with 8 figures, Latex, CEBAF-TH-94-1
One-loop evolution of parton pseudo-distribution functions on the lattice
We incorporate recent calculations of one-loop corrections for the reduced
Ioffe-time pseudo-distribution to extend the
leading-logarithm analysis of lattice data obtained by Orginos et al. We
observe that the one-loop corrections contain a large term reflecting the fact
that effective distances involved in the most important diagrams are much
smaller than the nominal distance . The large correction in this case may
be absorbed into the evolution term, and the perturbative expansion used for
extraction of parton densities at the GeV scale is under
control. The extracted parton distribution is rather close to global fits in
the region, but deviates from them for .Comment: 10 pages, 11 figures, version to be published in Phys. Rev.
QCD Sum Rules and Compton Scattering
We extend QCD sum rule analysis to moderate energy fixed angle Compton
scattering. In this kinematic region there is a strong similarity to the sum
rule treatment of electromagnetic form factors, although the four-point
amplitude requires a modification of the Borel transform. To illustrate our
method, we derive the sum rules for helicity amplitudes in pion Compton
scattering and estimate their large- behavior in the local duality
approximation.Comment: 30 pages in Latex, 6 figures not included, available upon request
(send email to: [email protected]), ITP-SB-92-70, CEBAF-TH-92-3
Generalized Parton Distributions and Pseudodistributions
We derive one-loop matching relations for the Ioffe-time distributions (ITDs) related to the pion distribution amplitude (DA) and generalized parton distributions (GPDs). They are obtained from a universal expression for the one-loop correction in an operator form, and will be used in the ongoing lattice calculations of the pion DA and GPDs within the parton pseudodistributions approach
Virtuality Distributions in Application to ɣɣ* → π\u3csup\u3e0\u3c/sup\u3e Transition Form Factor at Handbag Level
We outline basics of a new approach to transverse momentum dependence in hard processes. As an illustration, we consider hard exclusive transition process ɣ*ɣ -\u3e π0 at the handbag level. Our starting point is coordinate representation for matrix elements of operators (in the simplest case, bilocal O(0, z)) describing a hadron with momentum p. Treated as functions of (pz) and z2, they are parametrized through virtuality distribution amplitudes (VDA) Φ(x, σ), with x being Fourier-conjugate to (pz) and σ Laplace-conjugate to z2. For intervals with z+ = 0, we introduce the transverse momentum distribution amplitude (TMDA) Ѱ(x, k┴), and write it in terms of (VDA) Φ(x, σ). The results of covariant calculations, written in terms of Φ(x, σ) are converted into expressions involving Ѱ(x, k┴) Starting with scalar toy models, we extend the analysis onto the case of spin-1/2 quarks and QCD. We propose simple models for soft VDAs/TMDAs, and use them for comparison of handbag results with experimental (BaBar and BELLE) data on the pion transition form factor. We also discuss how one can generate high-k┴ tails from primordial soft distributions
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