arXiv subjects

Anatoly Radyushkin

Publications and source records attributed to Anatoly Radyushkin.

35 records · Page 2Linked to original sources

arXiv2020

Parton distributions and lattice QCD calculations: toward 3D structure

The strong force which binds hadrons is described by the theory of Quantum Chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the Parton Distribution Functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the opportunity to additionally explore the transverse structure of hadrons which is described by Generalized Parton Distributions (GPDs) and Transverse Momentum Dependent Parton Distribution Functions (TMD PDFs). In our previous review, we compared and contrasted the two main approaches used to determine the collinear PDFs: the first based on perturbative QCD factorization theorems, and the second based on lattice QCD calculations. In the present report, we provide an update of recent progress on the collinear PDFs, and also expand the scope to encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state of the various calculations, and consider what new data might be available in the near future. We also examine how a shared effort can foster dialog between the PDF and Lattice QCD communities, and yield improvements for these generalized PDFs.

hep-ph↗

arXiv2020

Parton Distribution Functions from Ioffe time pseudo-distributions

In this paper, we present a detailed study of the unpolarized nucleon parton distribution function (PDF) employing the approach of parton pseudo-distribution functions. We perform a systematic analysis using three lattice ensembles at two volumes, with lattice spacings $a=$ 0.127 fm and $a=$ 0.094 fm, for a pion mass of roughly 400 MeV. With two lattice spacings and two volumes, both continuum limit and infinite volume extrapolation systematic errors of the PDF are estimated. In addition to the $x$ dependence of the PDF, we compute their first two moments and compare them with the pertinent phenomenological determinations.

hep-lat↗

arXiv2019

Generalized Parton Distributions and Pseudo-Distributions

We derive one-loop matching relations for the Ioffe-time distributions 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 based on the parton pseudo-distributions approach.

hep-ph↗

arXiv2018

Structure of parton quasi-distributions and their moments

We discuss the structure of the parton quasi-distributions (quasi-PDFs) $Q(y, P_3)$ outside the "canonical" $-1 \leq y \leq 1$ support region of the usual parton distribution functions (PDFs). Writing the $y^n$ moments of $Q(y, P_3)$ in terms of the combined $x^{n-2l} k_\perp^{2l}$-moments of the transverse momentum distribution (TMD) ${\cal F} (x,k_\perp^2)$, we establish a connection between the large-$|y|$ behavior of $Q(y,P_3)$ and large-$k_\perp^2$ behavior of ${\cal F} (x,k_\perp^2)$. In particular, we show that the $1/k_\perp^2$ hard tail of TMDs in QCD results in a slowly decreasing $\sim 1/|y|$ behavior of quasi-PDFs for large $|y|$ that produces infinite $y^n$ moments of $Q(y,P_3)$. We also relate the $\sim 1/|y|$ terms with the $\ln z_3^2$-singulariies of the Ioffe-time pseudo-distributions $\mathfrak{M} (ν, z_3^2)$. Converting the operator product expansion for $\mathfrak{M} (ν, z_3^2)$ into a matching relation between the quasi-PDF $Q(y,P_3)$ and the light-cone PDF $f(x, μ^2)$, we demonstrate that there is no contradiction between the infinite values of the $y^n$ moments of $Q(y,P_3)$ and finite values of the $x^n$ moments of $f(x, μ^2)$.

hep-ph↗

arXiv2018

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 ${\mathfrak M} (ν,z_3^2)$ 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 $z_3$. 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 $μ\approx 2$ GeV scale is under control. The extracted parton distribution is rather close to global fits in the $x>0.1$ region, but deviates from them for $x<0.1$.

hep-ph↗

arXiv2017

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 $p_3 \gtrsim 3$ 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 $M(z_3,p_3)$ as distributions ${\cal M} (ν, z_3^2)$ depending on the Ioffe-time $ν= p_3 z_3$ and the distance parameter $z_3^2$. The rest-frame spatial distribution is given by ${\cal M} (0, z_3^2)$. Using the reduced Ioffe function ${\mathfrak M} (ν, z_3^2) \equiv {\cal M} (ν, z_3^2)/ {\cal M} (0, z_3^2)$ we divide out the rest frame effects,including the notorious link renormalization factors. The $ν$-dependence remains intact and determines the shape of PDFs in the small $z_3$ region. The residual $z_3^2$ dependence of the ${\mathfrak M} (ν, z_3^2)$ is governed by perturbative evolution. The Fourier transform of ${\cal M} (ν, z_3^2)$ produces pseudo-PDFs ${\cal P}(x, z_3^2)$ 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.

hep-ph↗

arXiv2017

Lattice QCD exploration of pseudo-PDFs

We demonstrate a new method of extracting parton distributions from lattice calculations. The starting idea is to treat the generic equal-time matrix element ${\cal M} (Pz_3, z_3^2)$ as a function of the Ioffe time $ν= Pz_3$ and the distance $z_3$. The next step is to divide ${\cal M} (Pz_3, z_3^2)$ by the rest-frame density ${\cal M} (0, z_3^2)$. Our lattice calculation shows a linear exponential $z_3$-dependence in the rest-frame function, expected from the $Z(z_3^2)$ factor generated by the gauge link. Still, we observe that the ratio ${\cal M} (Pz_3 , z_3^2)/{\cal M} (0, z_3^2)$ has a Gaussian-type behavior with respect to $z_3$ for 6 values of $P$ used in the calculation. This means that $Z(z_3^2)$ factor was canceled in the ratio. When plotted as a function of $ν$ and $z_3$, the data are very close to $z_3$-independent functions. This phenomenon corresponds to factorization of the $x$- and $k_\perp$-dependence for the TMD ${\cal F} (x, k_\perp^2)$. For small $z_3 \leq 4a$, the residual $z_3$-dependence is explained by perturbative evolution, with $α_s/π=0.1$.

hep-ph↗

arXiv2017

Parton distribution functions on the lattice and in the continuum

Ioffe-time distributions, which are functions of the Ioffe-time $ν$, are the Fourier transforms of parton distribution functions with respect to the momentum fraction variable $x$. These distributions can be obtained from suitable equal time, quark bilinear hadronic matrix elements which can be calculated from first principles in lattice QCD, as it has been recently argued. In this talk I present the first numerical calculation of the Ioffe-time distributions of the nucleon in the quenched approximation.

hep-lat↗

arXiv2017

Target Mass Effects in Parton Quasi-Distributions

We study the impact of non-zero (and apparently large) value of the nucleon mass $M$ on the shape of parton quasi-distributions $Q(y,p_3)$, in particular on its change with the change of the nucleon momentum $p_3$. We observe that the usual target-mass corrections induced by the $M$-dependence of the twist-2 operators are rather small. Moreover, we show that within the framework based on parametrizations by transverse momentum dependent distribution functions (TMDs) these corrections are canceled by higher-twist contributions. We identify a novel source of kinematic target-mass dependence of TMDs and build models corrected for such dependence. We find that resulting changes may be safely neglected for $p_3 \gtrsim 2M$.

hep-ph↗

arXiv2017

Nonperturbative Evolution of Parton Quasi-Distributions

Using our formalism of parton virtuality distribution functions (VDFs) we establish a connection between the transverse momentum dependent distributions (TMDs) ${\cal F} (x, k_\perp^2)$ and quasi-distributions $Q(y,P_z)$ introduced recently by X. Ji for lattice QCD extraction of parton distributions $f(x)$. We build models for PQDs from the VDF-based models for soft TMDs, and analyze the $P_z$ dependence of the resulting PQDs. We observe a strong nonperturbative evolution of PQDs for small and moderately large values of $P_z$ reflecting the transverse momentum dependence of TMDs. Thus, the study of PQDs on the lattice in the domain of strong nonperturbative effects opens a new perspective for investigation of the 3-dimensional hadron structure.

hep-ph↗

arXiv2014

Pre-Town Meeting on Spin Physics at an Electron-Ion Collider

A polarized $ep/eA$ collider (Electron--Ion Collider, or EIC), with polarized proton and light-ion beams and unpolarized heavy-ion beams with a variable center--of--mass energy $\sqrt{s} \sim 20$ to $\sim100$~GeV (upgradable to $\sim 150$ GeV) and a luminosity up to $\sim 10^{34} \, \textrm{cm}^{-2} \textrm{s}^{-1}$, would be uniquely suited to address several outstanding questions of Quantum Chromodynamics, and thereby lead to new qualitative and quantitative information on the microscopic structure of hadrons and nuclei. During this meeting at Jefferson Lab we addressed recent theoretical and experimental developments in the spin and the three--dimensional structure of the nucleon (sea quark and gluon spatial distributions, orbital motion, polarization, and their correlations). This mini--review contains a short update on progress in these areas since the EIC White paper~\cite{Accardi:2012qut}.

hep-ph↗

arXiv2006

Higher Fock State Contributions to the Generalized Parton Distribution of Pion

We discuss the higher Fock state (q \bar q g) contributions to the nonzero value of the pion GPD at the crossover point x = zeta between the DGLAP and ERBL regions. Using the phenomenological light-front constituent quark model, we confirm that the higher Fock state contributions indeed give a nonzero value of the GPD at the crossover point. Iterating the light-front quark model wave function of the lowest q \bar q Fock state with the Bethe-Salpeter kernel corresponding to the one-gluon-exchange, we include all possible time-ordered q \bar q g Fock state contributions and obtain the pion GPD satisfying necessary sum rules and continuity conditions.

hep-ph↗

arXiv2004

QCD Sum Rules and Models for Generalized Parton Distributions

I use QCD sum rule ideas to construct models for generalized parton distributions. To this end, the perturbative parts of QCD sum rules for the pion and nucleon electromagnetic form factors are interpreted in terms of GPDs and two models are discussed. One of them takes the double Borel transform at adjusted value of the Borel parameter as a model for nonforward parton densities, and another is based on the local duality relation. Possible ways of improving these Ans{ä}tze are briefly discussed.

hep-ph↗

arXiv1998

Sudakov suppression in the soft heavy to light meson transition form factor

We calculate hard gluon contribution to the decay vertex that determines the heavy-to-light meson transition form factor at large recoil. It is found that resulting Sudakov suppression significantly decreases the soft, wave function dependent contribution to the form factor. Phenomenological implications of these findings are discussed.

hep-ph↗

arXiv1997

Consistent Analysis of O(α_s) Corrections to Pion Elastic Form Factor

We examine the role of O(α_s) perturbative corrections to the pion elastic form factor F_π(Q^2). We express the quark current three-point function in terms of light cone variables and use Borel transformation to simultaneously model the Feynman mechanism contribution determined by the soft part of the pion light cone wave function and the hard term involving one gluon exchange. We find that for Q^2 \sim 5 GeV^2 the total one gluon exchange contribution may reach 40% of the soft contribution, even though its hard, factorization scale dependent part remains relatively small.

hep-ph↗

arXiv1994

Pion Wave Function from QCD Sum Rules with Nonlocal Condensates

We investigate a model QCD sum rule for the pion wave function $φ_π(x)$ based on the non-diagonal correlator whose perturbative spectral density vanishes and $Φ(x,M^2)$, the theoretical side of the sum rule, consists of condensate contributions only. We study the dependence of $Φ(x,M^2)$ on the Borel parameter $M^2$ and observe that $Φ(x,M^2)$ has a humpy form, with the humps becoming more and more pronounced when $M^2$ increases. We demonstrate that this phenomenon reflects just the oscillatory nature of the higher states wave functions, while the lowest state wave function $φ_π(x)$ extracted from our QCD sum rule analysis,has no humps, is rather narrow and its shape is close to the asymptotic form $φ_π^{as}(x) = 6x(1-x)$.

hep-ph↗

arXiv1993

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-$t$ behavior in the local duality approximation.

hep-ph↗