arXiv subjects

A. V. Radyushkin

Publications and source records attributed to A. V. Radyushkin.

At least 19 recordsLinked to original sources

arXiv2024

Double Distributions and Pseudo-Distributions

We describe the approach to lattice extraction of Generalized Parton Distributions (GPDs) that is based on the use of the double distributions (DDs) formalism within the pseudo-distribution framework. The advantage of using DDs is that GPDs obtained in this way have the mandatory polynomiality property, a non-trivial correlation between $x$- and $ξ$-dependences of GPDs. Another advantage of using DDs is that the $D$-term appears as an independent entity in the DD formalism rather than a part of GPDs $H$ and $E$. We relate the $ξ$-dependence of GPDs to the width of the $α$-profiles of the corresponding DDs, and discuss strategies for fitting lattice-extracted pseudo-distributions by DDs.

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arXiv2020

Theory and applications of parton pseudodistributions

We review the basic theory of the parton pseudodistributions approach and its applications to lattice extractions of parton distribution functions. The crucial idea of the approach is the realization that the correlator $M(z,p)$ of the parton fields is a function ${\cal M} (ν, -z^2)$ of Lorentz invariants $ν=-(zp)$, the Ioffe time, and the invariant interval $z^2$. This observation allows to extract the Ioffe-time distribution ${\cal M} (ν, -z^2)$ from Euclidean separations $z$ accessible on the lattice. Another basic feature is the use of the ratio ${\mathfrak M} (ν,-z^2) \equiv {\cal M} (ν, -z^2)/{\cal M} (0, -z^2)$, that allows to eliminate artificial ultraviolet divergence generated by the gauge link for space-like intervals. The remaining $z^2$-dependence of the reduced Ioffe-time distribution ${\mathfrak M} (ν,-z^2) $ corresponds to perturbative evolution, and can be converted into the scale-dependence of parton distributions $f(x,μ^2)$ using matching relations. The $ν$-dependence of ${\mathfrak M} (ν,-z^2) $ governs the $x$-dependence of parton densities $f(x,μ^2)$. The perturbative evolution was successfully observed in exploratory quenched lattice calculation. The analysis of its precise data provides a framework for extraction of parton densities using the pseudodistributions approach. It was used in the recently performed calculations of the nucleon and pion valence quark distributions. We also discuss matching conditions for the pion distribution amplitude and generalized parton distributions, the lattice studies of which are now in progress.

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arXiv2018

Quark Pseudo-Distributions at Short Distances

We perform a one-loop study of the small-$z_3^2$ behavior of the Ioffe-time distribution (ITD) ${\cal M} (ν, z_3^2)$, the basic function that may be converted into parton pseudo- and quasi-distributions. We calculate the corrections at the operator level, so that our results may be later used for pseudo-distribution amplitudes and generalized parton pseudo-distributions. We separate two sources of the $z_3^2$-dependence at small $z_3^2$. One is related to the ultraviolet (UV) singularities generated by the gauge link, and another to short-distance logarithms generating perturbative evolution of parton densities. Our calculation explicitly shows that, for a finite UV cut-off, the UV-singular terms vanish when $z_3^2=0$. The UV divergences are absent in the ratio ${\cal M} (ν, z_3^2)/{\cal M} (0, z_3^2)$ ("reduced" ITD). Still, it has a non-trivial short-distance behavior due to $\ln z_3^2 Λ^2$ terms generating perturbative evolution of the parton densities. We give an explicit expression, up to constant terms, for the reduced ITD at one loop. It may be used in extraction of PDFs from the lattice QCD simulations. We also use our results to get new insights concerning the structure of parton quasi-distributions at one-loop level.

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arXiv2017

Quasi-PDFs, momentum distributions and pseudo-PDFs

We show that quasi-PDFs may be treated as hybrids of PDFs and primordial rest-frame momentum distributions of partons. This results in a complicated convolution nature of quasi-PDFs that necessitates using large $p_3 \sim 3$ GeV momenta to get reasonably close to the PDF limit. As an alternative approach, we propose to use pseudo-PDFs $P(x, z_3^2)$ that generalize the light-front PDFs onto spacelike intervals and are related to Ioffe-time distributions $M (ν, z_3^2)$, the functions of the Ioffe time $ν= p_3 z_3$ and the distance parameter $z_3^2$ with respect to which it displays perturbative evolution for small $z_3$. In this form, one may divide out the $z_3^2$ dependence coming from the primordial rest-frame distribution and from the problematic factor due to lattice renormalization of the gauge link. The $ν$-dependence remains intact and determines the shape of PDFs.

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arXiv2015

Pion Electromagnetic Form Factor in Virtuality Distribution Formalism

We discuss two applications of the {\it Virtuality Distribution Amplitudes} (VDA) formalism developed in our recent papers. We start with an overview of the main properties of the pion distribution amplitude emphasizing the quantitative measures of its width, and possibility to access them through the pion transition form factor studies. We formulate the basic concepts of the VDA approach and introduce the pion transverse momentum distribution amplitude (TMDA) which plays, in a covariant Lagrangian formulation, a role similar to that of the pion wave function in the 3-dimensional Hamiltonian light-front approach. We propose simple factorized models for soft TMDAs, and use them to describe existing data on the pion transition form factor, thus fixing the scale determining the size of the transverse-momentum effects. Finally, we apply the VDA approach to the one-gluon exchange contribution for the pion electromagnetic form factor. We observe a very late $Q^2 \gtrsim 20$ GeV$^2$ onset of transition to the asymptotic pQCD predictions and show that in the $Q^2 \lesssim 10$ GeV$^2$ region there is essentially no sensitivity to the shape of the pion distribution amplitude. Furthermore, the magnitude of the one-gluon exchange contribution in this region is estimated to be an order of magnitude below the Jefferson Lab data, thus leaving the Feynman mechanism as the only one relevant to the pion electromagnetic form factor behavior for accessible $Q^2$.

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arXiv2015

Virtuality and Transverse Momentum Dependence of Pion Distribution Amplitude

We describe basics of a new approach to transverse momentum dependence in hard exclusive processes. We develop it in application to the transition process γ^* γ-> π^0 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 z^2, they are parametrized through virtuality distribution amplitudes (VDA) Φ(x, σ), with x being Fourier-conjugate to (pz) and σLaplace-conjugate to z^2. For intervals with z^+=0, we introduce the transverse momentum distribution amplitude (TMDA) Ψ(x, k_\perp), 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 Ψ(x, k_\perp). 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_\perp tails from primordial soft distributions.

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arXiv2014

Virtuality Distributions in Application to $γγ^* \to π^0$ 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 $γ^* γ\to π^0$ at the handbag level. Our starting point is coordinate representation for matrix elements of operators (in the simplest case, bilocal ${\cal O}(0,z)$) describing a hadron with momentum $p$. Treated as functions of $(pz)$ and $z^2$, they are parametrized through virtuality distribution amplitudes (VDA) $Φ(x, σ)$, with $x$ being Fourier-conjugate to $(pz)$ and $σ$ Laplace-conjugate to $z^2$. For intervals with $z^+=0$, we introduce the transverse momentum distribution amplitude (TMDA) $Ψ(x, k_\perp)$, 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 $Ψ(x, k_\perp)$. 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-$k_\perp$ tails from primordial soft distributions.

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arXiv2014

Analytic Evolution of Singular Distribution Amplitudes in QCD

We describe a method of analytic evolution of distribution amplitudes (DA) that have singularities, such as non-zero values at the end-points of the support region, jumps at some points inside the support region and cusps. We illustrate the method by applying it to the evolution of a flat (constant) DA, antisymmetric flat DA and then use it for evolution of the two-photon generalized distribution amplitude. Our approach has advantages over the standard method of expansion in Gegenbauer polynomials, which requires infinite number of terms in order to accurately reproduce functions in the vicinity of singular points, and over a straightforward iteration of an initial distribution with evolution kernel. The latter produces logarithmically divergent terms at each iteration, while in our method the logarithmic singularities are summed from the start, which immediately produces a continuous curve, with only one or two iterations needed afterwards in order to get rather precise results.

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arXiv2013

Sum Rules for Nucleon GPDs and Border Function Formulation

The newy developed approach to model nucleon generalized parton distributions (GPDs) H and E$ is based on two types of their representation in terms of double distributions. Within this approach, we re-consider the derivation of GPD sum rules that allow to use border functions H(x,x) and E(x,x) instead of full GPDs H(x,ξ) and E(x,ξ) in the integrals producing Compton form factors of deeply virtual Compton scattering. Using factorized DD Ansatz to model GPDs, we discuss the relation between the border functions and underlying parton densities. We find that a substantial contribution to H(x,x) border function comes from the extra term required by new DD representations and related to E(x,ξ) GPD.

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arXiv2013

Modeling Nucleon Generalized Parton Distributions

We discuss building models for nucleon generalized parton distributions (GPDs) H and E that are based on the formalism of double distributions (DDs). We found that the usual "DD+D-term" construction should be amended by an extra term, ξE^1_+(x,ξ) built from the α/βmoment of the DD e(β,α) that generates GPD E(x,ξ). Unlike the D-term, this function has support in the whole -1 \leq x \leq 1 region, and in general does not vanish at the border points |x|=ξ.

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arXiv2012

Regge trajectories in QCD

We discuss some problems concerning the application of perturbative QCD to high energy soft processes. We show that summing the contributions of the lowest twist operators for non-singlet $t$-channel leads to a Regge-like amplitude. Singlet case is also discussed.

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arXiv2011

Generalized Parton Distributions and Their Singularities

A new approach to building models of generalized parton distributions (GPDs) is discussed that is based on the factorized DD (double distribution) Ansatz within the single-DD formalism. The latter was not used before, because reconstructing GPDs from the forward limit one should start in this case with a very singular function f(β)/β rather than with the usual parton density f(β). This results in a non-integrable singularity at β=0 exaggerated by the fact that f(β)'s, on their own, have a singular β^{-a} Regge behavior for small β. It is shown that the singularity is regulated within the GPD model of Szczepaniak et al., in which the Regge behavior is implanted through a subtracted dispersion relation for the hadron-parton scattering amplitude. It is demonstrated that using proper softening of the quark-hadron vertices in the regions of large parton virtualities results in model GPDs H(x,ξ) that are finite and continuous at the "border point" x=ξ. Using a simple input forward distribution, we illustrate implementation of the new approach for explicit construction of model GPDs. As a further development, a more general method of regulating the β=0 singularities is proposed that is based on the separation of the initial single DD f(β, α) into the "plus" part [f(β,α)]_{+} and the D-term. It is demonstrated that the "DD+D" separation method allows to (re)derive GPD sum rules that relate the difference between the forward distribution f(x)=H(x,0) and the border function H(x,x) with the D-term function D(α).

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arXiv2009

Nucleon Form Factors from Generalized Parton Distributions

We discuss the links between Generalized Parton Distributions (GPDs) and elastic nucleon form factors. These links, in the form of sum rules, represent powerful constraints on parametrizations of GPDs. A Regge parametrization for GPDs at small momentum transfer, is extended to the large momentum transfer region and it is found to describe the basic features of proton and neutron electromagnetic form factor data. This parametrization is used to estimate the quark contribution to the nucleon spin.

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arXiv2009

Shape of Pion Distribution Amplitude

A scenario is investigated in which the leading-twist pion distribution amplitude phi_pi (x) is approximated by the pion decay constant f_pi for all essential values of the light-cone fraction x. A model for the light-front wave function Psi(x,k_perp) is proposed that produces such a distribution amplitude and has a rapidly decreasing (exponential for definiteness) dependence on the light-front energy combination k_perp^2/x(1-x). It is shown that this model easily reproduces the fit of recent large-Q^2 BaBar data on the photon-pion transition form factor. Some aspects of scenario with flat pion distribution amplitude are discussed.

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arXiv2008

Anomalous Form Factor of the Neutral Pion in Extended AdS/QCD Model with Chern-Simons Term

We propose an extension of the hard-wall AdS/QCD model by including the Chern-Simons term required to reproduce the chiral anomaly of QCD. In the framework of this holographic model, we study the vertex function F_{πγ^* γ^*}(Q_1^2,Q_2^2) which accumulates information about the coupling of the pion to two (in general virtual) photons. We calculate the slope of the form factor with one real and one slightly virtual photon and show that it is close to experimental findings. We analyze the formal limit of large virtualities and establish that predictions of the holographic model analytically (including nontrivial dependence on the ratio of photon virtualities) coincide with those of perturbative QCD with asymptotic pion distribution amplitude. We also investigate the generalized VMD structure of F_{πγ^* γ^*}(Q_1^2,Q_2^2) in the extended AdS/QCD model.

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arXiv2007

Structure of Vector Mesons in Holographic Model with Linear Confinement

Wave functions and form factors of vector mesons are investigated in the holographic dual model of QCD with a smooth oscillator-like wall. We introduce wave functions conjugate to solutions of the 5D equation of motion and develop a formalism based on these wave functions, which are very similar to those of a quantum-mechanical oscillator. For the lowest bound state (rho-meson), we show that, in this model, the basic elastic form factor exhibits the perfect vector meson dominance, i.e., it is given by the rho-pole contribution alone. The electric radius of the rho-meson is calculated, _C = 0.655 fm^2, which is larger than in case of the hard-wall cutoff. The squared radii of higher excited states are found to increase logarithmically rather than linearly with the radial excitation number. We calculate the coupling constant f_rho and find that the experimental value is closer to that calculated in the hard-wall model.

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arXiv2007

Pion Form Factor in Chiral Limit of Hard-Wall AdS/QCD Model

We develop a formalism to calculate form factor and charge density distribution of pion in the chiral limit using the holographic dual model of QCD with hard-wall cutoff. We introduce two conjugate pion wave functions and present analytic expressions for these functions and for the pion form factor. They allow to relate such observables as the pion decay constant and the pion charge electric radius to the values of chiral condensate and hard-wall cutoff scale. The evolution of the pion form factor to large values of the momentum transfer is discussed, and results are compared to existing experimental data.

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arXiv2007

Holographic Wave Functions, Meromorphization and Counting Rules

We study the large-Q^2 behavior of the meson form factor F_M (Q^2) constructed using the holographic light-front wave functions proposed recently by Brodsky and de Teramond. We show that this model can be also obtained within the Migdal's regularization approach (``meromorphization''), if one applies it to 3-point function for scalar currents made of scalar quarks. We found that the asymptotic 1/Q^2 behavior of F_M (Q^2) is generated by soft Feynman mechanism rather than by short distance dynamics, which causes very late onset of the 1/Q^2 asymptotic behavior. Using meromorphization for spin-1/2 quarks, we demonstrated that resulting form factor F^{spinor}_M (Q^2) has 1/Q^4 asymptotic behavior. Now, owing to the late onset of this asymptotic pattern, F^{spinor}_M (Q^2) imitates the 1/Q^2 behavior in the few GeV^2 region. We discuss analogy between meromorphization and local quark-hadron duality model for the pion form factor, and show that adding the O(α_s) correction to the spectral function brings in the hard pQCD contribution that has the dimensional counting $1/Q^2$ behavior at large Q^2. At accessible Q^2, the O(α_s) term is a rather small fraction of the total result. We conclude that the ``observed'' quark counting rules for hadronic form factors is an approximate phenomenon resulting from Feynman mechanism in its preasymptotic regime.

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