arXiv subjects

Anatoly Radyushkin

Publications and source records attributed to Anatoly Radyushkin.

At least 19 recordsLinked to original sources

arXiv2026

Femtoscale imaging of the proton with Ioffe-time distributions

Mapping how strongly interacting constituents are distributed within protons is a key goal of nuclear physics and a major direction of the future Electron Ion Collider program. We propose a novel space-time description of hadron structure in terms of impact-parameter Ioffe-time distributions, relating spatial density in the plane transverse to the proton momentum and the time between the probe's absorption and the product's emission in the longitudinal direction. Using lattice Quantum Chromodynamics, we perform the first calculation of the Ioffe-time-dependent mean squared proton radii and compare our results with estimates in the Goloskokov-Kroll model. We derive a relationship between the experimentally measurable Compton form factor and the generalized Ioffe-time distribution, which allows us to perform the first extraction of the Compton form factor from lattice calculations.

hep-ph↗

arXiv2026

Reconstructing the full kinematic dependence of GPDs from pseudo-distributions

We propose a reconstruction of the full $(x, ξ, t)$ dependence of unpolarized isovector proton generalized parton distributions (GPDs) $H^{u-d}$ and $E^{u-d}$ from lattice QCD data in the pseudo-distribution formalism. For the first time, we extract double distributions (DDs) directly from lattice data, enforcing therefore an important property of GPDs linked to Lorentz symmetry. We use the flexible framework of multidimensional Gaussian process regression to regularize the inverse problem and present an assessment of the impact of model dependence on the systematic uncertainty. Our lattice ensemble corresponds to a pion mass $m_π= 358$~MeV and a lattice spacing $a = 0.094$~fm. We use larger hadron momenta, up to 2.7~GeV, and kinematic coverage compared to our previous computations and extract additional skewness-dependent moments of the GPD.

hep-lat↗

arXiv2026

Inverse problem in the LaMET framework

One proposal to compute parton distributions from first principles is the large momentum effective theory (LaMET), which requires the Fourier transform of matrix elements computed non-perturbatively. Lattice quantum chromodynamics (QCD) provides calculations of these matrix elements over a finite range of Fourier harmonics that are often noisy or unreliable in the largest computed harmonics. It has been suggested that enforcing an exponential decay of the missing harmonics helps alleviate this issue. Using non-perturbative data, we show that the uncertainty introduced by this inverse problem in a realistic setup remains significant without very restrictive assumptions, and that the importance of the exact asymptotic behavior is minimal for values of $x$ where the framework is currently applicable. We show that the crux of the inverse problem lies in harmonics of the order of $λ=zP_z \sim 5-15$, where the signal in the lattice data is often barely existent in current studies, and the asymptotic behavior is not firmly established. We stress the need for more sophisticated techniques to account for this inverse problem, whether in the LaMET or related frameworks like the short-distance factorization. We also address a misconception that, with available lattice methods, the LaMET framework allows a "direct" computation of the $x$-dependence, whereas the alternative short-distance factorization only gives access to moments or fits of the $x$-dependence.

hep-lat↗

arXiv2025

Comment on "LaMET's Asymptotic Extrapolation vs. Inverse Problem"

In arXiv:2504.17706 {Dutrieux:2025jed} we criticized the excessive model-dependence introduced by rigid few-parameter fits to extrapolate lattice data in the large momentum effective theory (LaMET) when the data are noisy and lose signal before an exponential asymptotic behavior of the space-like correlators is established. In reaction, arXiv:2505.14619 {Chen:2025cxr} claims that even when the data is of poor quality, rigid parametrizations are better than attempts at representing the uncertainty using what they call "inverse problem methods". We clarify the fundamental differences in our perspectives regarding how to meaningfully handle noisy lattice matrix elements, especially when they exhibit a strong sensitivity to the choice of regularization in the inverse problem. We additionally correct misunderstandings of {Chen:2025cxr} on our message and methods.

hep-lat↗

arXiv2025

Non-local Nucleon Matrix Elements in the Rest Frame

Extracting parton structure from lattice quantum chromodynamics (QCD) calculations requires studying the coordinate scale $z_3$ dependence of the matrix elements of bilocal operators. The most significant contribution comes from the $z_3$ dependence induced by ultraviolet (UV) renormalization of the Wilson line. We demonstrate that the next-to-leading order perturbative calculations of the renormalization factor can describe, to a few percent accuracy, the logarithm of the lattice QCD rest frame matrix elements with separations up to distances of 0.6~fm on multiple lattice spacings. The residual discrepancies can be modeled by a leading effect from the structure of the nucleon.

hep-lat↗

arXiv2024

Towards Unpolarized GPDs from Pseudo-Distributions

We present an exploration of the unpolarized isovector proton generalized parton distributions (GPDs) $H^{u-d}(x, ξ, t)$ and $E^{u-d}(x, ξ, t)$ in the pseudo-distribution formalism using distillation. Taking advantage of the large kinematic coverage made possible by this approach, we present results on the moments of GPDs up to the order $x^3$ -- including their skewness dependence -- at a pion mass $m_π= 358$ MeV and a lattice spacing $a = 0.094$ fm.

hep-lat↗

arXiv2024

Extracting the Pion Distribution Amplitude from Lattice QCD through Pseudo-Distributions

The Light-Cone Distribution Amplitude (LCDA) encodes the non-perturbative information of the leading Fock component of the hadron wave function, therefore required for processes including exclusive hadron production. As the pseudo-Nambu-Goldstone boson of QCD, the nonperturbative structure of the pion is of particular interest. Progress on the Lattice QCD calculation of the pion LCDA on ${\cal O}(a)$-improved Wilson fermion ensembles at several lattice spacings is presented. Excited-state systematics are taken into account within a Bayesian Model Averaging framework. A Renormalization-Group-Invariant (RGI) ratio of matrix elements is formed for further extraction of the pion LCDA.

hep-lat↗

arXiv2022

Non-singlet quark helicity PDFs of the nucleon from pseudo-distributions

The non-singlet helicity quark parton distribution functions (PDFs) of the nucleon are determined from lattice QCD, by jointly leveraging pseudo-distributions and the distillation spatial smearing paradigm. A Lorentz decomposition of appropriately isolated space-like matrix elements reveals pseudo-distributions that contain information on the leading-twist helicity PDFs, as well as an invariant amplitude that induces an additional $z^2$ contamination of the leading-twist signal. An analysis of the short-distance behavior of the space-like matrix elements using matching coefficients computed to next-to-leading order (NLO) exposes the desired PDF up to this additional $z^2$ contamination. Due to the non-conservation of the axial current, we elect to isolate the helicity PDFs normalized by the nucleon axial charge at the same scale $μ^2$. The leading-twist helicity PDFs as well as several sources of systematic error, including higher-twist effects, discretization errors, and the aforementioned $z^2$ contaminating amplitude are jointly determined by characterizing the computed pseudo-distribution in a basis of Jacobi polynomials. The Akaike Information Criterion is exploited to effectively average over distinct model parameterizations and cuts on the pseudo-distribution. Encouraging agreement is observed with recent global analyses of each non-singlet quark helicity PDF, notably a rather small non-singlet anti-quark helicity PDF for all quark momentum fractions.

hep-lat↗

arXiv2022

Towards the determination of the gluon helicity distribution in the nucleon from lattice quantum chromodynamics

We present the first exploratory lattice quantum chromodynamics (QCD) calculation of the polarized gluon Ioffe-time pseudo-distribution in the nucleon. The Ioffe-time pseudo-distribution provides a frame-independent and gauge-invariant framework to determine the gluon helicity in the nucleon from first principles. We employ a high-statistics computation using a $32^3\times 64$ lattice ensemble characterized by a $358$ MeV pion mass and a $0.094$ fm lattice spacing. We establish the pseudo-distribution approach as a feasible method to address the proton spin puzzle with successive improvements in statistical and systematic uncertainties anticipated in the future. Within the statistical precision of our data, we find a good comparison between the lattice determined polarized gluon Ioffe-time distribution and the corresponding expectations from the state-of-the-art global analyses. We find a hint for a nonzero gluon spin contribution to the proton spin from the model-independent extraction of the gluon helicity pseudo-distribution over a range of Ioffe-time, $ν\lesssim 9$.

hep-lat↗

arXiv2022

Parton distribution function for topological charge at one loop

We present results for the $gg$-part of the one-loop corrections to the recently introduced "topological charge" GPD $\widetilde F(x,q^2)$. In particular, we give expression for its evolution kernel. To enforce strict compliance with the gauge invariance requirements, we have used on-shell states for external gluons, and have obtained identical results both in Feynman and light-cone gauges. No "zero mode" $δ(x)$ terms were found for the twist-4 gluon GPD $\widetilde F(x,q^2)$.

hep-ph↗

arXiv2022

Polarized Gluon Pseudodistributions at Short Distances

We formulate the basic points of the pseudo-PDF approach to the lattice calculation of polarized gluon PDFs. We present the results of our calculations of the one-loop corrections for the bilocal $G_{μα}(z) \widetilde G_{λβ}(0)$ correlator of gluonic fields. Expressions are given for a general situation when all four indices are arbitrary, and also for specific combinations of indices corresponding to three matrix elements that contain the twist-2 invariant amplitude related to the polarized PDF. We study the evolution properties of these matrix elements, and derive matching relations between Euclidean and light-cone Ioffe-time distributions. These relations are necessary for extraction of the polarized gluon distributions from the lattice data.

hep-ph↗

arXiv2021

Short-Distance Structure of Unpolarized Gluon Pseudodistributions

We present the results that form the basis for calculations of the unpolarized gluon parton distributions (PDFs) using the pseudo-PDF approach. We give the results for the most complicated box diagram both for gluon bilocal operators with arbitrary indices, and for combinations of indices corresponding to three matrix elements that are most convenient to extract the twist-2 invariant amplitude. We also present detailed results for the gluon-quark transition diagram. The additional results for the box diagram and the gluon-quark contribution may be used for extractions of the gluon PDF from different matrix elements, with a possible cross-check of the results obtained in this way.

hep-ph↗

arXiv2021

One-loop structure of parton distribution for the gluon condensate and "zero modes"

We present results for one-loop corrections to the recently introduced "gluon condensate" PDF $F(x)$. In particular, we give expression for the $gg$-part of its evolution kernel. To enforce strict compliance with the gauge invariance requirements, we have used on-shell states for external gluons, and have obtained identical results both in Feynman and light-cone gauges. No "zero mode" $δ(x)$ terms were found for the twist-4 gluon PDF $F(x)$. However a $q^2 δ(x)$ term was found for the $ξ=0$ GPD $F(x,q^2)$ at nonzero momentum transfer $q$. Overall, our results do not agree with the original attempt of one-loop calculations of $F(x)$ for gluon states, which sets alarm warning for calculations that use matrix elements with virtual external gluons and for lattice renormalization procedures based on their results.

hep-ph↗

arXiv2021

The transversity parton distribution function of the nucleon using the pseudo-distribution approach

We present a determination of the non-singlet transversity parton distribution function (PDF) of the nucleon, normalized with respect to the tensor charge at $μ^2=2$ GeV$^2$ from lattice quantum chromodynamics. We apply the pseudo-distribution approach, using a gauge ensemble with a lattice spacing of 0.094 fm and the light quark mass tuned to a pion mass of 358 MeV. We extract the transversity PDF from the analysis of the short-distance behavior of the Ioffe-time pseudo-distribution using the leading-twist next-to-leading order (NLO) matching coefficients calculated for transversity. We reconstruct the $x$-dependence of the transversity PDF through an expansion in a basis of Jacobi polynomials in order to reduce the PDF ansatz dependence. Within the limitations imposed by a heavier-than-physical pion mass and a fixed lattice spacing, we present a comparison of our estimate for the valence transversity PDF with the recent global fit results based on single transverse spin asymmetry. We find the intrinsic nucleon sea to be isospin symmetric with respect to transversity.

hep-lat↗

arXiv2021

Unpolarized gluon distribution in the nucleon from lattice quantum chromodynamics

In this study, we present a determination of the unpolarized gluon Ioffe-time distribution in the nucleon from a first principles lattice quantum chromodynamics calculation. We carry out the lattice calculation on a $32^3\times 64$ ensemble with a pion mass of $358$ MeV and lattice spacing of $0.094$ fm. We construct the nucleon interpolating fields using the distillation technique, flow the gauge fields using the gradient flow, and solve the summed generalized eigenvalue problem to determine the glounic matrix elements. Combining these techniques allows us to provide a statistically well-controlled Ioffe-time distribution and unpolarized gluon PDF. We obtain the flow time independent reduced Ioffe-time pseudo-distribution, and calculate the light-cone Ioffe-time distribution and unpolarized gluon distribution function in the $\overline{\rm MS}$ scheme at $μ= 2$ GeV, neglecting the mixing of the gluon operator with the quark singlet sector. Finally, we compare our results to phenomenological determinations.

hep-lat↗

arXiv2021

Gluon Pseudo-Distributions at Short Distances: Forward Case

We present the results that are necessary in the ongoing lattice calculations of the gluon parton distribution functions (PDFs) within the pseudo-PDF approach. We give a classification of possible two-gluon correlator functions and identify those that contain the invariant amplitude determining the gluon PDF in the light-cone $z^2 \to 0$ limit. One-loop calculations have been performed in the coordinate representation and in an explicitly gauge-invariant form. We made an effort to separate ultraviolet (UV) and infrared (IR) sources of the $\ln (-z^2)$-dependence at short distances $z^2$. The UV terms cancel in the reduced Ioffe-time distribution (ITD), and we obtain the matching relation between the reduced ITD and the light-cone ITD. Using a kernel form, we get a direct connection between lattice data for the reduced ITD and the normalized gluon PDF. We also show that our results may be used for a rather straightforward calculation of the one-loop matching relations for quasi-PDFs.

hep-ph↗

arXiv2021

The Continuum and Leading Twist Limits of Parton Distribution Functions in Lattice QCD

In this study, we present continuum limit results for the unpolarized parton distribution function of the nucleon computed in lattice QCD. This study is the first continuum limit using the pseudo-PDF approach with Short Distance Factorization for factorizing lattice QCD calculable matrix elements. Our findings are also compared with the pertinent phenomenological determinations. Inter alia, we are employing the summation Generalized Eigenvalue Problem (sGEVP) technique in order to optimize our control over the excited state contamination which can be one of the most serious systematic errors in this type of calculations. A crucial novel ingredient of our analysis is the parameterization of systematic errors using Jacobi polynomials to characterize and remove both lattice spacing and higher twist contaminations, as well as the leading twist distribution. This method can be expanded in further studies to remove all other systematic errors.

hep-lat↗

arXiv2021

Neural-network analysis of Parton Distribution Functions from Ioffe-time pseudodistributions

We extract two nonsinglet nucleon Parton Distribution Functions from lattice QCD data for reduced Ioffe-time pseudodistributions. We perform such analysis within the NNPDF framework, considering data coming from different lattice ensembles and discussing in detail the treatment of the different source of systematics involved in the fit. We introduce a recipe for taking care of systematics and use it to perform our extraction of light-cone PDFs.

hep-ph↗