Kostas Orginos

A bstract: The extraction of parton distribution functions (PDFs) from experimental or lattice QCD data is an ill-posed inverse problem, where regularization strongly impacts both systematic uncertainties and the reliability of the results. We study a framework based on Gaussian Process Regression (GPR) to reconstruct PDFs from lattice QCD matrix elements. Within a Bayesian framework, Gaussian processes serve as flexible priors that encode uncertainties, correlations, and constraints without imposing rigid functional forms. We investigate a wide range of kernel choices, mean functions, and hyperparameter treatments. We quantify information gained from the data using the Kullback-Leibler divergence. Synthetic data tests demonstrate the consistency and robustness of the method. Our study establishes GPR as a systematic and non-parametric approach to PDF reconstruction, offering controlled uncertainty estimates and reduced model bias in lattice QCD analyses.

We calculate the gluon momentum fraction of the nucleon using lattice quantum chromodynamics (QCD), with a nonperturbative renormalization technique based on the gradient flow. The gluon momentum fraction is determined on a single Wilson-clover ensemble using Nf = 2+1 flavors with pion mass 358 MeV and lattice spacing 0.094 fm. We employ the variational method to reduce excited-state contamination and apply the distillation framework to ensure a large operator basis. To reduce systematic uncertainties, we apply Bayesian model averaging to all fit procedures. We apply matching coefficients to the flow-time dependent lattice results to recover the gluon momentum fraction in the MS-scheme at 2 GeV. Our final result is _g(μ= 2 GeV) = 0.482(35), where we quote only statistical uncertainties.

Global analysis of collider and fixed-target experimental data and calculations from lattice quantum chromodynamics (QCD) are used to gain complementary information on the structure of hadrons. We propose novel “window observables” that allow for higher precision cross-validation between the different approaches, a critical step for studies that wish to combine the datasets. Global analyses are limited by the kinematic regions accessible to experiment, particularly in a range of Bjorken- x , and lattice QCD calculations also have limitations requiring extrapolations to obtain the parton distributions. We provide two different window observables that can be defined within a region of x where extrapolations and interpolations in global analyses remain reliable and where lattice QCD results retain sensitivity and precision.

Some calculations of parton distributions from first principles only give access to a limited range of Fourier modes of the function to reconstruct. We present a physically motivated procedure to regularize the inverse integral problem using a Gaussian process as a Bayesian prior. We propose to fix the hyperparameters of the prior in a meaningful physical fashion, offering a simple implementation, great numerical efficiency, and allowing us to understand and keep control easily of the uncertainty of the reconstruction.

A bstract: 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.

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.

The two dimensional O(3) sigma model, just as quantum chromodynamics, is an asymptotically free theory with a mass gap. Therefore, it is an interesting and simple toy model to investigate algorithms for Markov Chain Monte Carlo simulations of quantum chromodynamics. In this talk, we discuss the construction of a trivializing map, a field transformation from a given theory to a trivial one, through a suitably chosen gradient flow. An analytic solution for the generating functional of this trivializing flow has been obtained by a perturbative expansion in the flow time. Utilizing this solution allows for new approaches to be considered when proposing updates for a Markov Chain Monte Carlo algorithm.

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.