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

We study chiral-odd quark-antiquark correlation functions suitable for lattice calculations of twist-three nucleon parton distribution functions hL(x) and e(x), and also the twist-two transversity distribution δq(x). The corresponding factorized expressions are derived in terms of the twist-two and twist-three collinear distributions to one-loop accuracy. The results are presented both in position space, as the factorization theorem for Ioffe-time distributions, and in momentum space, for quasi- and pseudo-distributions. We demonstrate that the twist-two part of the hL quasi(pseudo)-distribution can be separated from the twist-three part by virtue of an exact Jaffe-Ji-like relation.

Section: Introductionmentioning

confidence: 99%

QCD factorization for chiral-odd parton quasi- and pseudo-distributions

Braun

Vladimirov

2021

“…The quality of data, however, hints that a future calculation of a distribution less constrained by experiment may benefit from the use of distillation. By validating the distillation method in the unpolarized nucleon PDF, our study opens new avenues of synergy between lattice and phenomenology in the spirit of [11,99,100]. We performed a careful study of the correct extraction of the matrix elements that yield the pseudo-ITD and we analyzed in detail its real and imaginary components.…”

Section: Discussionmentioning

confidence: 99%

Towards high-precision parton distributions from lattice QCD via distillation

Egerer

Edwards

Kallidonis

et al. 2021

Self Cite

We apply the Distillation spatial smearing program to the extraction of the unpolarized isovector valence PDF of the nucleon. The improved volume sampling and control of excited-states afforded by distillation leads to a dramatically improved determination of the requisite Ioffe-time Pseudo-distribution (pITD). The impact of higher-twist effects is subsequently explored by extending the Wilson line length present in our non-local operators to one half the spatial extent of the lattice ensemble considered. The valence PDF is extracted by analyzing both the matched Ioffe-time Distribution (ITD), as well as a direct matching of the pITD to the PDF. Through development of a novel prescription to obtain the PDF from the pITD, we establish a concerning deviation of the pITD from the expected DGLAP evolution of the pseudo-PDF. The presence of DGLAP evolution is observed once more following introduction of a discretization term into the PDF extractions. Observance and correction of this discrepancy further highlights the utility of distillation in such structure studies.

“…In previous lattice PDF studies [34,65,74,75,80,86,87,110], the chosen functional forms are similar to those used in phenomenological analyses of PDFs [123][124][125][126]. Progress has also been made on the application of neural networks to parameterize the PDF [67,99,127]. In this work, all of the unknown functions, q − (x), q + (x), P 1 (ν), R 1 (ν), and B 1 (ν), are parameterized using Jacobi polynomials.…”

Section: Parameterization Of Unknown Functionsmentioning

confidence: 99%

“…If sufficiently many distinct models are used, the possible biases from choices of model can be averaged away through this AICc weighted average. For example, including fits which use neural networks, which were performed for lattice PDFs in [67,99], which likely would have distinct model dependent biases from the Jacobi polynomials fits. Unfortunately in this preliminary study which only uses Jacobi polynomial based models, the systematic errors may not be sufficiently distinct.…”

Section: Model Weighted Averagesmentioning

confidence: 99%

The continuum and leading twist limits of parton distribution functions in lattice QCD

Karpie

Orginos

Radyushkin

et al. 2021

Self Cite

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.