Related papers: EKO: Evolution Kernel Operators
uPDFevolv2 is a software package designed for evolving collinear and Transverse Momentum Dependent (TMD) parton densities using the DGLAP evolution equation. A comprehensive description of both the theoretical framework and technical…
Automated kernel design is critical for overcoming software ecosystem barriers in emerging hardware platforms like RISC-V. While large language models (LLMs) have shown promise for automated kernel optimization, demonstrating success in…
A new code for the scale evolution of modified-minimal-subtraction-scheme parton densities is described. Through next-to-leading order the program uses exact splitting functions. In next-to-next-to-leading order approximate splitting…
We briefly discuss recent results on the evolution of unpolarized parton densities and structure functions in massless perturbative QCD. Present partial results on the next-to-next-to-leading order (NNLO) evolution kernels prove sufficient…
Numerical solution of partial differential equations (PDEs) plays a vital role in various fields of science and engineering. In recent years, deep neural networks (DNNs) have emerged as a powerful tool for solving PDEs, leveraging their…
We complete the construction of the non-forward evolution kernels in next-to-leading order responsible for the scale dependence of e.g. parity even singlet distribution amplitudes. Our formalism is designed to avoid any explicit two-loop…
The non-singlet structure functions have been obtained by solving Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations in leading order (LO) and next-to-leading order (NLO) at the small-x limit. Here a Taylor series…
Aspects of the QCD parton densities are briefly reviewed, drawing some parallels to the density matrix formulation of quantum mechanics, exemplified by Wigner functions. We elaborate on the solution of their evolution equations using…
Evolutionary transfer optimization(ETO) serves as "a new frontier in evolutionary computation research", which will avoid zero reuse of experience and knowledge from solved problems in traditional evolutionary computation. In scheduling…
We suggest a new procedure for extrapolating the parton distributions from HERA to much higher energies. The procedure suggested consists of two steps. First, we solve the non-linear evolution equation. Second, we introduce a correcting…
Results for the two real parton differential distributions needed for implementing a next-to-leading order (NLO) parton shower Monte Carlo are presented. They are also integrated over the phase space in order to provide solid numerical…
We discuss the effect of QED corrections in the evolution of polarized parton distributions. We solve the corresponding evolution equations exactly to ${\cal O}(\alpha )$ and ${\cal O}(\alpha_s^2)$ in Mellin $N$-space, extending the…
We show for a first time ever a prototype of a fully exclusive QCD NLO parton shower for the initial state (albeit for a limited set of diagrams). It is based on the rigorous theorems of the collinear factorisation, however the standard…
Evolution equations of YFS and DGLAP types in leading order are considered. They are compared in terms of mathematical properties and solutions. In particular, it is discussed how the properties of evolution kernels affect solutions.…
Reinforcement learning is increasingly finding success across domains where the problem can be represented as a Markov decision process. Evolutionary computation algorithms have also proven successful in this domain, exhibiting similar…
In this work, we present an analytical solution for QCD$\otimes$QED coupled Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations at the leading order (LO) accuracy in QED and next-to-leading order (NLO) accuracy in…
A method of obtaining parton distributions directly from data is revealed in this series. In the process, the first step would be developing appropriate matrix solutions of the evolution equations in $x$ space. A division into commuting and…
Inspired by natural evolutionary processes, Evolutionary Computation (EC) has established itself as a cornerstone of Artificial Intelligence. Recently, with the surge in data-intensive applications and large-scale complex systems, the…
In this paper, using the stochastic modeling of the non-equilibrium statistical mechanics in the momentum space, the evolution equations of the parton distribution functions (PDF) usually used in the hadrons phenomenology are generated.…
Using recent and updated world data on polarized structure functions $g_1$ and $g_2$ we perform QCD analysis at the next-next-to-leading-order (NNLO) accuracy. We include also target mass correction and higher twist effect to get more…