Two-loop Electron and Photon Structure Functions Fully Calculated, Enabling Next-to-Next-to-Leading Order Analysis

Understanding the internal structure of particles, even fundamental ones like electrons, remains a central challenge in modern physics, and new research provides a remarkably precise picture of this complexity. Marvin Schnubel and Robert Szafron, both from Brookhaven National Laboratory, present a complete analytical calculation of electron and photon structure functions, detailing how these particles split into their constituent parts at an unprecedented level of accuracy. This work extends calculations to two-loop order, significantly refining our understanding of quantum electrodynamic (QED) effects within particles and providing a crucial benchmark for theoretical predictions, while also offering valuable insights into the behaviour of matter under extreme conditions. The detailed results confirm existing calculations and offer a powerful new tool for exploring the fundamental constituents of matter and the forces that govern them.

Precision Calculations and Parton Distribution Functions

This collection of research focuses on high-energy physics, specifically the precise calculation of parton distribution functions (PDFs) and the theoretical tools used to achieve this. PDFs describe the probability of finding constituent particles, quarks and gluons, within a hadron like a proton or neutron, and are essential for predicting the outcomes of high-energy collisions. A significant portion of the work involves calculating higher-order corrections to fundamental processes in both Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD), crucial for comparing theoretical predictions with experimental data from particle colliders. Researchers are developing increasingly sophisticated techniques to improve the accuracy of these calculations, including methods for handling complex mathematical integrals and employing symbolic manipulation tools. This work extends to understanding the spin structure of hadrons through the study of polarized PDFs, and preparing for future experiments at facilities like the Electron-Ion Collider (EIC), which will probe the internal structure of matter with unprecedented detail. Ultimately, these calculations aim to refine the Standard Model of particle physics and search for new phenomena beyond it.

Analytic Calculation of NNLO Parton Distributions

Researchers have performed a detailed analytical calculation of electron and photon parton distribution functions (PDFs) within the framework of Quantum Electrodynamics (QED), extending the precision of these calculations to next-to-next-to-leading order (NNLO). This advancement involves employing modern techniques to simplify complex integrals and solve them using a differential equation method, resulting in explicit expressions for the distributions of various particles within electrons and photons. The team validated these results against existing calculations and a recent analysis using a soft-collinear effective theory, ensuring the reliability and accuracy of their findings. The calculated photon PDFs are particularly relevant for proposed γ−γ and e−γ colliders, as well as for accurately modeling beam spectra in future lepton and wakefield colliders where secondary photons play a significant role. By focusing on obtaining analytical forms of the PDFs, this study provides a framework for precise calculations needed for planned future colliders, enabling detailed predictions of collision outcomes and facilitating the interpretation of experimental data.

NNLO Parton Distributions in Quantum Electrodynamics

This research presents a complete analytical determination of electron and photon parton distribution functions (PDFs) within Quantum Electrodynamics (QED), extending calculations to next-to-next-to-leading order (NNLO). Scientists achieved this by employing modern techniques, specifically reducing complex integrals to master integrals and solving them using a differential equation method. The research delivers explicit expressions for the distributions of electrons and positrons within electrons, photons within electrons, and electrons and photons within photons, all calculated at the NNLO level. The team meticulously validated these results against existing calculations and a recent analysis using a soft-collinear effective theory, confirming the accuracy and consistency of the new NNLO determinations. Measurements confirm the successful computation of a complete basis of NNLO photon PDFs, a novel contribution of this study, which are particularly relevant for future colliders designed for gamma-gamma and electron-gamma collisions. The calculations provide a complete set of NNLO QED PDFs essential for precision computations needed in planned future collider experiments.

Precise QED Parton Distributions to High Order

This research presents a comprehensive analytical calculation of electron and photon parton distribution functions (PDFs) within the framework of Quantum Electrodynamics (QED), extending the precision of these calculations to next-to-next-to-leading order. By employing modern techniques for simplifying complex calculations and solving differential equations, the team derived explicit expressions for various particle distributions within the electron, including electrons, positrons, and photons. These results provide a more complete understanding of the internal structure of electrons and the probabilities of finding different constituent particles within them. Unlike Quantum Chromodynamics (QCD), where PDFs are largely non-perturbative, QED PDFs are entirely calculable through perturbative methods, allowing for highly precise predictions. This calculation offers a complementary approach by explicitly defining and calculating partonic distributions, distinguishing between collinear and soft scales.