Quark Generalized Parton Distributions Achieves One-Loop Accuracy in Chromodynamics Calculations

The fundamental structure of protons and neutrons, and how quarks contribute to their properties, remains a central question in particle physics. Alessio Carmelo Alvaro, Ignacio Castelli, and Cédric Lorcé, along with colleagues from the University of Pavia, Temple University, and the École polytechnique, investigate the distribution of quarks within protons by calculating generalized parton distributions, which describe how these particles behave at high energies. Their work focuses on the behaviour of quarks when interacting with gluons, the particles that mediate the strong force, and represents a significant step forward in understanding the internal dynamics of matter. By performing precise calculations using a well-established theoretical framework, the team sheds light on the complex interplay between quarks and gluons, and provides crucial insights for interpreting experimental results from particle colliders.

Scientists investigate the distribution of quarks within protons by calculating generalized parton distributions, which describe how these particles behave at high energies. This work focuses on the behaviour of quarks when interacting with gluons, the particles that mediate the strong force, and represents a significant step forward in understanding the internal dynamics of matter.

Generalized parton distributions (GPDs) are a powerful theoretical tool extending the concept of parton distribution functions, offering a crucial spatial dimension to understanding the 3D structure of hadrons. While traditional methods describe the probability of finding a parton at a given momentum, GPDs describe the probability amplitude of finding a parton at a given momentum and spatial distribution within the hadron. Deeply Virtual Exclusive Processes (DVCS) are hard scattering processes used to access GPDs experimentally, involving the scattering of a lepton off a hadron.

By performing precise calculations using a well-established theoretical framework, the team sheds light on the complex interplay between quarks and gluons, and provides crucial insights for interpreting experimental results from particle colliders. The research investigates the dimensionality and internal structure of hadrons, and likely involves calculating higher-order perturbative QCD corrections to DVCS observables for accurate predictions. References to established evolution equations indicate the study of how GPDs evolve with energy, and connections to PDFs and timelike form factors link the theoretical framework to existing experimental knowledge.

Quark Distributions Calculated at One-Loop Accuracy

Scientists have achieved a significant breakthrough in understanding the fundamental structure of matter by calculating, at one-loop accuracy, the twist-2 unpolarized generalized parton distributions (GPDs) of quarks for an on-shell gluon target within the framework of quantum chromodynamics. This work parametrizes the leading-twist matrix elements of the nonlocal light-like flavor-singlet vector current, providing crucial insights into the behavior of quarks and gluons within nucleons. The team employed both a quark mass and dimensional regularization as infrared regulators in their perturbative calculations, meticulously examining the behavior of these GPDs as momentum transfer approaches zero.

Experiments revealed a novel contribution to the GPDs for off-forward kinematics, aligning with previous theoretical predictions and extending earlier investigations. The researchers demonstrated that this additional term is directly linked to the axial anomaly, a well-known phenomenon in particle physics, confirming its importance in understanding the internal structure of hadrons. Calculations confirm the decomposition of the matrix elements into two unpolarized quark GPDs, with specific conditions established for their behavior in the forward limit.

Notably, when utilizing a quark mass as an infrared regulator, this extra contribution does not exhibit singularity in the forward limit and, in fact, vanishes, a result consistent with the fundamental principle of angular momentum conservation. Calculations using a quark mass regulator show that one of these GPDs vanishes in the forward limit, a finding directly attributable to angular momentum conservation principles. This breakthrough delivers a refined understanding of parton distributions and their implications for factorization theorems in high-energy physics processes, paving the way for more precise theoretical predictions and interpretations of experimental data.

Gluon GPDs to One-Loop Accuracy Confirmed

This research presents a detailed investigation of quark generalized parton distributions (GPDs) within the framework of chromodynamics, specifically focusing on an on-shell gluon target. Scientists calculated these GPDs to one-loop accuracy, employing a quark mass and dimensional regularization as tools to manage complex calculations. The work extends previous studies concerning the axial current and provides a comprehensive description of how these distributions behave under various conditions, including scenarios with vanishing momentum transfer.

The results demonstrate that the calculated GPDs adhere to established theoretical constraints, notably reducing to the expected parton distribution function in the forward limit, where momentum transfer is zero. Importantly, the team found that a specific GPD, associated with helicity flips, vanishes as momentum transfer approaches zero, resolving a potential singularity issue identified in earlier work. This confirms the consistency of calculating these quantities in off-forward kinematics and then extrapolating to the forward limit.

The authors acknowledge that their calculations are performed at one-loop accuracy, representing an approximation within the more complex theory of quantum chromodynamics. Future research could extend these calculations to higher loop orders to refine the precision of the GPDs, and exploring the behavior of these distributions with different target configurations and kinematic regimes would further enhance understanding of the quark structure of gluons and contribute to a more complete picture of strong interactions.