The size of the proton, a subatomic particle that constitutes the nucleus of an atom, has been a subject of scientific inquiry for many years. Despite extensive research efforts, scientists have struggled to determine its exact radius. In 2010, a new measurement technique involving laser spectroscopy of muonic hydrogen yielded a significantly smaller proton radius compared to previous methods. This sparked widespread curiosity about the underlying reasons behind this discrepancy. Could it be evidence of new physics or simply a result of experimental uncertainties? Recent advancements in theoretical calculations have provided valuable insights into this fascinating puzzle.

A group of theoretical physicists at Johannes Gutenberg University Mainz (JGU) has made substantial progress in refining their calculations of the proton’s electric charge radius. In a groundbreaking development, they have achieved a level of precision that eliminates the need for experimental data. These calculations not only support the smaller value for the proton radius but also include a stable theory prediction for its magnetic charge radius. These significant findings have been published in three preprints on the arXiv server.

Unraveling the Mysteries of Nucleons

Protons and neutrons, collectively known as nucleons, make up all known atomic nuclei. Despite their ubiquitous presence, many aspects of these fundamental particles remain mysterious. Among these enigmas, the proton radius has been particularly challenging to determine. The deviation observed in the measurement of the muonic hydrogen’s proton radius prompted scientists to question whether it signified new physics beyond the Standard Model or arose from inherent systematic uncertainties in different measurement techniques. Recent evidence leans towards the smaller experimental value being accurate, suggesting no new physics at play.

Significant Advances in Calculation Precision

Building upon their previous lattice calculations in 2021, researchers at the Mainz Cluster of Excellence PRISMA+ have achieved notable improvements in determining the proton’s size. Through meticulous theoretical calculations, they have surpassed earlier estimates and provided additional evidence favoring the smaller proton radius. Doctoral student Miguel Salg, a member of the research group led by Prof. Dr. Hartmut Wittig, has played a pivotal role in obtaining these remarkable results. The team’s calculations have now achieved such a level of accuracy that they can discard the need for experimental data entirely.

Quantum Chromodynamics: Unraveling the Proton’s Secrets

The theoretical calculations performed by the Mainz physicists rely on the powerful framework of quantum chromodynamics (QCD). This theory elucidates the interplay of forces within atomic nuclei, describing the binding of quarks to form protons and neutrons. The strong interaction, mediated by exchange particles called gluons, reinforces these processes. To mathematically model such complexities, the Mainz scientists employ lattice field theory, which distributes the quarks over discrete points within a crystal-like lattice.

Calculating Proton Properties Using Supercomputers

Lattice field theory enables researchers to calculate various properties of nucleons using supercomputers. The initial step involves determining the electromagnetic form factors, which describe the distribution of electric charge and magnetization within the proton. From these form factors, it becomes possible to deduce the proton’s radius. Previous calculations mainly focused on the electric charge radius, while the magnetic charge radius remained another intriguing puzzle. However, the Mainz theoreticians have now tackled this challenge and generated stable predictions for the magnetic charge radius based purely on theoretical calculations.

Broadening the Scope: Zemach Radius and Experimental Measurements

The Mainz research group’s theoretical calculations have not only yielded insights into the electric and magnetic charge radii but have also facilitated the derivation of the proton’s Zemach radius. This quantity plays a crucial role in experimental measurements on muonic hydrogen. The successful determination of the Zemach radius showcases the substantial progress made in lattice QCD calculations, highlighting their increasing accuracy and reliability.

Through their groundbreaking calculations, the Mainz physicists have enhanced our understanding of the proton’s size. The mounting evidence supports the hypothesis that the smaller experimental value for the proton radius is indeed accurate. While scientific investigations continue, these advancements have brought us closer to unraveling the mysteries of the proton and shed light on the fundamental physics governing our universe.

The latest research by the theoretical physicists at JGU represents a significant step forward in the quest to determine the proton’s radius. By refining their calculations and eliminating the need for experimental data, they have provided compelling evidence favoring the smaller value. This progress not only enhances our understanding of nucleons but also demonstrates the astonishing advancements in theoretical physics. As scientists continue to push the boundaries of knowledge, these breakthroughs pave the way for further discoveries and contribute to the ever-evolving field of fundamental physics.


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