In the realm of theoretical physics, the quest to unravel the mysteries of the proton has been a longstanding challenge. The proton, one of the fundamental building blocks of atomic nuclei, has remained an enigma due to the elusive nature of its radius. However, a team of theoretical physicists at Johannes Gutenberg University Mainz (JGU) has made remarkable strides in improving their calculations of the proton’s electric charge radius. What makes their achievement even more remarkable is that their calculations were achieved without the use of any experimental data for the first time. These intriguing findings, along with a stable theory prediction for the proton’s magnetic charge radius, have been published in three preprints on the arXiv server. This article explores the essence of these breakthroughs and their implications for our understanding of the proton.

The proton, along with its counterpart, the neutron, forms the foundation of all known atomic nuclei. Despite their ubiquity, many of the characteristics of these nucleons remain enigmatic. The proton’s radius has proved to be particularly elusive, prompting scientists to search for novel methods to measure it accurately. In 2010, a breakthrough proton radius measurement technique involving laser spectroscopy of muonic hydrogen unveiled a significantly smaller value compared to previous measurements using traditional hydrogen or electron-proton scattering. This discrepancy sparked a fundamental question: Does the deviation suggest new physics beyond the Standard Model, or is it simply a reflection of inherent uncertainties in measuring methods? Recent evidence has leaned towards the validity of the smaller experimental value, implying the absence of new physics behind the proton radius puzzle. However, theoretical calculations play a vital role in definitively addressing this question.

Advancements in Lattice Calculations

In 2021, researchers led by Prof. Dr. Hartmut Wittig of the Mainz Cluster of Excellence PRISMA+ achieved a critical milestone in lattice calculations, which provided a reliable clue to the smaller proton radius. Building upon this foundation, Miguel Salg, a doctoral student in Prof. Wittig’s research group, made substantial progress in further refining and extending the previous calculations. Previously, the Mainz research group calculated the so-called isovector radius, which differs from the proton radius. They derived the proton radius by adding experimental data for the neutron radius. However, Salg’s recent work obviated the need for any experimental data and ensured a more comprehensive calculation by considering the missing fractions, refining statistical approaches, and constraining systematic errors. This breakthrough eliminates the dependence on experimental data, leading to greater confidence in the validity of the results.

The implications of these new calculations are profound. They strengthen the case for the correctness of the smaller proton radius, further supporting the notion that there is no new physics contributing to the proton radius puzzle. The power of the calculations lies in their reliance on the theory of quantum chromodynamics (QCD), which provides a mathematical framework for understanding the interplay of forces within atomic nuclei. QCD describes the strong interaction, which binds quarks (the elementary building blocks of matter) to form protons and neutrons through the exchange of gluons. By employing lattice field theory and utilizing advanced supercomputers, the Mainz scientists can simulate these complex processes and calculate the electromagnetic form factors of the nucleons, representing the distribution of electric charge and magnetization within the proton. From these form factors, the proton radius can be obtained.

Unveiling the Magnetic Charge Radius

Beyond the electric charge radius, the proton also possesses a magnetic charge radius, which presents its own puzzle. Expanding on their QCD-based calculations, the Mainz researchers have successfully predicted the magnetic charge radius for the first time using purely theoretical methods. This breakthrough not only demonstrates the progress made in lattice QCD calculations but also highlights the growing quality and reliability of these predictions.

Unraveling the Zemach Radius

Additionally, the precise knowledge of the electric and magnetic form factors has enabled the Mainz group to derive the Zemach radius of the proton purely from QCD. The Zemach radius is a crucial input quantity for experimental measurements on muonic hydrogen. This achievement illustrates the remarkable advancement of lattice QCD calculations and their immense potential to enhance our understanding of the proton and its intricate properties.

The recent breakthroughs in theoretical physics at Johannes Gutenberg University Mainz offer new insights into the elusive nature of the proton. The refined calculations of the proton’s electric charge radius, achieved without the need for experimental data, strengthen the case for the smaller value and provide evidence against new physics beyond the Standard Model. Additionally, the prediction of the magnetic charge radius and the derivation of the Zemach radius highlight the progress made in lattice QCD calculations and their increasing reliability. These discoveries not only contribute to our understanding of the proton but also underscore the power of theoretical physics in unraveling the mysteries of the universe. The journey to comprehending the fundamental nature of the proton continues, fueled by the ingenuity and perseverance of scientists on the frontiers of theoretical physics.


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