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Pohl et al. measured the energy difference between the 2P and 2S states of muonic hydrogen and used it to determine a precise value of the proton radius. The result disagreed significantly from values extracted from electronic hydrogen and…

Nuclear Experiment · Physics 2026-04-28 Gerald A. Miller

Determination of the proton charge radius by different methods has produced an inconsistency. The most precise value (from spectroscopy of muonic hydrogen) strongly disagrees with three less accurate values (from spectroscopy of ordinary…

High Energy Physics - Phenomenology · Physics 2015-03-05 Savely G. Karshenboim

The proton radius puzzle questions the self-consistency of theory and experiment in light muonic and electronic bound systems. Here, we summarize the current status of virtual particle models as well as Lorentz-violating models that have…

High Energy Physics - Phenomenology · Physics 2015-07-29 U. D. Jentschura

In 2010 the proton charge radius was extracted for the first time from muonic hydrogen, a bound state of a muon and a proton. The value obtained was five standard deviations away from the regular hydrogen extraction. Taken at face value,…

High Energy Physics - Phenomenology · Physics 2019-09-27 Gil Paz

The recent values of the proton charge radius obtained by means of muonic-hydrogen laser spectroscopy are about $4\%$ different from the electron scattering data. It has been suggested that the proton radius is actually measured in…

High Energy Physics - Phenomenology · Physics 2013-11-05 M. M. Giannini , E. Santopinto

High-precision hydrogen spectroscopy is an active field which helps to determine the Rydberg constant and proton charge radius, tests bound-state QED, and can search for Beyond Standard Model (BSM) Physics. Additionally, with recent…

Atomic Physics · Physics 2022-06-15 S. F. Cooper , C. Rasor , R. G. Bullis , A. D. Brandt , D. C. Yost

The proton size, specifically its charge radius, was thought known to about 1% accuracy. Now a new method probing the proton with muons instead of electrons finds a radius about 4% smaller, and to boot gives an uncertainty limit of about…

High Energy Physics - Phenomenology · Physics 2015-05-20 Carl E. Carlson

The proton size has been found, with a $6\,\sigma$ statistical significance, to be larger by 4% when it is measured relatively to the electron than to the muon [Pohl2010,Antognini2013]. We solve this proton radius puzzle by accounting for…

General Physics · Physics 2019-04-12 Laurent Nottale

Static properties of hadrons such as their radii and other moments of the electric and magnetic distributions can only be extracted using theoretical methods and not directly measured from experiments. As a result, discrepancies between the…

High Energy Physics - Phenomenology · Physics 2016-09-16 N. G. Kelkar , T. Mart , M. Nowakowski

Nucleons (protons and neutrons) are the building blocks of atomic nuclei, and are responsible for more than 99\% of the visible matter in the universe. Despite decades of efforts in studying its internal structure, there are still a number…

High Energy Physics - Phenomenology · Physics 2022-02-02 Haiyan Gao , Marc Vanderhaeghen

The rovibrational transition frequencies of molecular hydrogen ions (MHI) can be accurately computed using ab initio nonrelativistic quantum electrodynamics. A subset of the fundamental constants are required input. We analyze how, once…

Atomic Physics · Physics 2025-05-12 J. -Ph Karr , S. Schiller , V. I. Korobov , S. Alighanbari

We review recent experiments on HD$^+$ spectroscopy. The reduced proton-deuteron mass to electron mass ratio, $\mu_{pd}/m_e$, is inferred from the comparison of theory and experiment. Theoretical issues related to the calculations of the…

Atomic Physics · Physics 2022-09-07 Vladimir I. Korobov

The "proton radius puzzle" is the 7-standard-deviations difference of the charge radius of the proton as determined from the Lamb shift in electronic hydrogen and elastic electron scattering off the proton on the one side and the high…

Atomic Physics · Physics 2023-04-17 Thomas Walcher

Rydberg alkaline earth atoms are promising tools for quantum simulation and metrology. When one of the two valence electrons is promoted to long-lived circular states, the second valence electron can be optically manipulated without…

Atomic Physics · Physics 2024-06-04 L. Lachaud , B. Muraz , A. Couto , J. -M. Raimond , M. Brune , S. Gleyzes

The precision of experimental data and analysis techniques is a key feature of any discovery attempt. A striking example is the proton radius puzzle where the accuracy of the spectroscopy of muonic atoms challenges traditional electron…

A slight anomaly in optical spectra of the hydrogen atom led Willis E. Lamb to the search for the proton size. As a result, he found the shift of the 2S1/2 level, the first experimental demonstration of quantum electrodynamics. In return, a…

History and Philosophy of Physics · Physics 2021-04-01 Istvan Angeli

The relationship between the electric form factors for the proton in the rest frame and in the Breit momentum frame is used to provide a value for the difference in the mean squared charge radius of the proton evaluated in the two frames.…

Nuclear Theory · Physics 2015-01-28 D. Robson

Reinforcement of the puzzle about the proton charge radius r, stimulated by the recent experiments with muonic hydrogen induced news discussions on the subject, and now some physicists are ready to adopt the exotic properties of muon, lying…

Atomic Physics · Physics 2015-06-16 Alexander L Kholmetskii , Oleg V Missevitch , Tolga Yarman

We introduce a concept of proton cloud and calculate the radius of the proton cloud of the Hydrogen atom. Then, we estimate the radius of the proton cloud of a Hydrogen atom on highly excited Rydberg states. Based on the size of proton…

General Physics · Physics 2014-04-01 Li Yang , Ya-Qi Song

The proton, deuteron and triton masses can be determined relative to the electron mass via rovibrational spectroscopy of molecular hydrogen ions. This has to occur via comparison of the experimentally measured transition frequencies and the…

Atomic Physics · Physics 2025-05-13 Stephan Schiller , Jean-Philippe Karr