MUSE: The MUon Scattering Experiment

MUSE is a high-precision muon scattering experiment aiming to determine the proton radius. Muon, electron, and pion scattering will be measured at the same time. Two-photon exchange corrections will be determined with data using both beam polarities.

The origin of the proton radius puzzle

The dimension of the proton, the basic building block of matter, is still object of controversy. The most precise electron-proton scattering data at low transferred momenta are re-analyzed and the extraction of the proton radius is discussed. A recent experiment from the JLAB-CLAS collaboration gives a small value for the radius (The symbol $$R_E^\alpha $$ R E α stands for the root-mean-square charge radius of the proton $$\sqrt{\langle r_E^2\rangle }$$ ⟨ r E 2 ⟩ , obtained by the experimental or theoretical Collaboration $$\alpha $$ α .) $$R_E^\mathrm{CLAS}= (0.831\pm 0.007_\mathrm{stat}\pm 0.012_\mathrm{syst})$$ R E CLAS = ( 0.831 ± 0 . 007 stat ± 0 . 012 syst ) fm (Xiong et al. in Nature 575:147, 2019), in contrast with previous electron scattering experiments, in particular with the MAINZ experiment (Bernauer et al. (A1 Collaboration), Phys. Rev. C 90:015206, 2014) that concluded $$R_E^\mathrm{MAINZ}= (0.879\pm 0.005_\mathrm{stat}\pm 0.004_\mathrm{syst}\pm 0.002_\mathrm{model}\pm 0.004_\mathrm{group})$$ R E MAINZ = ( 0.879 ± 0 . 005 stat ± 0 . 004 syst ± 0 . 002 model ± 0 . 004 group ) fm. The experimental results are re-analyzed in terms of different fits of the cross section and of its discrete derivative with analyticity constraints. The uncertainty on the derivative is two orders of magnitude larger than the error on the measured observable, i.e., the cross section. The systematic error associated with the radius is evaluated taking into account the uncertainties from different sources, as the extrapolation to the static point, the choice of the class of fitting functions, and the range of the data sample.

Two-photon frequency comb spectroscopy of atomic hydrogen

We have performed two-photon ultraviolet direct frequency comb spectroscopy on the 1S-3S transition in atomic hydrogen to illuminate the so-called proton radius puzzle and to demonstrate the potential of this method. The proton radius puzzle is a significant discrepancy between data obtained with muonic hydrogen and regular atomic hydrogen that could not be explained within the framework of quantum electrodynamics. By combining our result [f1S-3S = 2,922,743,278,665.79(72) kilohertz] with a previous measurement of the 1S-2S transition frequency, we obtained new values for the Rydberg constant [R∞ = 10,973,731.568226(38) per meter] and the proton charge radius [rp = 0.8482(38) femtometers]. This result favors the muonic value over the world-average data as presented by the most recent published CODATA 2014 adjustment.

Alternating Quark Model: First Principles to Fusion

<div> <div> <p>A subnucleonic structure of light nuclei comprises an alternating up and down quark sequence (AQS) that accounts for the measured RMS charge radii with an agreement of >99% and statistical correlation of ρ = 0.99, p<0.001. An interpretation of the uncertainty principle in terms of uncertainty in energy and time, coupled with Chaos theory as relates to linked harmonic oscillators, allows localization of average quark position. Structures incorporate equally spaced quarks around regular polyhedron geometries. The distance between neighboring quarks in a sequence is constant and equal to the radius of the proton. Light nuclei from H-3 to Li-7 conform to ring structures whose radii are calculated from the formula of a regular polygon having <i>n</i> sides, each side equal to the radius of the proton, and <i>n</i> vertices, each occupied by a quark. Quark-quark interactions link nucleons to maintain a continuous sequence of alternating equally spaced quarks. Parallel strands of quark sequences overlap so that protons overlap with neutrons. Regular polyhedron structures yield better radius predictions; larger nuclei tend to be less regular and less predictable (with the exception of C-12). The relative certainty in the accepted radius of helium-4, and its geometric relationship tithe proton radius, allow a prediction for the proton radius of 0.8673±0.0014 fm.<br></p> </div> </div>

An Alternating Quark Sequence Predicts Nuclear Radius from Quark Number

<div> <div> <p>A subnucleonic structure of light nuclei comprises an alternating up and down quark sequence (AQS) that accounts for the measured RMS charge radii with an agreement of >99% and statistical correlation of ρ = 0.99, p<0.001. An interpretation of the uncertainty principle in terms of uncertainty in energy and time, coupled with Chaos theory as relates to linked harmonic oscillators, allows localization of average quark position. Structures incorporate equally spaced quarks around regular polyhedron geometries. The distance between neighboring quarks in a sequence is constant and equal to the radius of the proton. Light nuclei from H-3 to Li-7 conform to ring structures whose radii are calculated from the formula of a regular polygon having <i>n</i> sides, each side equal to the radius of the proton, and <i>n</i> vertices, each occupied by a quark. Quark-quark interactions link nucleons to maintain a continuous sequence of alternating equally spaced quarks. Parallel strands of quark sequences overlap so that protons overlap with neutrons. Regular polyhedron structures yield better radius predictions; larger nuclei tend to be less regular and less predictable (with the exception of C-12). The relative certainty in the accepted radius of helium-4, and its geometric relationship tithe proton radius, allow a prediction for the proton radius of 0.8673±0.0014 fm.<br></p> </div> </div>