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The essential characteristics of the proton, such as its mass and spin, are still poorly understood by physicists more than a century after the particle’s discovery. The size of the proton, which is a key factor in understanding nuclei, for example, is a special mystery. The radius of the proton was determined thanks to inelastic electron-proton scattering studies performed in the late 1950s that showed the proton’s charge distribution in space. Measuring the shift in the hydrogen atom’s lowest energy levels is a complementary method for figuring out this “charge radius,” which depends on accurate calculations in quantum-electrodynamics. Many experiments have been conducted throughout the years to more accurately determine the proton’s size.

The Council on Data for Science and Technology (CODATA) determined the proton charge radius to be 0.8760(78) fm in 2006 based on findings from scattering and spectroscopic observations. But, in 2010, something unexpected happened: the Paul Scherrer Institut’s (PSI) CREMA collaboration published a value of 0.8418(7) fm based on a brand-new, highly accurate spectroscopic measurement of muonic hydrogen. The “proton radius puzzle” was born as a result of the result, which was inconsistent with earlier spectroscopic measurements and more than 5 below the CODATA world average. The differences with earlier experiments are not yet completely understood, despite the closer agreement between the most recent muonic-hydrogen results and the most recent electron-proton scattering and hydrogen spectroscopic data.

Neutrino scattering has now been introduced as a novel measuring method by the MINERvA project. The weak charge distribution of the proton, which is represented by the analogous axial-vector form factor FA, can be measured by neutrinos, as opposed to the electric or magnetic charge distributions of the proton, which are encoded in vector form factors and are probed by conventional scattering measurements. FA is crucial to accurate measurements of neutrino-oscillation parameters at experiments like DUNE, Hyper-K, NOvA, and T2K in addition to serving as a complementary probe of proton structure.

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The segmented scintillator detector MINERvA has hexagonal planes that are perpendicular to the incoming beam and are constructed from strips of triangular cross-section. The MINERA researchers made the first high-statistics measurement of the p+n cross-section using the hydrogen atom in polystyrene by observing how a beam of muon antineutrinos produced by Fermilab’s NuMI neutrino beamline interacts with a polystyrene target, which contains hydrogen tightly bonded to carbon. They determined the nucleon axial charge radius to be 0.73(17) fm by extracting FA from 5580 180 signal occurrences (seen over an estimated background of 12,500), which is consistent with the electric charge radius determined via electron scattering.
Lead author Tejin Cai made the suggestion to use a polystyrene target to access neutrino-hydrogen scattering as a PhD student at the University of Rochester. “If we weren’t optimists, we’d claim [this experiment] was impossible,” adds Cai. Due to their chemical bonds, hydrogen and carbon interact at the same time in the detector. But then I understood that the very nuclear phenomena that complicated scattering on carbon also enabled us to choose hydrogen and would enable us to take the interactions with carbon out of the equation.

The proton charge radius will soon be seen from a different angle thanks to a brand-new experiment dubbed AMBER at the Super Proton Synchrotron’s M2 beamline at CERN. The predecessor to AMBER was COMPASS, which made significant contributions to resolving the proton “spin crisis” (the discovery by the European Muon Collaboration in 1987 that quarks account for less than a third of the total proton spin) by examining the role played by gluons in the proton’s spin. To achieve the tiny momentum transfer required to estimate the proton radius, AMBER will use muon scattering at previously unheard-of energy (about 100 GeV). Meanwhile, the MUSE experiment at PSI will detect muon- and electron-proton scattering simultaneously in order to calculate the proton radius.

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The aim of AMBER is to find a value for the proton radius in the range 0.84-0.88 fm, as expected from prior experiments, with an uncertainty of roughly 0.01 fm, starting with a pilot run in September 2023 and operating for up to three years. A spokeswoman for AMBER, Jan Friedrich of TU Munich, states, “Some colleagues believe that there is no proton-radius dilemma, merely faulty observations. The gap between theory and experiments, as well as between different experiments, must be reduced and brought as close to alignment as possible. As there is only one real proton radius,

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