Precise determination of the proton magnetic radius from electron scattering data

Abstract

We extract the proton magnetic radius from high-precision electron-proton elastic scattering cross section data. Our theoretical framework combines dispersion analysis and chiral effective field theory and implements the dynamics governing the shape of the low-Q 2 form factors. It allows us to use data up to Q 2 ≈ 0.5 GeV 2 for constraining the radii and overcomes the difficulties of empirical fits and Q 2 → 0 extrapolation. We obtain a magnetic radius r p M = 0.850 ± 0.001 (1σ fit uncertainty) +0.009 −0.004 (full-range theory uncertainty) fm, significantly different from earlier results obtained from the same data using empirical fits, and close to our extracted electric radius r p E = 0.842 ± 0.002 (1σ fit uncertainty) +0.005 −0.002 (full-range theory uncertainty) fm.

Dispersion-theoretical analysis of the electromagnetic form factors of the nucleon: Past, present and future

“…There has also been some related work in the so-called dispersively improved chiral perturbation theory, see [55][56][57][58]. The extracted proton charge radius is consistent with our result, but as noted in Ref.…”

Laser spectroscopy of light muonic atoms and the nuclear charge radii

“…There is a large, unexpected discrepancy with the values from both electron scattering [38] and H spectroscopy: this is the "proton radius puzzle" [39,40]. This has triggered various theoretical efforts including refinement of bound-state QED calculations for the atomic energy levels [41][42][43][44][45][46], refinement of techniques to extract the proton charge radius from scattering data [27,[47][48][49][50][51][52][53], investigations on the proton structure [8][9][10][11][12], investigation of beyond standard model physics [54][55][56][57], and refinements of laser spectroscopy systematic effects such as quantum interference [58,59]. These investigations have considerably advanced our understanding but have been unable to explain the observed discrepancy.…”

A theory vade mecum for PSI experiments

“…While the determination of the magnetic radius of the proton r (p) M 0.8 fm was discussed less controversially, there is also quite a spread in the values obtained from different extractions [83]. This spread is typically attributed to different treatment of TPE contributions.…”