High-Precision Determination of the Electric and Magnetic Form Factors of the Proton

Abstract

New precise results of a measurement of the elastic electron-proton scattering cross section performed at the Mainz Microtron MAMI are presented. About 1400 cross sections were measured with negative four-momentum transfers squared up to Q² = 1 (GeV/c)² with statistical errors below 0.2%. The electric and magnetic form factors of the proton were extracted by fits of a large variety of form factor models directly to the cross sections. The form factors show some features at the scale of the pion cloud. The charge and magnetic radii are determined to be <r²E>½ = 0.879(5)stat(4)syst(2)model(4)group fm and <r²M>½ = 0.777(13)stat(9)syst(5)model(2)group fm.

Baryons as relativistic three-quark bound states

“…Possible origins of the discrepancy include: (1) a problem with the electron measurements in the sense that the uncertainty in the proton radius extraction may be larger than expected; (2) missing hadronic effects; or (3) new physics beyond the Standard Model through so far undiscovered new interactions that violate lepton universality. The first point may seem obsolete in light of the available precise low-Q 2 electron scattering data which support the upper value for the proton radius [678]. It has been argued, however, that the data may be equally compatible with the smaller radius [679][680][681] although the issue is disputed [682].…”

Chiral perturbation theory of hyperfine splitting in muonic hydrogen

“…The apparent discrepancy between extractions of the proton radius from experiments performed with electronic [1,2,3] vs. muonic probes [4,5] -aka the proton-size puzzle -calls for a precise theoretical understanding of the hydrogen spectrum.…”

Deducing the proton energy configuration

“…If the energy is relativistic and contracted by α -1/3 the average radius would be 1.084fm, and a double pass per loop closure distributed over three dimension would effectively reduce the radius by 2 1/3 = 1.26, to r p = 0.8604fm (6) This radius value is comparable with empirical data by Pohl, Bernaur, and others. [8][9][10][11][12][13][14][15] Empirical values for the proton radius differ to a much greater extent than the current measurement uncertainty estimates. Bernaur obtained a value of 0.879±0.001 fm, using hydrogen spectroscopy and proton-electron scattering.…”

“…Bernaur obtained a value of 0.879±0.001 fm, using hydrogen spectroscopy and proton-electron scattering. 8 Pohl evaluated muonic hydrogen energy levels and obtained 0.8409±0.0004 fm. 9,10 The derived proton radius estimate (6) falls nominally halfway between the two empirical values.…”