Model independent extraction of the proton magnetic radius from electron scattering

Abstract

We combine constraints from analyticity with experimental electron-proton scattering data to determine the proton magnetic radius without model-dependent assumptions on the shape of the form factor. We also study the impact of including electron-neutron scattering data, and ππ → NN data. Using representative datasets we find for a cut of Q 2 ≤ 0.5 GeV 2 , r p M = 0.91 +0.03 −0.06 ± 0.02 fm using just proton scattering data; r p M = 0.87 +0.04 −0.05 ± 0.01 fm adding neutron data; and r p M = 0.87 +0.02 −0.02 fm adding ππ data. We also extract the neutron magnetic radius from these data sets obtaining r n M = 0.89 +0.03 −0.03 fm from the combined proton, neutron, and ππ data.

Theoretical constraints and systematic effects in the determination of the proton form factors

“…For the remaining coefficients, one can motivate bounds, as suggested in Refs. [15,54]. They parameterize the unit circle by z(t) = e iθ(t) and integrate over it.…”

On the $\pi\pi$ π π continuum in the nucleon form factors and the proton radius puzzle

“…Here, we address aspects of the radius extraction from scattering data, the systematics of which have been discussed vigorously in the literature recently [18][19][20][21][22][23][24][25][26][27][28]. Irrespective of the challenges involved in data selection and radiative corrections, the extraction can be stabilized by respecting the analytic structure of the electromagnetic form factors [29], e.g., by employing a conformal expansion.…”

Effective field theory for large logarithms in radiative corrections to electron proton scattering

“…The operator definition identifying R(µ) as a ratio of Wilson loop matrix elements in n f = 1 and n f = 0 can be used to show that log R(µ) contains only a single power of the large logarithm, log(Q 2 /m 2 ), to all orders in perturbation theory [16]. 9 This ensures that high powers of large logarithms do not upset the power counting of the resummed perturbative expansion. (45) and (30), and the soft contribution to 9 In particular, d log R(µ)/d log µ is given by the difference of cusp anomalous dimensions with n f = 1 and n f = 0, cf.…”

“…9 This ensures that high powers of large logarithms do not upset the power counting of the resummed perturbative expansion. (45) and (30), and the soft contribution to 9 In particular, d log R(µ)/d log µ is given by the difference of cusp anomalous dimensions with n f = 1 and n f = 0, cf. Eqs.…”

“…The analysis of Ref. [6] included a critical examination of experimental systematic errors and a rigorous treatment of theoretical uncertainty associated with form factor shape [8,9]. When applied to the entire Q 2 range of the Mainz dataset, this treatment reinforces the anomaly with muonic hydrogen.…”