Nucleon polarizabilities: From Compton scattering to hydrogen atom

Abstract

To comply with the critique of the Comment [J. Arrington, arXiv:1602.01461], we consider another modification of the proton electric form factor, which resolves the "proton-radius puzzle". The proposed modification satisfies all the consistency criteria put forward in the Comment, and yet has a similar impact on the puzzle as that of the original paper. Contrary to the concluding statement of the Comment, it is not difficult to find an ad hoc modification of the form factor at low Q that resolves the discrepancy and is consistent with analyticity constraints. We emphasize once again that we do not consider such an ad hoc modification of the proton form factor to be a solution of the puzzle until a physical mechanism for it is found.

Baryons as relativistic three-quark bound states

“…The third term comprises two-photon effects and its currently accepted value is E TPE = 0.0332 (20) meV [677], with similar numbers obtained by various authors (see Table 6.1 in Ref. [643] for a compilation). Therefore, fitting theory to experiment allows one to extract the proton charge radius R E = 0.84087 (39).…”

“…There has been much recent interest in a precision determination of the nucleon's polarisabilities, which is reflected in a number of reviews on the topic [441,[638][639][640][641][642][643]. The electric polarisability α and magnetic polarisability β tell us how the nucleon responds to an external electromagnetic field, with current PDG values α = 11.2(4) × 10 −4 fm 3 and β = 2.5(4) × 10 −4 fm 3 for the proton [9].…”

“…In principle both relations hold for arbitrary η, which defines the generalized polarisabilities α(η) and β(η) and the generalized GDH integral. For extensive discussions of the various sum rules derived from CS we refer to the reviews [642,643].…”

“…In the forward limit this is particularly relevant for determining the subtraction function c 2 (η, 0) that appears in the dispersion relations and is related to the magnetic polarisability; see our comments on the proton radius puzzle below. The role of chiral effective field theory and its application to Compton scattering is discussed in the recent reviews [641,643].…”

“…A closely related issue that also depends on the magnitude of TPE corrections is the proton radius puzzle. We will only briefly sketch the problem here and refer to [1,643,[671][672][673][674] for detailed reviews. The basic outline is the same as in Fig.…”