On the physical meaning of Sachs form factors and on the violation of the dipole dependence of G_E and G_M on Q^2

TL;DR

This paper analyzes the interpretation of proton form factor measurements, proposing that the observed deviations from dipole behavior at certain Q^2 ranges are due to different spin-flip contributions in quark transitions, challenging previous assumptions.

Contribution

It introduces a detailed calculation of proton current matrix elements considering spin-flip and non-spin-flip quark contributions, explaining the violation of dipole dependence in form factors.

Findings

G_E/G_M ratio approaches 1 at certain conditions

Form factors behave as 1/Q^6 or 1/Q^4 depending on spin-flip contributions

Dipole dependence appears only when spin-flip transitions dominate at high Q^2

Abstract

We discuss questions related to the interpretation of unexpected results of measurements of the proton form factors ratio G_E/G_M in the polarization experiments done in JLab in the region of 0.5 < Q^2 < 8.5 GeV^2. For this purpose, in the case of the hard scattering mechanism we calculated (in the leading approximation) the matrix elements of the proton current J^{\pm \delta,\delta}_p for the full set of spin combinations corresponding to the number of the spin-flipped quarks, which contribute to the proton transition without spin-flip (J^{\delta,\delta}_p) and with the spin-flip (J^{-\delta,\delta}_p). This set is: (0,1), (0,3), (2,1), (2,3), where the first number in parentheses is the number of the spin-flipped quarks, which contribute to the J^{\delta,\delta}_p, and the second one is the number of the spin-flipped quarks which contribute to the J^{-\delta,\delta}_p. For the sets of (0,1) and (2,3), we found that the ratio G_E/G_M ~ 1, and the form factors G_E and G_M behave for the set of (0,1) as G_E, G_M ~ 1/Q^6, and for the set of (2,3) as G_E, G_M ~ 1/Q^4. At the same time the set of (0,1) is realized for \tau << 1, and the set (2,3) for \tau >> 1 (\tau=Q^2/4m^2). This allows us to suppose that: 1) at the lower boundary of the experimental measurements of the ratio G_E/G_M not dipole dependence appears but the law of G_E, G_M ~ 1/Q^6; 2) the conditions for the observation of the dipole dependence in the experiments has not yet been achieved; 3) since for quarks J^{\delta,\delta}_q ~ 1 and J^{-\delta,\delta}_q ~ \sqrt{\tau}, then the dipole dependence is realized when \tau >> 1 in the case when the quark transitions with spin-flip are dominate.