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

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 δ,δ}_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^{δ,δ}_p) and with the spin-flip (J^{-δ,δ}_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^{δ,δ}_p, and the second one is the number of the spin-flipped quarks which contribute to the J^{-δ,δ}_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 τ<< 1, and the set (2,3) for τ>> 1 (τ=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^{δ,δ}_q ~ 1 and J^{-δ,δ}_q ~ \sqrtτ, then the dipole dependence is realized when τ>> 1 in the case when the quark transitions with spin-flip are dominate.