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

In this work we discuss questions related to the interpretation of unexpected results of measurements of the proton form factors ratio GE/GM in the high-precision double 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 ±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 spinflipped quarks which contribute to the J −δ,δ p . For the sets of (0,1) and (2,3), we found that the ratio GE/GM ∼ 1, and the form factors GE and GM behave for the set of (0,1) as GE, GM ∼ 1/Q 6 , and for the set of (2,3) as GE, GM ∼ 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 GE/GM not dipole dependence appears but the law of GE, GM ∼ 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 ∼ √ τ , then the dipole dependence is realized when τ ≫ 1 in the case when the quark transitions with spin-flip are dominate; 4) the law of the linear decrease of GE/GM at τ < 1 is due to additional contributions to the J δ,δ p by spin-flip transitions of two quarks and an additional contribution to J −δ,δ p by spin-flip transitions of three quarks, in this case their relative contributions are small.

Nucleon structure and the high energy interactions

“…We added a small contribution from the energy-independent part of the spin-flip amplitude in a form similar to that proposed in Ref. [73].…”

High energy hadron spin flip amplitude

“…In our HEGS model , which describes the maximum experimental data in a wide energy region from √ s = 9 GeV √ s = 8 TeV with minimum fitting parameters, the odderon has the same intercept as the standard soft Pomeron. Taking into account the form of the spin-flip amplitude, proposed in the works of Galynskii-Kuraev [38,39], the energy independence of the differential cross sections at large momentum transfer is explained by the contribution of the energy independent part of the spin-flip amplitude. The obtained size and momentum transfer dependence of the spin-flip amplitude allow one to describe the differential cross sections in the region of the diffraction minimum and at large momentum transfer.…”

“…In [38,39] on the basis of generalization of the constituent-counting rules of the perturbative QCD the proton current matrix elements J ±δδ p for the full set of spin combinations corresponding to the number of the spin-flipped quarks was calculated. It leads to part of the spin-flip amplitude…”

Optimizing energetic light dark matter searches in dark matter and neutrino experiments

“…(A.13) 20 Note, however, that the ratio of the electric and magnetic form factor µpGE/GM decreases from 1 for larger Q 2 > 1 GeV 2 from the high precision double polarization experiments [110,111]. In our analysis, we assume that keeping the dipole approximation for Q 2 4 GeV 2 is reasonable in the region of elastic scattering of our proton target.…”