Alternative way to understand the unexpected results of the JLab polarization experiments to measure the Sachs form factors ratio

Abstract

In the one-photon exchange approximation we discuss questions related to the interpretation of unexpected results of the JLab polarization experiments to measure the Sachs form factors ratio $G_E/G_M$ in the region $1. 0 \leq Q^2 \leq 8.5$ GeV$^2$. For this purpose, we developed an approach which essentially is a generalization of the constituent-counting rules of the perturbative QCD (pQCD) for the case of massive quarks. We assume that at the lower boundary of the considered region the hard-scattering mechanism of pQCD is realized. Within the framework of the developed approach we calculated the hard kernel of the proton current matrix elements $J^{\pm \delta, \delta }_{p}$ 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 allows us to state that (i) around the lower boundary of the considered region, the leading scaling behavior of the Sachs form factors has the form $G_E, G_M \sim 1/Q^6$, (ii) the dipole dependence ($G_E, G_M \sim 1/Q^4$) is realized in the asymptotic regime of pQCD when $\tau \gg 1$ ($\tau=Q^2/4M^2$) in the case when the quark transitions with spin-flip dominate, (iii) the asymptotic regime of pQCD in the JLab experiments has not yet been achieved, and (iv) the linear decrease of the ratio $G_{E}/G_{M}$ at $\tau < 1$ is due to additional contributions to $J^{\delta, \delta }_{p}$ by spin-flip transitions of two quarks and an additional contribution to $J^{-\delta, \delta }_{p}$ by spin-flip transitions of three quarks.