Spiral structure and logarithmic evolution of deuteron form factors: evidence for a transitional regime in QCD

Abstract

We present a consistent analysis of elastic electron--deuteron scattering combining perturbative quantum chromodynamics (pQCD) scaling, helicity amplitudes, and phenomenological parameterizations of deuteron form factors. Particular attention is paid to logarithmic corrections governed by anomalous dimensions of six-quark operators and to two-photon exchange (TPE). Three classes of parameterizations corresponding to different dynamical regimes are considered: pre-asymptotic valence-quark dominance, effective higher-twist contributions, and modified logarithmic evolution. A global fit to the world data for the structure functions $A(Q^2)$ and $B(Q^2)$, differential cross sections, and tensor polarization observables is performed using a combined strategy of global and local minimization. The best description of the complete data set is achieved within the $f_1$ parameterization, which incorporates pre-asymptotic logarithmic behavior and correlated valence-quark dynamics. Among the considered models, $f_1$ gives the smallest value of $\chi^2/\mathrm{dof}$. The obtained results indicate that the presently accessible momentum-transfer region corresponds to a transitional regime between hadronic and quark--gluon descriptions. Helicity-conserving amplitudes dominate, whereas the asymptotic pQCD regime has not yet been fully realized. This may indicate nontrivial multiquark correlations related to hidden-color configurations in the short-distance deuteron structure. The tensor polarization observable $t_{21}$ is especially sensitive to the asymptotic behavior of the helicity amplitudes. Future measurements at larger $Q^2$ may provide a decisive test for distinguishing between the considered dynamical scenarios.