Q^2-evolution of Delta N gamma form factors up to 4 (GeV/c)^2 from JLab data

Abstract

We present the results on the ratios $E_{1+}^{(3/2)}/M_{1+}^{(3/2)}$ and $S_{1+}^{(3/2)}/M_{1+}^{(3/2)}$ for the $\gamma^* N \to \Delta(1232)$ transition at $Q^2\leq 4 (GeV/c)^2$ extracted from the $p(e,e'p)\pi^0$ cross section using two approaches: dispersion relations and modified version of unitary isobar model. The obtained results are in good agreement with the results of other analyses obtained using truncated multipole expansion at $Q^2=0.4,~0.525,~0.65,~0.75,~0.9,~1.15,~1.45,~1.8 (GeV/c)^2 $ and within dynamical and unitary isobar models at $Q^2=2.8,~4 (GeV/c)^2 $. According to obtained results the ratio $E_{1+}^{(3/2)}/M_{1+}^{(3/2)}$ remains small in all investigated region of $Q^2$ with very unclear tendency to cross zero above $2 (GeV/c)^2$. The absolute value of the ratio $S_{1+}^{(3/2)}/M_{1+}^{(3/2)}$ is clearly increasing with increasing $Q^2$, while it should be a constant value in the pQCD asymptotics. So, at $Q^2\leq4 (GeV/c)^2$ there is no evidence of approaching pQCD regime for these ratios. None of the soft approaches gives satisfactory description of the obtained results.