Probing ∆ Structure with Pion Electromagnetic Production

The Dubna-Mainz-Taipei dynamical model for pion electromagnetic production, which can describe well the existing data from threshold up to 1 GeV photon lab energy, is presented and used to analyze the recent precision data in the ∆ region. We find that, within our model, the bare ∆ is almost spherical while the physical ∆ is oblate. The deformation is almost saturated by the pion cloud effects. We further find that up to Q2 = 4.0(GeV/c)2, the extracted helicity amplitude A3/2 and A1/2 remain comparable with each other, implying that hadronic helicity is not conserved at this range of Q2. The ratio E1+/M1+ obtained show, starting from a small and negative value at the real photon point, a clear tendency to cross zero, and to become positive with increasing Q2. This is a possible indication of a very slow approach toward the pQCD region. Finally, we find that the bare helicity amplitude A1/2 and S1/2, but not A3/2, starts exhibiting the scaling behavior at about Q2 ≥ 2.5(GeV/c)2.