Pion Electroproduction and VCS at the \Delta(1232) Resonance Region

TL;DR

This paper reviews the experimental and theoretical study of the $ ightarrow$ reaction near the $ ext{Delta}(1232)$ resonance, highlighting the measurement of non-spherical amplitudes and comparing various models' predictions.

Contribution

It provides a comprehensive overview of experimental results and compares them with theoretical models including quark models, lattice QCD, and chiral effective field theory.

Findings

Significant non-spherical electric and Coulomb quadrupole amplitudes observed.

Quark models underestimate these amplitudes by at least an order of magnitude.

Lattice QCD and chiral effective field theory are in approximate agreement with experimental data.

Abstract

The study of the $\gamma^* N\rightarrow \Delta$ reaction presents the best quantitative method to explore the deviation of hadron shapes from spherical symmetry (nonspherical amplitudes). Significant non-spherical electric (E2) and Coulomb quadrupole (C2) amplitudes have been observed with good precision as a function of $Q^2$ from photon point up to $\approx 7 ~(GeV/c)^2$. Quark model calculations for these quadrupole amplitudes are at least an order of magnitude too small and even have the wrong sign. Lattice QCD, chiral effective field theory, and dynamic model calculations which include the effects of the pion-cloud are in approximate agreement with experiment.