Ovrview: The Shape of Hadrons

TL;DR

This paper reviews experimental and theoretical insights into the non-spherical shapes of hadrons, especially nucleons and Δ particles, highlighting the role of pion-cloud effects and recent measurements of quadrupole amplitudes.

Contribution

It provides a comprehensive overview of experimental methods, results, and theoretical models explaining hadron shape deviations from spherical symmetry, emphasizing the importance of pion-cloud effects.

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 theories align better with experimental data.

Abstract

In this article we address the physical basis of the deviation of hadron shapes from spherical symmetry (non-spherical amplitudes) with focus on the nucleon and $\Delta$. An overview of both the experimental methods and results and the current theoretical understanding of the issue is presented. At the present time the most quantitative method is the $\gamma^{*} p \to \Delta$ reaction for which significant non-spherical electric (E2) and Coulomb quadrupole (C2) amplitudes have been observed with good precision as a function of Q^{2} from the photon point through 6 GeV^{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. This is expected due to the spontaneous breaking of chiral symmetry in QCD and the resulting, long range (low Q^{2}) effects of the pion-cloud. Other observables such as nucleon form factors and virtual Compton scattering experiments indicate that the pion-cloud is playing a significant role in nucleon structure. Semi-inclusive deep inelastic scattering experiments with transverse polarized beam and target also show the effect of non-zero quark angular momentum.