Ovrview: The Shape of Hadrons

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 ${\gamma }^{\ast }p\to \Delta$ 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.

Cited by in corpus (18)

• The nucleon to Delta electromagnetic transition form factors in lattice QCD
• Delta-baryon electromagnetic form factors in lattice QCD
• D-state effects in the electromagnetic N-Delta transition
• Nucleon to Delta transition form factors with $N_F=2+1$ domain wall fermions
• Large-$N_c$ relations for the electromagnetic N to Delta(1232) transition
• Baryon octupole moments
• Electric Quadrupole and Magnetic Octupole Moments of the Light Decuplet Baryons Within Light Cone QCD Sum Rules
• A Study of Hadron Deformation in Lattice QCD
• Electroexcitation of the ${\Delta }^{+}(1232)$ at low momentum transfer
• Virtual Compton Scattering measurements in the ${\gamma }^{\ast }N\to \Delta$ transition
• Virtual Compton Scattering measurements in the nucleon resonance region
• On hadron deformation: a model independent extraction of EMR from pion photoproduction data
• Non-spherical proton shape and hydrogen hyperfine splitting
• Energy Dependence of the Delta Resonance: Chiral Dynamics in Action
• Nucleon to $\Delta$ transition form factors and empirical transverse charge densities
• Electromagnetic multipole moments of baryons
• Ernest Henley and the shape of baryons
• Pion electroproduction measurements in the nucleon resonance region