The Shape of Hadrons

TL;DR

This paper critically examines the concept of hadron shape, especially the proton, integrating theoretical predictions with recent high-precision experimental data and lattice calculations to understand their non-spherical structures.

Contribution

It provides a comprehensive analysis of the shape of hadrons, combining theoretical frameworks with experimental evidence, focusing on the nucleon to Δ(1232) transition.

Findings

Evidence suggests hadrons are non-spherical in shape.

Experimental data aligns with lattice and phenomenological models.

Insights into the electromagnetic transition between nucleon and Δ(1232).

Abstract

This colloquium addresses the issue of the shape of hadrons and in particular that of the proton. The concept of shape in the microcosm is critically examined. Special attention is devoted to properly define the meaning of shape for bound-state systems of near massless quarks. The ideas that lead to the expectation of non-sphericity in the shape of hadrons, the calculations that predict it, and the experimental information obtained from recent high-precision measurements are examined. Particular emphasis is given to the study of the electromagnetic transition between the nucleon and its first excited state, the $\Delta$(1232)-resonance. The experimental evidence is is critically examined and compared with lattice calculations, as well as with effective-field theories and phenomenological models.