Chiral sum rule on the light front and the 3D image of the pion

TL;DR

This paper derives a chiral sum rule for the pion on the light front, linking its Goldstone boson nature and quark-gluon structure, and validates it using a holographic model consistent with chiral symmetry breaking.

Contribution

It introduces a novel sum rule for the pion's light-front wave function that unifies its elementary and structured aspects, supported by a holographic model.

Findings

The pion's density is mostly uniform inside its radius.

The sum rule aligns with chiral symmetry breaking in AdS/QCD.

The model agrees well with experimental pion form factors.

Abstract

The lightest meson, the pion, features two faces -- one is the elementary Goldstone boson of QCD and the other is the structured bound state of quarks and gluons. To accommodate both in a single light-front wave function in the valence space, we obtain a sum rule by analyzing the conserved axial-vector current and the general structures of the wave functions. Using an analytic model motivated by holography, we show this sum rule is consistent with requirements of chiral symmetry breaking in AdS/QCD. Within this model, we find a remarkable feature of the pion, namely that the density is mostly uniform inside its radius; furthermore, we obtain good agreement with the experimental pion form factor at spacelike momenta.