Chiral symmetry breaking and the spin content of hadrons

TL;DR

This paper investigates the spin content of hadrons, especially mesons, using lattice simulations and chiral basis transformations, revealing that the rho meson is predominantly a 3S1 state with no spin crisis.

Contribution

It introduces a method to determine meson spin content via chiral basis analysis and lattice measurements, challenging the conventional spin crisis interpretation.

Findings

The rho meson is mainly a 3S1 state.

The spin crisis does not appear in the rho meson.

Lattice simulations can quantify chiral mixture in mesons.

Abstract

From the parton distributions in the infinite momentum frame one finds that only about 30% of the nucleon spin is carried by spins of the valence quarks, which gave rise to the term "spin crisis". Similar results hold for the lowest mesons, as it follows from the lattice simulations. We define the spin content of a meson in the rest frame and use a complete and orthogonal $\bar q q$ chiral basis and a unitary transformation from the chiral basis to the (2S+1)LJ basis. Then, given a mixture of different allowed chiral representations in the meson wave function at a given resolution scale, one can obtain its spin content at this scale. To obtain the mixture of the chiral representations in the meson we measure in dynamical lattice simulations a ratio of couplings of interpolarors with different chiral structure. For the rho meson we obtain practically the 3S1 state with no trace of the spin crisis. Then a natural question arises: which definition does reflect the spin content of a hadron?