Chiral symmetry breaking and the spin content of the rho and rho' mesons

TL;DR

This study uses lattice QCD simulations with dynamical quarks to analyze the chiral symmetry breaking and spin structure of rho and rho' mesons, revealing differences in their chiral and angular momentum content.

Contribution

It introduces a method to measure chiral symmetry breaking and angular momentum content of mesons using interpolators and a unitary transformation, providing new insights into meson structure.

Findings

Ground state rho meson exhibits strong chiral symmetry breaking.

Rho' meson shows reduced chiral symmetry breaking and a significant D-wave component.

Rho meson is mainly a 3S_1 state with no spin crisis evidence.

Abstract

Using interpolators with different SU(2)_L \times SU(2)_R transformation properties we study the chiral symmetry and spin contents of the rho- and rho'-mesons in lattice simulations with dynamical quarks. A ratio of couplings of the $\qbar\gamma^i{\tau}q$ and $\qbar\sigma^{0i}{\tau}q$ interpolators to a given meson state at different resolution scales tells one about the degree of chiral symmetry breaking in the meson wave function at these scales. Using a Gaussian gauge invariant smearing of the quark fields in the interpolators, we are able to extract the chiral content of mesons up to the infrared resolution of ~1 fm. In the ground state rho meson the chiral symmetry is strongly broken with comparable contributions of both the (0,1) + (1,0) and (1/2,1/2)_b chiral representations with the former being the leading contribution. In contrast, in the rho' meson the degree of chiral symmetry breaking is manifestly smaller and the leading representation is (1/2,1/2)_b. Using a unitary transformation from the chiral basis to the {2S +1}L_J basis, we are able to define and measure the angular momentum content of mesons in the rest frame. This definition is different from the traditional one which uses parton distributions in the infinite momentum frame. The rho meson is practically a 3S_1 state with no obvious trace of a "spin crisis". The rho' meson has a sizeable contribution of the 3D_1 wave, which implies that the rho' meson cannot be considered as a pure radial excitation of the rho meson.