The chiral and angular momentum content of the $\rho$-mesons in lattice QCD

TL;DR

This study uses lattice QCD to analyze the chiral and angular momentum structure of rho mesons, revealing strong chiral symmetry breaking in the rho and unexpected D-wave contributions in the excited rho' state.

Contribution

It introduces a gauge-invariant method to determine the chiral and partial wave content of mesons in lattice QCD, providing new insights into their internal structure.

Findings

Strong chiral symmetry breaking in the rho meson.

Infrared rho predominantly has a $^3S_1$ wave composition.

The rho' shows a small chiral symmetry breaking and a leading $^3D_1$ partial wave.

Abstract

The variational method allows one to study the mixing of interpolators with different chiral transformation properties in the nonperturbatively determined physical state. It is then possible to define and calculate in a gauge-invariant manner the chiral as well as the partial wave content of the quark-antiquark component of a meson in the infrared, where mass is generated. Using a unitary transformation from the chiral basis to the $^{2S+1}L_J$ basis one may extract the partial wave content of a meson. We present results for the $\rho$- and $\rho'$-mesons using a simulation with $N_f=2$ dynamical quarks, all for lattice spacings close to 0.15 fm. Our results indicate a strong chiral symmetry breaking in the $\rho$ state and its simple $^3S_1$-wave composition in the infrared. For the $\rho'$-meson we find a small chiral symmetry breaking in the infrared as well as a leading contribution of the $^3D_1$ partial wave, which is contradictory to the quark model.