Hadron masses in cavity quantum chromodynamics to order $\alpha_s^2$

TL;DR

This paper calculates hadron masses using cavity QCD to order α_s^2, fitting parameters to experimental data, and successfully predicts low-lying hadron states and mass splittings.

Contribution

It introduces a calculation of two-gluon exchange and annihilation diagrams in cavity QCD, improving the theoretical prediction of hadron masses and splittings.

Findings

Predicted hadron masses agree well with experimental data.

Two-gluon annihilation lifts π-η degeneracy.

Accurate η meson mass obtained from Hamiltonian diagonalization.

Abstract

The non-divergent diagrams describing two-gluon exchange and annihilation between quarks and antiquarks are calculated in the Feynman gauge, based on quantum chromodynamics in a spherical cavity. Using the experimental $N$, $\Delta$, $\Omega$, and $\rho$ masses to fit the free parameters of the M.I.T.\ bag model, the predicted states agree very well with the observed low-lying hadrons. As expected, the two-gluon annihilation graphs lift the degeneracy of the $\pi$ and $\eta$, while the $\rho$ and $\omega$ remain degenerate. Diagonalizing the $\eta - \eta'$ subspace Hamiltonian yields a very good value for the mass of the $\eta$ meson.