Light Hadron Masses from a Matrix Model for QCD

The $SU(3)$ Yang-Mills matrix model coupled to fundamental fermions is an approximation of quantum chromodynamics (QCD) on a 3-sphere of radius $R$. The spectrum of this matrix model Hamiltonian is estimated using standard variational methods, and is analyzed in the strong coupling limit. By employing a matching prescription to determine the dependence of the Yang-Mills coupling constant $g$ on $R$, we relate the asymptotic values of the energy eigenvalues in the $R\to \mathrm{\infty }$ (flat space) limit to the masses of light hadrons. We find that the matrix model estimates the light hadron spectrum fairly accurately, with the light baryon masses falling within $10\mathrm{\%}$, and most light meson masses falling within about $30\mathrm{\%}$ of their observed values.