Determination of the chiral-SU(4) × SU(4)-breaking parameters

We consider broken chiral SU(4) × SU(4) symmetry. From the observed mass spectrum of pseudoscalar charmed mesons, we are able to solve for the symmetry-breaking parameters of the theory. We find that both vacuum and Hamiltonian breaking play an important role as far as charmed states are concerned. Purely from the masses of $D$ and $F$ mesons we deduce the current-algebra mass ratio $\frac{m_c}{m_s}<5\mathrm{}$. This differs greatly from values obtained using linear or quadratic mass formulas. Considering $\eta$, ${\eta }^{\prime }$, and ${\eta }_c$ mixing we further obtain a good solution with $\frac{m_c}{m_s}\simeq 3.2$ and $\frac{〈\overline{c}c〉}{〈\overline{u}u〉}\simeq 5.67$.