Making use of chiral SU(4) ⊗ SU(4) and scale-symmetry breaking together with $\epsilon$ saturation we obtain limits for the charmed-pseudoscalar-meson masses. These limits only allow charmed ($C=\pm 1$) pseudoscalar states with masses below 2.5 GeV. The existence of such states with masses above 1.5 GeV would imply strong restrictions on the theory: $\delta$ has at least dimension $l_{\delta }=1\mathrm{}$, $u$ has at least dimension $l_u=2\mathrm{}$ and the $\epsilon$ mass is higher than the upper limit noted in the Particle Data Group table. If the masses of these states are above 2 GeV, it furthermore follows than $l_u=3\mathrm{}$ and $l_{\delta }=2\mathrm{}$. Assuming the Gaillard-Lee-Rosner relation between the masses of the vector mesons and the quarks, identification of the $\psi \mathrm{}\left(3.1\right)\mathrm{}$ with the ${\phi }_c$ implies $l_u=3\mathrm{}$, $l_{\delta }=2\mathrm{}$, $m_{\epsilon }\approx 0.92$ GeV, ${\Gamma }_{\epsilon }\approx 0.42$ GeV, and $m_D=2.2\mathrm{}$ GeV. We have assumed integer dimensions. We have furthermore assumed that the effective $m_{\epsilon }$ is not much above 0.9 GeV.

• Received 13 January 1975

DOI:https://doi.org/10.1103/PhysRevD.12.1429