Isψ′(3700)a radial excitation ofψ(3100)?

Abstract

The proposal that ${\psi }^{\prime }\mathrm{}\left(3700\right)\mathrm{}$ and ${\psi }^{\prime \prime }\mathrm{}\left(4200\right)\mathrm{}$ are radial excitations of the $\psi \mathrm{}\left(3100\right)\mathrm{}$ charmed-quark-antiquark bound state is reexamined within the context of linear-potential models. If the interaction energy per unit length is universal, this assignment of ${\psi }^{\prime }$ and ${\psi }^{\prime \prime }$ must be retained. If this potential differs for each system, then one may abandon this assignment of ${\psi }^{\prime }$ and ${\psi }^{\prime \prime }$ at the expense of making the $\psi$ system relativistic and the charmed-quark mass light. A harmonic-oscillator model is also considered, with substantially the same conclusions.