We construct a mass formula for the stringlike properties of $q\overline{q}$ mesons, based on the spectrum-generating algebra $\mathrm{U}\mathrm{}\left(4\right)\mathrm{}\otimes \mathrm{S}{\mathrm{U}}_s\mathrm{}\left(2\right)\mathrm{}\otimes \mathrm{S}{\mathrm{U}}_f\mathrm{}\left(n\right)\mathrm{}\otimes \mathrm{S}{\mathrm{U}}_c\mathrm{}\left(3\right)\mathrm{}$, with U(4) ⊃ SO(4) dynamic symmetry. We determine the parameters appearing in this mass formula from fits to 57 well-established mesons in the Particle Data Group summary table. The average deviation for the mass squared of these mesons is 5.7% for our fit of all meson families combined. The mass formula allows us to distinguish meson states which are not $q\overline{q}$ type, such as $a_0\mathrm{}\left(980\right)\mathrm{}$.

• Received 7 February 1991

DOI:https://doi.org/10.1103/PhysRevD.44.898