Symmetry breaking in the harmonic-oscillator quark model

We extend a recent $\mathrm{Sp}(12, R)$ analysis of the symmetry breaking induced in the harmonic-oscillator quark model by an anharmonic two-body perturbation to a more general type of symmetry-breaking perturbation previously considered by Gromes and Stamatescu in the context of explicit wave-function calculations. A new algebraic mass formula for the $N=2\mathrm{}$ multiplets of the model is derived.