Spin-averaged mass formulas and the mass spectrum of low lying Δ-resonances in harmonic-oscillator-like quark models

Abstract

By spin-averaging the masses of one species of particle over a sufficient number of multiplets we argue that the resulting spin-averaged mass is insensitive to mass operators which are not spin-scalar. This approach may be applied to averaging over quantum numbers other than spin. We discuss the assumptions necessary to restricting the average to only relatively few multiplets and show how mass formulas between averaged masses may be constructed. This approach reduces the number of parameters and predicts patterns of splittings which should be common to many analyses. We apply our results to the low lying Δ-resonances in harmonic-oscillator-like models and examine the comparison of theory with experiment for four different assumptions about which states should be included in particular averages. Using data from experiment we find that the prediction for the spin-averaged mass of the Δ-resonances from (56,1 ⁻₃ ) is, on average, 150 MeV higher than the spin-averaged mass of the experimental Δ states plausibly assigned to the (56,1 ⁻₃ ). This result is insensitive to which of the assumptions is made. Some suggestions are made about rectifying this discrepancy.