In Section 6.2.4 we used (6.36) to derive the masses of the Πand Σ baryons in Table 6.9. Derive the mass formulas for the

In Section 6.2.4 we used (6.36) to derive the masses of the Λ and Σ^ˆ—baryons in Table 6.9. Derive the mass formulas for the remaining baryons listed in this table.

²⁵These analyses also determine the mean square radii 

of the various states, where the wavefunctions are determined by the solutions of the Schr¨odinger equation for successful potentials like (6.66) and (6.67). The resulting values of r₀ for the various states shown in Figure 6.10 span just the range (6.68) in which the potential is well-determined.

Figure 6.10

Table 6.9 Baryon masses (in GeV/c) in the approximation (6.36) compared with experimental values. These have been obtained using m = 0.362 GeV/, m, = 0.539 GeV/c and b= 0.0256 (GeV/c). Particle Mass Prediction Experiment 3b 0.94 0.939 4m2 36 2m + ms 1.12 1.116 4m2 2m + m, + 4 1.193 1.18 m, + 2m, + 4 1.32 1.318 m, 36 + 4m? 1.23 1.232 2m + ms 2 1.38 1.385 m2 m, + 2m, + 1.53 1.533 ? 36 , + 4m? 1.68 1.673 [1] in /- p? Ieb(r)/ dr ri = 72