Determination of Asymptotic Parameters in the Statistical Bootstrap Model

Abstract

The statistical bootstrap model predicts that the density of hadron states ρ(m) approaches cmaebm asymptotically. We consider the consequences of extending the bootstrap condition in the model from asymptotic down to finite masses. This allows us to determine the parameters a, b, and c for various assignments of the hadron volume and low-mass input spectrum, and for the extreme cases of excluding all exotic particles or including all of them. In all cases, a=-3 for ρtot (summed over all internal quantum numbers). The parameter b varies somewhat from case to case but is always of order mπ^-1; thus we predict the maximum temperature T0=b^-1≈mπ in rough agreement with Hagedorn's empirical determination. The inclusion of exotic states has little effect on ρtot but does redistribute the partial level densities according to a simple rule. The predicted level densities (excluding exotic states) are compared with present data.