Statistical Bootstrap Model of Hadrons with Spin

Abstract

We formulate the statistical bootstrap model of hadrons so that it includes angular momentum. Several types of solutions that the bootstrap admits are studied. One self-consistent solution, which has a strong physical motivation founded within the model, has a spin ($J$) distribution of resonances at mass $m$ in which most resonances occur below a $J$ proportional to $\sqrt{m}$, the constant of proportionality being bounded by the other parameters of the model. There is then a whole set of solutions, that have $J$ proportional to ${\left(\sqrt{m}\right)}^{\gamma }$, where $\gamma$ lies between 0 and 1. This set of solutions cannot be excluded within the accuracy to which we can work. We also find a third class of solutions, very similar to the resonance spin spectrum of the Veneziano model, in which most resonances occur below a spin proportional to $m$. Finally, we have discovered a second solution to the bootstrap of the total level density.