Asymptotic mass spectrum and thermodynamics of the Abelian bag model

Abstract

A statistical evaluation of the mass spectrum in the bag model is made using the microcanonical ensemble. The mass spectrum behaves asymptotically as $\ensuremath{\rho}(m)\ensuremath{\sim}c{m}^{\ensuremath{-}3}\mathrm{exp}(\frac{m}{{T}_{0}})$, where $c$ and ${T}_{0}$ depend on the bag constant, on the number of degrees of freedom of massless elementary fields in the bag, and on whether those fields obey Bose-Einstein, Fermi-Dirac, or Maxwell-Boltzmann statistics. Hence this model satisfies the strong bootstrap condition. The case of eight elementary Abelian vector fields is focused on. The thermodynamics of a system of such composite hadrons naively exhibits a maximum temperature ${T}_{0}$. However, due to the finite size of hadrons, many-body effects cause the mass spectrum to have a density-dependent cutoff. A first-order phase transition to a gas of free elementary fields is found at a temperature ${T}_{c}=1.05{T}_{0}$.