Explaining the universal Hagedorn temperature in string models of hadrons with fixed endpoints or baryon junctions

We derive the mass formulas and more accurate asymptotic expressions for the densities of states for string models of hadrons with one fixed heavy endpoint or a baryon junction. We show that strings with one fixed endpoint have the same Hagedorn temperature as ordinary open strings at the same tension and number of polarizations, despite the different Regge slopes of heavy-light and light mesons. This provides a microscopic explanation for the universality of the Hagedorn temperature recently found phenomenologically. We also find that the baryon-junction and quark-diquark pictures share this Hagedorn temperature and yield the same asymptotic mass dependence of the density of states, differing only by an overall normalization. The observed baryon mass spectrum provides little discrimination between the two pictures, although the baryon-junction model has a larger discrepancy with the observed Regge slopes.