Bootstrap equations for fireball decay

Abstract

We study various bootstrap equations which describe successive decay of fireballs. These equations are generalizations of the original statistical bootstrap equation of Hagedorn and of Frautschi. In particular, we investigate the average pion multiplicity as a function of the fireball mass for various kernels, and the constraint due to the conservation of energy on the correlation parameter ƒ 2 = 〈n(n−1)〉−〈n〉 2 . This latter constraint tends to give rise to a negative ƒ 2 . We also derive the pion energy distribution for a constant kernel model. An exponential fall off in this distribution is found in the small energy region. Lastly, we present a bootstrap equation which includes both the π and the ϱ as the ground states. A possible connection between this model and the slope of the 〈 n 0〉 -; versus n -; data is given.