A truncated statistical bootstrap equation

Abstract

An extension of the thermodynamic bootstrap model in which the volume parameter depends on the number of subfireballs N is proposed. Based on the conventional threepoint resonance coupling, we suggest as a first approximation that N ⩾ 3 terms should be dropped. One can then describe the many-particle system in terms of two-body interaction dynamics. Three kernels for the bootstrap integral equation are considered, with an analytic solution presented for one of them. Properties of the fireball deduced from our truncated equation are presented. Most properties are insensitive to the kernel used. The observed average pion multiplicity in p p annihilation at rest is reproduced with the two-body interaction ranger r = 1.22 λ π . The dependence of the average pion mulplicity on the fireball mass m is given by ( n π ) ≈ 2.0 m + 0.62. This slope agrees with the empirical value found in the Nova model. For a fireball with mass less than 2 GeV/ c, the truncated equation predicts that over 50% of the events have successive emission of pions at each step along the decay chain. This provides some justification for the random-walk assumption for Nova decay. The momentum distribution of pions, neglecting the fireball recoil effect, in the small- p region has the form d σ/d p 2 ≈ exp(− p 2/ K 2) with K ≈ 0.23 GeV. Finally with the duality coupling scheme, fireballs are associated with exotic states dual to the cross-channel exchange. The weak version of the strong central absorption prescription for two-body scattering is in accord with this scheme. This scheme also explains the presence of the Ericson fluctuations in the non-exotic elastic differential cross sections, but not in the exotic ones.