Statistical treatment of the average resonance width

Abstract

Saturation of hadron scattering amplitudes by direct channel resonances implies that the average level width Γ( m), level density ϱ( m), and number of open channels N( m) are related by Γ( m) ϱ( m) = N( m)/2 π. From this relation and the dependence of N on ϱ there results, for any given ϱ( m), a definite Γ( m). We find that: 1. (i) A power law growth ϱ( m) ∼ m a results in an experimentally disfavored exponential growth of Γ( m). 2. (ii) The exponentially growing ϱ( m) of the statistical bootstrap model results in Γ( m) → constant. 3. (iii) The forms of ϱ( m) suggested by various versions of the dual resonance model result in Γ( m) → constant, or decreasing to zero, or at most a power law increase. Arguments are given why Γ( m) → constant is the most physically reasonable choice. Studies of Ericson fluctuations in reactions such as elastic πN scattering at a few GeV offer the best hope of experimentally determining the behavior of Γ( m).