New relations for two-body reactions from inclusive finite-mass sum rules

Abstract

Finite-mass sum rule and duality considerations for the inclusive process ab→cX lead to a number of interesting relations amongst the quasi-two-body cross sections ab→cd i , where d i denotes the prominent resonances in the missing-mass channel. The processes π( K )N → NX are studied in detail, and the main results are the following: 1. (i) A superconvergence relation for reggeon (ϱ)-particle (π) scattering gives a sum rule connecting the ϱ-exchange cross sections (d σ /d t ) [ π − p→( gp °, ω , A 2 0 )n]. 2. (ii) Semi local duality considerations in reggeon-particle scattering relate the resonance production cross section ( d σ/ d t) [π( K )N → N d i ] to the resonance mass in terms of the trajectory α ( t ) of the exchangedreggeon. From this the two following corollaries follow: 3. (iii) The ratio of π to (f-ω) exchange contributions increases linearly with the resonance (mass) 2 . 4. (iv) The resonance production cross sections get less peripheral with increasing resonance mass. All the above predictions agree reasonably with the available data on mesonic resonance production.