Inequalities for the s and pWave ππ PartialWave Amplitudes
Abstract
An infinite number of inequalities are derived for integrals over the s and pwave ππ amplitudes in the interval 0<=s<=4m_{π}^{2} in terms of the ππ total cross sections and other experimentally accessible data. The main ingredients in the derivations are corssing symmetry, the positivity of the even l>=2 partial waves of the reactions π^{0}π^{0}>π^{0}π^{0} and π^{0}π^{0}>π^{+}π^{} in the interval 0<=s<=4m_{π}^{2}, and some known bounds on the crossedchannel absorptive parts of these reactions. It is shown that if the partialwave sum over any subset of π^{0}π^{0}>π^{0}π^{0} partial waves is itself invariant under permutations of s, t, and u, and this subset contains the s wave, then the entire π^{0}π^{0}>π^{0}π^{0} amplitude has to vanish identically. (Actually, a somewhat stronger result is proved for the amplitudes of both the processes π^{0}π^{0}>π^{0}π^{0} and π^{0}π^{0}>π^{+}π^{} or for any linear combination of these amplitudes with positive coefficients.)
 Publication:

Physical Review D
 Pub Date:
 June 1971
 DOI:
 10.1103/PhysRevD.3.3133
 Bibcode:
 1971PhRvD...3.3133B