Rigorous Absolute Bounds for Pion Pion Scattering. 1. Solving a First Extremum Problem

Auberson, G.; Epele, L.; Mahoux, G.; Simao, F.R.A.

doi:10.1016/0550-3213(74)90022-4

Rigorous Absolute Bounds for Pion Pion Scattering. 1. Solving a First Extremum Problem

Feb, 1974

25 pages

Published in:

Nucl.Phys.B 73 (1974) 314-338

Published: 1974

DOI:

10.1016/0550-3213(74)90022-4

Report number:

SACLAY-DPh-T/73-89

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Abstract: (Elsevier)

This paper is the first of a series of three where we reconsider the derivation of rigorous absolute bounds for strong interactions. It is devoted to the solution of a preliminary extremum problem. From the knowledge, at a given physical energy s and unphysical angle cos θ 0 > 1, of the absorptive part A ( s , cos θ 0 ) of the elastic scattering amplitude for two spinless particles, we find, by exploiting the unitarity condition, the least upper bound of the modulus | F ( s , cos θ 1 )| of the scattering amplitude for the same energy s and various angles θ 1 . Upper (but not least upper) bounds given by previous authors are numerically compared with ours.

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