Unitary states for three pions

Journal Article · Tue Jul 01 04:00:00 EDT 1975 · Phys. Rev., D, v. 12, no. 1, pp. 43-58

DOI:https://doi.org/10.1103/PhysRevD.12.43· OSTI ID:4169002

Ascoli, G; Wyld, H W

Recent angular momentum analyses of the three-pion system produced in the reaction $pi$$sup -$p $Yields$ $pi$$sup -$$pi$$sup +$$pi$$sup -$p have been criticized because the three-pion states used in the analysis do not satisfy unitarity. In order to answer this criticism we develop a set of unitarity equations which can be solved to yield a set of three-pion states which explicitly satisfy both three-particle unitarity and two-particle unitarity (Watson's theorem). A numerical method for solving the equations is given. When the unitary states are used to reanalyze the data for the reaction $pi$$sup -$p $Yields$ $pi$$sup -$$pi$$sup +$$pi$$sup -$p we find some changes in the detailed numerical fits but no change in the general conclusions. In particular, the phase of the amplitude for the A$sub 1$ state varies only slightly in the A$sub 1$ mass region, in contrast with the behavior expected for a resonant state.

• Research Organization: Department of Physics, University of Illinois, Urbana, Illinois 61801
• Sponsoring Organization: USDOE
• NSA Number: NSA-33-002021
• OSTI ID: 4169002
• Journal Information: Phys. Rev., D, v. 12, no. 1, pp. 43-58, Journal Name: Phys. Rev., D, v. 12, no. 1, pp. 43-58; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

*PION-PROTON INTERACTIONS-- UNITARITY
641106*
A1-1070 RESONANCES
MATRIX ELEMENTS
N64260* --Physics (High Energy)--Particle Interactions & Properties (Theoretical)--Strong (Baryon No. = 1)
PARTICLE DECAY
PARTICLE PRODUCTION
PIONS MINUS
PIONS PLUS
PROTONS
S MATRIX
SCATTERING AMPLITUDES