Multiple solutions of the Roy equations: N/D method on a finite interval

Journal Article · Thu Sep 15 04:00:00 EDT 1977 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.16.1948· OSTI ID:5350131

Atkinson, D; Warnock, R L

The Roy equations, combined with unitarity, can be regarded as a system of integral equations for the ..pi..-..pi.. scattering amplitude in a finite energy region. Even when the partial-wave absorptive parts above this finite range are prescribed, and the two S-wave scattering-length parameters are held fixed, the singular equations have multiple solutions, some of which could be missed in a direct numerical study. We regularize the system by a modified N/D method, in which the full manifold of solutions is parametrized explicitly. If delta (s/sub 0/) is the phase shift of a particular wave at the cutoff point, then that wave carries a number of arbitrary, real parameters equal to the integer part of 2delta (s/sub 0/)/..pi.., provided delta (s/sub 0/) > or = - ..pi../2. We suggest that the N/D formulation is appropriate for applications of the Roy equations.

• Research Organization: University of Groningen, Groningen, Netherlands
• OSTI ID: 5350131
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 16:6; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645205* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Strong Interactions
Baryon No. = 0-- (-1987)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
EQUATIONS
HADRON-HADRON INTERACTIONS
INTEGRAL EQUATIONS
INTERACTIONS
MESON-MESON INTERACTIONS
MULTIPLICITY
N-D METHOD
PARTIAL WAVES
PARTICLE INTERACTIONS
PHASE SHIFT
PION-PION INTERACTIONS
S WAVES
SCATTERING AMPLITUDES
UNITARITY