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

D. Atkinson, R. L. Warnock

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The Roy equations, combined with unitarity, can be regarded as a system of integral equations for the π-π 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 ND method, in which the full manifold of solutions is parametrized explicitly. If δ(s0) is the phase shift of a particular wave at the eutoff point, then that wave carries a number of arbitrary, real parameters equal to the integer part of 2δ(s0)π, provided δ(s0)≥−π2. We suggest that the ND formulation is appropriate for applications of the Roy equations.
Original languageEnglish
Pages (from-to)1948-1961
Number of pages14
JournalPhysical Review D
Issue number6
Publication statusPublished - 15-Sep-1977

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