Abstract
In this talk, we present a coupled system of integral equations for the πN → πN (s-channel) and ππ → N̅N (t-channel) lowest partial waves, derived from Roy–Steiner equations for pion–nucleon scattering. After giving a brief overview of this system of equations, we present the solution of the t-channel sub-problem by means of Muskhelishvili–Omnès techniques, and solve the s-channel sub-problem after finding a set of phase shifts and subthreshold parameters which satisfy the Roy–Steiner equations.
Highlights
A precise determination of the pion–nucleon ( N ) scattering amplitude is relevant for different aspects of nuclear and particle physics
After giving a brief overview of this system of equations, we present the solution of the t-channel sub-problem by means of Muskhelishvili–Omnès techniques, and solve the s-channel sub-problem after finding a set of phase shifts and subthreshold parameters which satisfy the Roy–Steiner equations
Roy–Steiner (RS) equations [5] solve this problem by combining the s- and t- channel physical region by means of hyperbolic dispersion relations (HDRs)
Summary
A precise determination of the pion–nucleon ( N ) scattering amplitude is relevant for different aspects of nuclear and particle physics. Despite numerous investigations performed, the N scattering amplitude is still not known to sufficient precision in the low-energy region. This is striking in the scalar-isoscalar sector, where the determination of the pion–nucleon -term is still far from satisfactory. Dispersion relations have repeatedly proven to be a powerful tool for studying processes at low energies with high precision [1,2,3,4]. They are built upon very general principles such as Lorentz invariance, unitarity, crossing symmetry, and analyticity. In the case of N scattering, a full system of PWDRs has to include dispersion relations for two distinct physical processes, N → N (s-channel) and → N N (t-channel), and the use of s ↔ t crossing symmetry will intertwine s- and t-channel equations
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