Dynamical fit to low-energyπ−Nphase shifts and determination of the threshold parameters
- 1 July 1977
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 16 (1), 85-93
- https://doi.org/10.1103/physrevd.16.85
Abstract
For the description of low-energy scattering, [1/1] Padé approximants have had limited success starting from Lagrangian-induced power series. We have shown elsewhere that, from a formal power series whose generating kernel can in principle be approximated by a kernel of finite rank , we can construct a democratic approximant with perturbative terms which provides as good an approximation to the true solution as a Padé approximant [] with perturbative terms. Here we use the two available orders of perturbative terms and of the Lagrangian to construct a democratic approximant . We apply it to the low-energy phase-shift analysis of Carter, Bugg, and Carter and show empirically that a reasonably good fit can be obtained in the low-energy region with the two available orders of perturbative terms. Extrapolating this fit to threshold we determine scattering lengths and effective ranges for and waves which are in reasonably good agreement with more conventional dispersion-relation determinations. The method indicates how the concept of Lagrangian can be made dynamically relevant in a strong-interaction context.
Keywords
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