Khuri-Treiman equations for $\pi\pi$ scattering

JPAC Collaboration; M. Albaladejo; N. Sherrill; C. Fernandez-Ramirez; A. Jackura; V. Mathieu; M. Mikhasenko; J. Nys; A. Pilloni; A. P. Szczepaniak

arXiv · 1803.06027

Khuri-Treiman equations for $\pi\pi$ scattering

JPAC Collaboration·M. Albaladejo·N. Sherrill·C. Fernandez-Ramirez·A. Jackura·V. Mathieu·M. Mikhasenko·J. Nys·A. Pilloni·A. P. Szczepaniak

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Abstract

The Khuri-Treiman formalism models the partial-wave expansion of a scattering amplitude as a sum of three individual truncated series, capturing the low-energy dynamics of the direct and cross channels. We cast this formalism into dispersive equations to study $\pi\pi$ scattering, and compare their expressions and numerical output to the Roy and GKPY equations. We prove that the Khuri-Treiman equations and Roy equations coincide when both are truncated to include only $S$- and $P$-waves. When higher partial waves are included, we find an excellent agreement between the Khuri-Treiman and the GKPY results. This lends credence to the notion that the Khuri-Treiman formalism is a reliable low-energy tool for studying hadronic reaction amplitudes.

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JPAC Collaboration, M. Albaladejo, N. Sherrill, C. Fernandez-Ramirez, A. Jackura, V. Mathieu, M. Mikhasenko, J. Nys, A. Pilloni, A. P. Szczepaniak. 2018-03-15. Khuri-Treiman equations for $\pi\pi$ scattering. https://arxiv.org/abs/1803.06027

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