Khuri–Treiman equations for $$\pi \pi $$ ππ scattering

• Main Authors: M. Albaladejo, N. Sherrill, C. Fernández-Ramírez, A. Jackura, V. Mathieu, M. Mikhasenko, J. Nys, A. Pilloni, A. P. Szczepaniak, Joint Physics Analysis Center
• Format: Article
• Language: English
• Published: SpringerOpen 2018-07-01
• Series: European Physical Journal C: Particles and Fields
• Online Access: http://link.springer.com/article/10.1140/epjc/s10052-018-6045-0

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 $$\pi \pi $$ ππ 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.