https://doi.org/10.1140/epjc/s10052-019-6566-1
Regular Article - Theoretical Physics
Phenomenology of relativistic 
reaction amplitudes within the isobar approximation
1
Center for Exploration of Energy and Matter, Indiana University, Bloomington, IN, 47403, USA
2
Physics Department, Indiana University, Bloomington, IN, 47405, USA
3
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, 04510, Mexico City, Mexico
4
Theory Center, Thomas Jefferson National Accelerator Facility, Newport News, VA, 23606, USA
5
Helmholtz-Institut für Strahlen- und Kernphysik, Universität Bonn, 53115, Bonn, Germany
6
Department of Physics and Astronomy, Ghent University, Ghent, Belgium
7
European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*) and Fondazione Bruno Kessler, 38123, Villazzano, TN, Italy
8
California State University, Bakersfield, CA, 93311, USA
* e-mail: ajackura@iu.edu
Received:
6
November
2018
Accepted:
20
December
2018
Published online:
22
January
2019
Further progress in hadron spectroscopy necessitates the phenomenological description of three particle reactions. We consider the isobar approximation, where the connected part of the amplitude is first expressed as a sum over initial and final pairs, and then expanded into a truncated partial wave series. The resulting unitarity equation is automatically fulfilled by the B-matrix solution, which is an integral equation for the partial wave amplitudes, analogous to the K-matrix parameterization used to describe 
amplitudes. We study the one particle exchange and how its analytic structure impacts rescattering solutions such as the triangle diagram. The analytic structure is compared to other parameterizations discussed in the literature. We briefly discuss the analogies with recent formalisms for extracting scattering amplitudes in lattice QCD.
© The Author(s), 2019
