Phenomenology of relativistic $$\mathbf {3}\rightarrow \mathbf {3}$$ reaction amplitudes within the isobar approximation

Jackura, A.; Fernández-Ramírez, C.; Mathieu, V.; Mikhasenko, M.; Nys, J.; Pilloni, A.; Saldaña, K.; Sherrill, N.; Szczepaniak, A. P.

doi:10.1140/epjc/s10052-019-6566-1

Title: Phenomenology of relativistic $$$$\mathbf {3}\rightarrow \mathbf {3}$$$$ reaction amplitudes within the isobar approximation

Journal Article · Tue Jan 22 00:00:00 EST 2019 · European Physical Journal. C, Particles and Fields

DOI:https://doi.org/10.1140/epjc/s10052-019-6566-1· OSTI ID:1619890

Jackura, A.; Fernández-Ramírez, C.; Mathieu, V.; Mikhasenko, M.; Nys, J.; Pilloni, A.; Saldaña, K.; Sherrill, N.; Szczepaniak, A. P.

Further progress in hadron spectroscopy necessitates the phenomenological description of three particle reactions. We consider the isobar approximation, where the connected part of the $$\mathbf{3}\to\mathbf{3}$$ 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 $$\mathbf{2}\to\mathbf{2}$$ 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 $$\mathbf{3}\to\mathbf{3}$$ scattering amplitudes in lattice QCD.

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Research Organization:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Contributing Organization:: Joint Physics Analysis Center

Grant/Contract Number:: AC05-06OR23177; FG02- 87ER40365; IA101717; IA101819; PHY-1415459; 251817; FG02-87ER40365

OSTI ID:: 1619890

Alternate ID(s):: OSTI ID: 1574436

Report Number(s):: JLAB-THY-18-2817; DOE/OR/23177-4550; arXiv:1809.10523; 56; PII: 6566

Journal Information:: European Physical Journal. C, Particles and Fields, Journal Name: European Physical Journal. C, Particles and Fields Vol. 79 Journal Issue: 1; ISSN 1434-6044

Publisher:: Springer Science + Business MediaCopyright Statement

Country of Publication:: Germany

Language:: English

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Cited by: 26 works

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