Phenomenology of relativistic $$$$\mathbf {3}\rightarrow \mathbf {3}$$$$ reaction amplitudes within the isobar approximation
Abstract
Further progress in hadron spectroscopy necessitates the phenomenological description of three particle reactions. We consider the isobar approximation, where the connected part of the $$\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}$$ scattering amplitudes in lattice QCD.
- Authors:
- Publication Date:
- Research Org.:
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- Contributing Org.:
- Joint Physics Analysis Center
- OSTI Identifier:
- 1619890
- Alternate Identifier(s):
- OSTI ID: 1574436
- Report Number(s):
- JLAB-THY-18-2817; DOE/OR/23177-4550; arXiv:1809.10523
Journal ID: ISSN 1434-6044; 56; PII: 6566
- Grant/Contract Number:
- AC05-06OR23177; FG02- 87ER40365; IA101717; IA101819; PHY-1415459; 251817; FG02-87ER40365
- Resource Type:
- Published Article
- Journal Name:
- European Physical Journal. C, Particles and Fields
- Additional Journal Information:
- Journal Name: European Physical Journal. C, Particles and Fields Journal Volume: 79 Journal Issue: 1; Journal ID: ISSN 1434-6044
- Publisher:
- Springer Science + Business Media
- Country of Publication:
- Germany
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Joint Physics Analysis Center, Jackura, A., Fernández-Ramírez, C., Mathieu, V., Mikhasenko, M., Nys, J., Pilloni, A., Saldaña, K., Sherrill, N., and Szczepaniak, A. P. Phenomenology of relativistic $$\mathbf {3}\rightarrow \mathbf {3}$$ reaction amplitudes within the isobar approximation. Germany: N. p., 2019.
Web. doi:10.1140/epjc/s10052-019-6566-1.
Joint Physics Analysis Center, Jackura, A., Fernández-Ramírez, C., Mathieu, V., Mikhasenko, M., Nys, J., Pilloni, A., Saldaña, K., Sherrill, N., & Szczepaniak, A. P. Phenomenology of relativistic $$\mathbf {3}\rightarrow \mathbf {3}$$ reaction amplitudes within the isobar approximation. Germany. https://doi.org/10.1140/epjc/s10052-019-6566-1
Joint Physics Analysis Center, Jackura, A., Fernández-Ramírez, C., Mathieu, V., Mikhasenko, M., Nys, J., Pilloni, A., Saldaña, K., Sherrill, N., and Szczepaniak, A. P. Tue .
"Phenomenology of relativistic $$\mathbf {3}\rightarrow \mathbf {3}$$ reaction amplitudes within the isobar approximation". Germany. https://doi.org/10.1140/epjc/s10052-019-6566-1.
@article{osti_1619890,
title = {Phenomenology of relativistic $$\mathbf {3}\rightarrow \mathbf {3}$$ reaction amplitudes within the isobar approximation},
author = {Joint Physics Analysis Center and Jackura, A. and Fernández-Ramírez, C. and Mathieu, V. and Mikhasenko, M. and Nys, J. and Pilloni, A. and Saldaña, K. and Sherrill, N. and Szczepaniak, A. P.},
abstractNote = {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.},
doi = {10.1140/epjc/s10052-019-6566-1},
journal = {European Physical Journal. C, Particles and Fields},
number = 1,
volume = 79,
place = {Germany},
year = {Tue Jan 22 00:00:00 EST 2019},
month = {Tue Jan 22 00:00:00 EST 2019}
}
https://doi.org/10.1140/epjc/s10052-019-6566-1
Web of Science
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