Khuri-Treiman equations for 3$$π$$ decays of particles with spin

Journal Article · 13 March 2020 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.101.054018 · OSTI ID:1604504

Albaladejo, M.; Winney, D.; Danilkin, I. V.; Fernández-Ramírez, C.; Mathieu, V.; Mikhasenko, M.; Pilloni, A.; Silva-Castro, J. A.; Szczepaniak, A. P.

Khuri-Treiman equations have proven to be a useful theoretical tool in the analysis of three-body decays, especially into the 3$$π$$ final state. In this work we present in full detail the necessary generalization of the formalism to study the decays of particles with arbitrary spin, parity, and charge conjugation. To this extent, we find it most convenient to work with helicity amplitudes instead of the so-called invariant amplitudes, especially when dealing with the unitarity relations. The isobar expansions in the three possible (s-, t-, and u-) final channels are related with the appropriate crossing matrices. We pay special attention to the kinematical singularities and constraints of the helicity amplitudes, showing that these can be derived by means of the crossing matrix.

• Research Organization: Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
• Sponsoring Organization: Comunidad Autónoma de Madrid; Consejo Nacional de Ciencia y Tecnología (CONACYT); Deutsche Forschungsgemeinschaft (DFG); German Excellence Strategy; Ministerio de Ciencia, Innovación y Universidades (Spain); National Autonomous University of Mexico (UNAM); National Science Foundation (NSF); USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
• Contributing Organization: JPAC Collaboration
• Grant/Contract Number: AC05-06OR23177; FG02-87ER40365
• OSTI ID: 1604504
• Report Number(s): DOE/OR/23177--4788; JLAB-THY--19-3066; 054018
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 5 Vol. 101; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English