Partial-wave projection of relativistic three-body amplitudes

Briceño, Raúl A.; Costa, Caroline S. R.; Jackura, Andrew W.

doi:10.1103/PhysRevD.111.036029

Title: Partial-wave projection of relativistic three-body amplitudes

Journal Article · 21 February 2025 · Physical Review D

DOI: https://doi.org/10.1103/PhysRevD.111.036029 · OSTI ID:2522126

Briceño, Raúl A. ^[1]; Costa, Caroline S. R. ^[2];

^[3]

University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
William & Mary, Williamsburg, VA (United States)

We derive the integral equations for partial-wave projected three-body scattering amplitudes, starting from the integral equations for three-body amplitudes developed for lattice QCD analyses. The results, which hold for generic three-body systems of spinless particles, build upon the recently derived partial-wave projected one-particle exchange, a primary component of the relativistic framework proven to satisfy 𝑆 matrix unitarity. We derive simplified expressions for factorizable short-distance interactions, 𝒦₃, in two equivalent formalisms—one symmetric under particle interchange and one asymmetric. For the asymmetric case, we offer parametrizations useful for amplitude analysis. Finally, we examine toy models for 3⁢𝜋 systems at unphysically heavy pion masses with total isospins 0, 1, and 2.

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Research Organization:: Indiana University, Bloomington, IN (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: AC02-05CH11231; AC05-06OR23177; SC0019229; SC0023598

OSTI ID:: 2522126

Report Number(s):: DOE/OR/23177--7690; JLAB-THY--24-4199

Journal Information:: Physical Review D, Journal Name: Physical Review D Journal Issue: 3 Vol. 111; ISSN 2470-0010; ISSN 2470-0029

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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71 CLASSICAL AND QUANTUM MECHANICS
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Title: Partial-wave projection of relativistic three-body amplitudes

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