Direct solution of Minkowski-space Bethe-Salpeter equation in the massive Wick-Cutkosky model

Journal Article · 19 February 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/physrevd.109.036020 · OSTI ID:2309765

Jia, Shaoyang  ^[1]

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1. Argonne National Laboratory (ANL), Argonne, IL (United States); Argonne National Laboratory

Here in order to solve the Bethe-Salpeter equation (BSE) in the Minkowski space, we first introduce the Nakanishi integral representations of the Bethe-Salpeter amplitude and the Bethe-Salpeter wave function. We then derive the explicit integral equations for the corresponding spectral functions from the BSE for states of two scalar particles bound by a scalar-particle exchange interaction, where the propagators of constituents are allowed to be fully dressed. These integral equations are subsequently solved numerically in the variation of the Wick-Cutkosky model with massive exchange particles, where an algorithm of adaptive mash grid is proposed. The equations and algorithm we develop here serve as the foundation of Minkowski-space formulation of BSE for bound states of fermions.

• Research Organization: Argonne National Laboratory (ANL), Argonne, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Nuclear Physics (NP)
• Grant/Contract Number: AC02-06CH11357
• OSTI ID: 2309765
• Alternate ID(s): OSTI ID: 2474231; OSTI ID: 2529447
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 3 Vol. 109; ISSN 2470-0010
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English