Different versions of soft-photon theorems exemplified at leading and next-to-leading terms for pion-pion and pion-proton scattering

• Verfasst von: Lebiedowicz, Piotr [VerfasserIn]
• Verfasst von: Nachtmann, Otto [VerfasserIn]
• Verfasst von: Szczurek, Antoni [VerfasserIn]
• Titel: Different versions of soft-photon theorems exemplified at leading and next-to-leading terms for pion-pion and pion-proton scattering
• Verf.angabe: Piotr Lebiedowicz, Otto Nachtmann, and Antoni Szczurek
• E-Jahr: 2024
• Jahr: 29 May 2024
• Umfang: 18 S.
• Illustrationen: Illustrationen
• Fussnoten: Gesehen am 23.01.2025
• Titel Quelle: Enthalten in: Physical review
• Ort Quelle: Ridge, NY : American Physical Society, 2016
• Jahr Quelle: 2024
• Band/Heft Quelle: 109(2024), 9, Artikel-ID 094042, Seite 094042-1-094042-18
• ISSN Quelle: 2470-0029
• DOI: doi:10.1103/PhysRevD.109.094042
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1915492149

Abstract

We investigate the photon emission in pion-pion and pion-proton scattering in the soft-photon limit where the photon energy ???? →0. The expansions of the ????−⁢????0 →????−⁢????0⁢???? and the ????±⁢???? →????±⁢????⁢???? amplitudes, satisfying the energy-momentum relations, to the orders ????−1 and ????0 are derived. We show that these terms can be expressed completely in terms of the on-shell amplitudes for ????−⁢????0 →????−⁢????0 and ????±⁢???? →????±⁢????, respectively, and their partial derivatives with respect to ???? and ????. The structure term which is nonsingular for ???? →0 is determined to the order ????0 from the gauge-invariance constraint using the generalized Ward identities for pions and the proton. For the reaction ????−⁢????0 →????−⁢????0⁢???? we discuss in detail the soft-photon theorems in the versions of both Low and Weinberg. We show that these two versions are different and must not be confounded. Weinberg’s version gives the pole term of a Laurent expansion in ???? of the amplitude for ????−⁢????0 →????−⁢????0⁢???? around the phase-space point of zero radiation. Low’s version gives an approximate expression for the above amplitude at a fixed phase-space point, corresponding to nonzero radiation. Clearly, the leading and next-to-leading terms in theses two approaches must be, and are indeed, different. We show their relation. We also discuss the expansions of differential cross sections for ????−⁢????0 →????−⁢????0⁢???? with respect to ???? for ???? →0.