Δ-Baryon axialvector and pseudoscalar form factors, and associated PCAC relations

• Published in: The European physical journal. A, Hadrons and nuclei Vol. 59; no. 7
• Main Authors: Yin, Pei-Lin, Chen, Chen, Fischer, Christian S., Roberts, Craig D.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 18.07.2023
• Subjects: Hadrons; Heavy Ions; Nuclear Fusion; Nuclear Physics; Particle and Nuclear Physics; Physics; Physics and Astronomy; Regular Article - Theoretical Physics
• ISSN: 1434-601X
• DOI: 10.1140/epja/s10050-023-01066-9

A quark + diquark Faddeev equation treatment of the baryon bound state problem in Poincaré-invariant quantum field theory is used to deliver parameter-free predictions for all six Δ -baryon elastic weak form factors. Amongst the results, it is worth highlighting that there are two distinct classes of such Δ -baryon form factors, ( g 1 , g 3 , G π Δ Δ ) , ( h 1 , h 3 , H π Δ Δ ) , the functions within each of which are separately linked via partial conservation of axial current (PCAC) and Goldberger-Treiman (GT) relations. Respectively within each class, the listed form factors possess qualitatively the same structural features as the nucleon axial, induced pseudoscalar, and pion-nucleon coupling form factors. For instance, the Δ -baryon g 1 axial form factor can reliably be approximated by a dipole function, characterised by an axial charge g A Δ + = 0.71 ( 9 ) and mass-scale m A Δ = 0.95 ( 2 ) m Δ . Moreover, the two distinct Δ -baryon PCAC form factor relations are satisfied to a high degree of accuracy on a large range of Q 2 ; the associated GT relations present good approximations only on Q 2 / m Δ 2 ≃ 0 ; and pion pole dominance approximations are reliable within both classes. There are two π Δ Δ couplings: g π Δ Δ = 10.46 ( 1.88 ) ; h π Δ Δ = 35.73 ( 3.75 ) ; and the associated form factors are soft. Such couplings commonly arise in phenomenology, which may therefore benefit from our analyses. A flavour decomposition of the axial charges reveals that quarks carry 71% of the Δ -baryon spin. The analogous result for the proton is ≈ 65 %.