Pion electroproduction, PCAC, chiral Ward identities, and the axial form factor revisited

Abstract

We re-investigate Adler's PCAC relation in the presence of an external electromagnetic field within the framework of QCD coupled to external fields. We discuss pion electroproduction within a tree-level approximation to chiral perturbation theory and explicitly verify a chiral Ward identity referred to as the Adler-Gilman relation. We critically examine soft-momentum techniques and point out how inadmissable approximations may lead to results incompatible with chiral symmetry. As a result we confirm that threshold pion electroproduction is indeed a tool to obtain information on the axial form factor of the nucleon.

33 pages, RevTex, 9 figures

References in corpus (4)

• Axial structure of the nucleon
• Hadron structure and the limitations of phenomenological models in electromagnetic reactions
• On the pion electroproduction amplitude
• Comment about pion electro-production and the axial form factors

Cited by in corpus (16)

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• Nucleon axial and pseudoscalar form factors from lattice QCD at the physical point
• Solving the PCAC puzzle for nucleon axial and pseudoscalar form factors
• Chiral Perturbation Theory: Introduction and Recent Results in the One-Nucleon Sector
• Nucleon Form Factors of the Isovector Axial-Vector Current: Situation of Experiments and Theory
• Nucleon axial-vector and pseudoscalar form factors, and PCAC relations
• Testing axial and electromagnetic nucleon form factors in time-like regions in the processes $\bar{p}+n\to {\pi }^{-}+{\ell }^{-}+{\ell }^{+}$ and $\bar{p}+p\to {\pi }^0+{\ell }^{-}+{\ell }^{+}$, $\ell =e$, $\mu$
• Chiral perturbation theory - Success and challenge
• Baryon chiral perturbation theory
• The pseudo scalar form factor of the nucleon, the sigma-like term, and the $L_0^{+}$ amplitude for charged pion electro-production near threshold
• Recent developments in effective field theory
• The axial-vector form factor of the nucleon in a finite box
• Chiral, parity-doublet, effective-Lagrangian mean-field theories for nuclear and astrophysical phenomenology