Contribution of the $a_1$ meson to the axial nucleon-to-$\Delta$ transition form factors

Abstract

We analyze the low-$Q^2$ behavior of the axial form factor $G_A(Q^2)$, the induced pseudoscalar form factor $G_P(Q^2)$, and the axial nucleon-to-$\Delta$ transition form factors $C_5^A(Q^2)$ and $C_6^A(Q^2)$. Building on the results of chiral perturbation theory, we first discuss $G_A(Q^2)$ in a chiral effective-Lagrangian model including the $a_1$ meson and determine the relevant coupling parameters from a fit to experimental data. With this information, the form factor $G_P(Q^2)$ can be predicted. For the determination of the transition form factor $C_5^A(Q^2)$ we make use of an SU(6) spin-flavor quark-model relation to fix two coupling constants such that only one free parameter is left. Finally, the transition form factor $C_6^A(Q^2)$ can be predicted in terms of $G_P(Q^2)$, the mean-square axial radius $⟨r_A^2⟩$, and the mean-square axial nucleon-to-$\Delta$ transition radius $⟨r_{AN\Delta }^2⟩$.

22 pages, 6 figures, typo in Eq. (55) fixed, matches published version

References in corpus (15)

• Nucleon Electromagnetic Form Factors
• First Measurement of the Muon Neutrino Charged Current Quasielastic Double Differential Cross Section
• A study of quasi-elastic muon neutrino and antineutrino scattering in the NOMAD experiment
• Vector and Axial Nucleon Form Factors:A Duality Constrained Parameterization
• $C_5^A$ axial form factor from bubble chamber experiments
• Axial, induced pseudoscalar, and pion-nucleon form factors in manifestly Lorentz-invariant chiral perturbation theory
• N-Delta(1232) axial form factors from weak pion production
• Study of quasielastic scattering using charged-current nu_mu-iron interactions in the MINOS Near Detector
• Measurement of Muon Capture on the Proton to 1% Precision and Determination of the Pseudoscalar Coupling g_P
• The axial N to Delta transition form factors from Lattice QCD
• Electroweak Form Factors of the $\Delta$(1232) Resonance
• Nucleon-to-Delta axial transition form factors in relativistic baryon chiral perturbation theory
• Chiral symmetry and the axial nucleon to Delta(1232) transition form factors
• Light Cone QCD Sum Rules Analysis of the Axial N -> Delta Transition Form Factors
• Nucleon-to-Delta transition form factors in chiral effective field theory using the complex-mass scheme

Cited by in corpus (3)

• Model dependence of the polarization asymmetries in weak pion production off the nucleon
• Low-energy axial-vector transitions from decuplet to octet baryons
• Axial-vector nucleon-to-delta transition form factors using the complex-mass renormalization scheme