The axial-vector nucleon form factor in the meson dominance picture: the role triangle singularities from a dispersive view
Abstract
The nucleon axial form factor is analyzed in terms of a dispersion relation comprising chiral perturbation theory (ChPT) and perturbative QCD (pQCD) in the low- and high-momentum regimes respectively, which implies a set of superconvergence sum rules for the A → N N̅ spectral function. In the timelike region below the N N̅ production threshold we include the a1 and a1' resonances, with finite-width effects modeled through ρπ and σπ intermediate states. Above the N N̅ threshold, we model an infinite tower of radially excited 1++ resonances with a non-integer power fall-off, eventually matching pQCD. In this setup, we find that both the ChPT and pQCD contributions are tiny. In turn, the dominant ρπ triangle provides the leading deviations from axial meson dominance. Our calculation is not a fit; it contains parameters with a priori uncertainties estimates. The axial radius is predicted to be rA2 =(0.28−0.33) fm2 = ( 0.47−0.57 fm)2 in agreement with recent lattice QCD results but inconsistent with the MINERνA determination. A simple semiempirical formula is provided accounting for the main physical effects.
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BibTeX
@misc{arriola2026axialvector,
title = {{The axial-vector nucleon form factor in the meson dominance picture: the role triangle singularities from a dispersive view}},
author = {Enrique Ruiz Arriola and Pablo Sanchez-Puertas},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05109},
eprint = {2609.05109},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05109},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The axial-vector nucleon form factor in the meson dominance picture: the role triangle singularities from a dispersive view
AU - Enrique Ruiz Arriola
AU - Pablo Sanchez-Puertas
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05109
UR - https://arxiv.org/abs/2609.05109
AB - The nucleon axial form factor is analyzed in terms of a dispersion relation comprising chiral perturbation theory (ChPT) and perturbative QCD (pQCD) in the low- and high-momentum regimes respectively, which implies a set of superconvergence sum rules for the A → N N̅ spectral function. In the timelike region below the N N̅ production threshold we include the a_1 and a_1' resonances, with finite-width effects modeled through ρπ and σπ intermediate states. Above the N N̅ threshold, we model an infinite tower of radially excited 1^++ resonances with a non-integer power fall-off, eventually matching pQCD. In this setup, we find that both the ChPT and pQCD contributions are tiny. In turn, the dominant ρπ triangle provides the leading deviations from axial meson dominance. Our calculation is not a fit; it contains parameters with a priori uncertainties estimates. The axial radius is predicted to be r_A^2 =(0.28−0.33) fm^2 = ( 0.47−0.57 fm)^2 in agreement with recent lattice QCD results but inconsistent with the MINERνA determination. A simple semiempirical formula is provided accounting for the main physical effects.
ER -