Determine the a_1(1640) resonance lineshape and parameter correspondence

Determine the experimentally consistent lineshape of the a_1(1640), including possible rho-prime-pion contributions, and establish its correspondence with the parameters reported by the Particle Data Group.

Background

The paper notes that the a_1(1640) does not appear prominently in three-pion spectra and that a rho-prime-pion channel may be relevant. Because the rho(1450) is broad and its threshold is near the a_1(1640) mass, a suitable treatment of the resonance lineshape is unresolved. The mapping between the model parameters and the Particle Data Group parameters is also uncertain, motivating further experimental and phenomenological clarification.

References

Given that $m_{\rho'} +m_\pi \sim m_{a_1'}$ and the large $\rho(1450)$ width, an appropriate description of its lineshape would also be required. Finally, the connection to the parameters in the PDG for each scenario is uncertain.

— The axial-vector nucleon form factor in the meson dominance picture: the role triangle singularities from a dispersive view  (2609.05109 - Arriola et al., 4 Sep 2026) in Footnote to Section 5, subsection “Resonances below N \bar N”