Determine the a_1(1230) to sigma-pion branching fraction

Determine the experimentally precise sigma-pion branching fraction of the a_1(1230) resonance to fix the a_1-sigma-pion coupling entering the triangle contribution to the axial nucleon form factor.

Background

The sigma-pion triangle contribution depends on the coupling g_{a_1\sigma\pi}, which is inferred from the a_1 decay width and the branching fraction into sigma-pion. The paper states that this branching fraction is not precisely known experimentally and therefore adopts a theoretical estimate of 9 percent. A direct experimental determination would reduce the uncertainty of the triangle contribution.

References

The latter BR is not precisely known experimentally and we adopt the theoretical result $\textrm{BR}_{\sigma\pi}=9\%$ from Ref..

— 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 Appendix, Section “Input parameters”