Determine the number of complex zeros of the axial nucleon form factor

Determine the number of zeros of the axial nucleon form factor G_A(t) in the complex t-plane beyond the rigorous lower bound of two zeros implied by the superconvergence sum rules and perturbative-QCD asymptotics.

Background

The phase-modulus representation uses the argument principle to relate the asymptotic phase of G_A(t) to the numbers of zeros and poles on the first Riemann sheet. Although the paper derives that the spectral function must have at least two zeros, the total number of complex zeros is not fixed by the analysis. This unresolved count affects the detailed analytic structure of the axial form factor and its spectral function.

References

While there are no poles ($P=0$), the number of zeros in the complex plane is unknown ($N \ge 0$), so pQCD implies that the spectral function has at least two zeros.

— 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 Section 2, subsection “Phase-modulus dispersion relations”