Fix the matching prescription for the timelike ALP–baryon form factors

Determine the matching scale, relative normalizations, and complex timelike phases of the ALP–baryon form factors used to continue the chiral description into the few-GeV region.

Background

To estimate ALP decays above the baryon-pair threshold, the paper multiplies the chiral source contributions by phenomenological dressing factors chosen to reproduce asymptotic QCD scaling. The construction is explicitly a model rather than a derivation of the full timelike form factors.

The asymptotic scaling laws constrain powers of momentum and the strong coupling but do not fix where the transition from the chiral regime to the hard-scattering regime occurs. They also do not determine the relative strengths or phases of the different timelike form-factor contributions, leaving substantial uncertainty in the predicted exclusive widths.

References

The asymptotic form factor scaling derived in the spacelike region motivates the timelike envelopes, but does not determine the matching scale, the relative normalisations, or the generally complex phases of the timelike form factors.

— ALP interactions with mesons and baryons at $\mathcal{O}(1/f_a)$: a general field redefinition invariant approach  (2610.13671 - Alda et al., 9 Oct 2026) in Section IV.B, paragraph following Eq. (IV.30)

The anomalous Ward identity constrains the complete matrix elements, but does not uniquely determine the separate dressing factors assigned to the different chiral source contributions.

— ALP interactions with mesons and baryons at $\mathcal{O}(1/f_a)$: a general field redefinition invariant approach  (2610.13671 - Alda et al., 9 Oct 2026) in Section IV.B, paragraph following Eq. (IV.30)