Connection between full-amplitude singularities and observed scaling in pp elastic scattering

Determine how the singularities generated by the full proton-proton elastic scattering amplitude relate to the observed scaling properties at moderate but nonzero momentum transfer, given that the scaling ansatz for the t-channel partial waves yields only single-pole singularities and no standard Regge singularities in the complex l-plane.

Background

Within the Regge formalism, the authors analyze scaling proton-proton elastic scattering amplitudes and derive an analytic continuation for t-channel partial waves. Using a scaling ansatz, they show that only single-pole singularities arise from Γ(−λ) at positive integer λ, with no additional Regge poles or cuts appearing in the complex l-plane for the scaling form.

However, scaling is observed only at moderate but nonzero momentum transfer, suggesting that the full amplitude (beyond the scaling ansatz) should generate additional singularities. The authors explicitly note that understanding how these full-amplitude singularities connect to the empirically observed scaling behavior remains unresolved.

References

Note however that scaling is only seen at moderate but nonzero mementum transfer, so the full amplitude will probably generate the singularities. The problem remains open to see the connection with the scaling properties.

— The scaling Pomeron  (2604.01822 - Peschanski et al., 2 Apr 2026) in Section 3 (Regge formalism: Determination of the t-channel partial waves), paragraph discussing singularities after Eq. (secondform)