Wavefunction Momentum-Transfer Dependence at Next-to-Eikonal Order

Investigate whether next-to-eikonal classical observables are sensitive to the momentum-transfer dependence of the incoming wavefunctions, which is neglected in the sharp-packet approximation.

Background

The incoming matter state is described by wavefunctions evaluated at midpoint momenta shifted by one half of the momentum transfer. The paper replaces the product of shifted wavefunctions by its unshifted leading approximation, while explicitly noting that this is a choice and that next-to-eikonal observables might detect the omitted dependence.

The unresolved issue is whether retaining this momentum-transfer dependence produces classical contributions to observables beyond the leading eikonal approximation.

References

Inside the wavefunctions, we will choose to drop the q corrections, however we recognise that this is a choice: it is not necessarily the case that no classical observable is sensitive to it, and indeed we expect that next-to-eikonal effects could indeed be sensitive to the q-dependence of the wavefunction. We leave this interesting problem to the future and for now we will take φi(˜pi + q/2)φ∗i(˜pi − q/2) → |φi(˜pi)|2.

— Inclusive Radiation and Backreaction from the Phase-Space S-Matrix  (2608.21318 - Moynihan, 21 Aug 2026) in Section 2.4, around equations (2.40)–(2.42), p. 13