Towards all-order factorization of QED amplitudes at next-to-leading power

We generalize the factorization of Abelian gauge theory amplitudes to next-to-leading power (NLP) in a soft scale expansion, following a recent generalization for Yukawa theory. From an all-order power counting analysis of leading and next-to-leading regions, we infer the factorized structure for both a parametrically small and zero fermion mass. This requires the introduction of new universal jet functions, for nonradiative and single-radiative QED amplitudes, which we compute at one-loop order. We show that our factorization formula reproduces the relevant regions in one- and two-loop scattering amplitudes, appropriately addressing endpoint divergences. It provides a description of virtual collinear modes and accounts for nontrivial hard-collinear interplay present beyond the one-loop level, making this a first step toward a complete all-order factorization framework for gauge-theory amplitudes at NLP.

Automated summary

We extend the factorization of Abelian gauge theory amplitudes to the next-to-leading power (NLP) level in a soft scale expansion, introducing new universal jet functions and addressing endpoint divergences. This new factorization framework provides a first step towards a complete all-order description of gauge-theory amplitudes at NLP, considering virtual collinear modes and the interplay of nontrivial hard-collinear effects beyond one-loop level.