Abstract
We generalise the factorization of abelian gauge theory amplitudes to next-to-leading power (NLP) in a soft scale expansion, following a recent generalisation 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 non-radiative 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 non-trivial hard-collinear interplay present beyond the one-loop level, making this a first step towards a complete all-order factorization framework for gauge-theory amplitudes at NLP.
Highlights
Deepening our understanding of gauge theory scattering amplitudes in the limit where radiation is soft has important phenomenological benefits as well as significant intrinsic value
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
For definiteness we focus on the fγ- and f∂γ-contributions to our NLP factorization formula, corresponding to Nγ 1⁄4 1 and Nf 1⁄4 1 in Eq (28)
Summary
Deepening our understanding of gauge theory scattering amplitudes in the limit where radiation is soft has important phenomenological benefits as well as significant intrinsic value. We derive our results by power counting the pinch surfaces, that underlie the collinear (and soft) contributions we wish to describe in terms of jet (and soft) functions, for a general QED scattering amplitude This was done recently for Yukawa theory in [46] for the same two mass scenarios. In practice, γG can be expressed as function of the number of fermion and photon connections between the hard, soft and collinear subgraphs and, in presence of fermion mass, on the internal structure of the soft subgraph Such a formula tells us, at any perturbative order, which pinch surfaces contribute up to NLP and guides us in setting up a consistent and complete NLP factorization framework for QED. To support the factorization analysis in Sec. (44), we show in some detail the derivation leading to the final power-counting formula in Eq (30)
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