Abstract
For scattering amplitudes in strong background fields, it is — at least in principle — possible to perturbatively expand the background to obtain higher-point vacuum amplitudes. In the case of self-dual plane wave backgrounds we consider this expansion for two-point, one-loop amplitudes in pure Yang-Mills, QED and QCD. This enables us to obtain multicollinear limits of 1-loop vacuum amplitudes; the resulting helicity configurations are surprisingly restricted, with only the all-plus helicity amplitude surviving. These results are shown to be consistent with well-known vacuum amplitudes. We also show that for both abelian and non-abelian supersymmetric gauge theories, there is no helicity flip (and hence no vacuum birefringence) on any plane wave background, generalising a result previously known in the Euler-Heisenberg limit of super-QED.
Highlights
When this is possible, the resulting amplitudes can be far more complex than those in vacuum, and exhibit new structures with important phenomenological consequences
We extracted maximally collinear limits of one-loop scattering amplitudes in vacuum through the expansion of one-loop, 2-point amplitudes in gauge theories on self-dual plane wave backgrounds. These 2-point amplitudes are calculated for arbitrary background strength and profile due to the high degree of symmetry of the plane wave, and as such contain structures not found in vacuum amplitudes, which in turn leads to novel physics such as vacuum birefringence
While self-duality of the background ensures that the perturbative expansion truncates at 4-point vacuum amplitudes, matching the perturbative expressions with those vacuum amplitudes is surprisingly subtle, in the massive case and at higher orders
Summary
Abelian plane waves are characterised by the same functional degrees of freedom, in both form and number, as the on-shell degrees of freedom of a photon. (Analogous statements hold for Yang-Mills plane waves and gluons, see below). Since a coherent state is itself a superposition of states of definite photon number, It follows that if z is characterised by some amplitude a0, the coefficient of aN0 in the amplitude on background, out| S[eA + a] |in , is proportional to the sum of all vacuum amplitudes including N photons in all possible incoming/outgoing configurations, weighted with numerical factors and convoluted with the field profile [26, 63, 64]. In the four-point case, the resulting amplitudes are rational functions of the momenta, with extremely compact expressions in the spinor helicity formalism In a sense, this is not surprising since the all-plus configuration arises from the purely self-dual sector of the theory, which is classically integrable, and the one-minus-rest-plus configuration is a first perturbation away from this integrable subsector (cf., [65, 66]). We consider the perturbative expansion of the 2-point, 1-loop amplitudes of strong field QED in a self-dual plane wave background. Self-duality ensures that the perturbative expansion generates only positive helicity photons from the background
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