Abstract
We compute the leading probability for a gluon to flip helicity state upon traversing a background plane wave gauge field in pure Yang-Mills theory and QCD, with an arbitrary number of colours and flavours. This is a one-loop calculation in perturbative gauge theory around the gluonic plane wave background, which is treated without approximation (i.e., to all orders in the coupling). We introduce a background-dressed version of the spinor helicity formalism and use it to obtain simple formulae for the flip amplitude with pure external gluon polarizations. We also give in-depth examples for gauge group SU(2), and evaluate both the high- and low-energy limits. Throughout, we compare and contrast with the calculation of photon helicity flip in strong-field QED.
Highlights
(classical) background. (In QED this is referred to as the Furry expansion [9].) The functional utility of such methods relies, on being able to perform the perturbative calculations without making approximations to the background
We show that the spinor helicity formalism [18,19,20,21], an important tool in the modern study of scattering amplitudes which trivializes on-shell four-dimensional kinematics, generalizes naturally to plane wave backgrounds
Gluon helicity flip may occur for quantum chromodynamics (QCD) processes in the vicinity of colliding nuclei, which are described using an effective theory known as the Colour Glass Condensate (CGC) [28,29,30,31,32]
Summary
The interactions of a single probe gluon with a large number of coherently polarized gluons is modelled by representing the large coherent superposition as a background plane wave gauge field. The Lagrangians (2.1)–(2.3) define the Feynman rules for Yang-Mills and QCD perturbatively around the background A, as we review for the case of a background plane wave. Note that the background field appears in the kinetic terms for both the gluons and quarks, the propagators of the theory are non-trivially dressed by the background. These propagators can be constructed exactly (in particular, without resorting to perturbation theory) when the background is sufficiently simple, or highly symmetric, as is the case for plane waves
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