Leading quantum gravitational corrections to scalar QED

Abstract

We consider the leading post-Newtonian and quantum corrections to the non-relativistic scattering amplitude of charged scalars in the combined theory of general relativity and scalar QED. The combined theory is treated as an effective field theory. This allows for a consistent quantization of the gravitational field. The appropriate vertex rules are extracted from the action, and the nonanalytic contributions to the 1-loop scattering matrix are calculated in the non-relativistic limit. The non-analytical parts of the scattering amplitude, which are known to give the long range, low energy, leading quantum corrections, are used to construct the leading post-Newtonian and quantum corrections to the two-particle non-relativistic scattering matrix potential for two charged scalars. The result is discussed in relation to experimental verifications.

Light-like scattering in quantum gravity

“…This, for instance, was the path taken in refs. [11][12][13]. However, at high orders such an approach is clearly not very practical, since it quickly leads to very unmanageable computations, in part because of vast off-shell vertices and the occurrence of tensor contractions everywhere.…”

“…• For the massless fermion the non-singlet cut is non-vanishing as well only for the helicity conserving case, and we have 11) and (…”

“…Making the (classical) assumption that we can determine the impact parameter ρ(θ) from the cross-section dσ = πdρ 2 , we have 11) and in the small angle approximation θ 1 12) which gives the relation between the bending angle and the impact parameter…”

“…Though such a theory has yet to be found, today we can address profound practical and reliable (low energy) consequences of the (currently unknown) underlying quantum theory through the modern viewpoint of effective field theory (EFT) [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The EFT framework allows direct exploration of various quantitative phenomenological applications, see for example [24,25].…”

On-shell techniques and universal results in quantum gravity

“…We point out that other computations can be carried out with much greater ease using the cut method as well, for example the mixed electromagneticgravitational scattering case, previously computed in refs. [45,47].…”