Quantum gravitational corrections for spinning particles

TL;DR

This paper computes quantum gravitational corrections to the potentials of spinning particles, revealing new effects near the particle and confirming known behavior at large distances, with detailed analytic and numerical results.

Contribution

It introduces the first calculation of quantum corrections to spinning particles' gravitational potentials, including effects of various matter fields and near-particle behavior.

Findings

Massless field corrections dominate at large distances.

Massive fields' corrections are exponentially suppressed at large distances.

Near the particle, massive fields can enhance quantum corrections.

Abstract

We calculate the quantum corrections to the gauge-invariant gravitational potentials of spinning particles in flat space, induced by loops of both massive and massless matter fields of various types. While the corrections to the Newtonian potential induced by massless conformal matter for spinless particles are well-known, and the same corrections due to massless minimally coupled scalars [Class. Quant. Grav. 27 (2010) 245008], massless non-conformal scalars [Phys. Rev. D 87 (2013) 104027] and massive scalars, fermions and vector bosons [Phys. Rev. D 91 (2015) 064047] have been recently derived, spinning particles receive additional corrections which are the subject of the present work. We give both fully analytic results valid for all distances from the particle, and present numerical results as well as asymptotic expansions. At large distances from the particle, the corrections due to massive fields are exponentially suppressed in comparison to the corrections from massless fields, as one would expect. However, a surprising result of our analysis is that close to the particle itself, on distances comparable to the Compton wavelength of the massive fields running in the loops, these corrections can be enhanced with respect to the massless case.