Quantum corrections to symmetron fifth forces for planar sources

Abstract

We provide a semi-analytic calculation of the first quantum corrections to the symmetron fifth force around a planar source with nonzero thickness. We find a suppression of the fifth force compared with the classical prediction within a Compton wavelength of the source, which is of order 10% in the parameter region relevant to experiments like CANNEX, while the fifth force is enhanced at larger distances from the source. The resulting change in the spatial profile of the fifth force may be relevant to current and near future terrestrial and astrophysical tests of force laws, and has implications for the optimisation of experimental geometries, including atom interferometers. This work provides a key benchmark for future numerical studies of quantum-corrected fifth forces in screened scalar-tensor theories of gravity.