  Relaxing the Riemannian condition to incorporate geometric quantities such as
torsion and non-metricity may allow to explore new physics associated with
defects in a hypothetical space-time microstructure. Here we show that
non-metricity produces observable effects in quantum fields in the form of
4-fermion contact interactions, thereby allowing us to constrain the scale of
non-metricity to be greater than 1 TeV by using results on Bhabha scattering.
Our analysis is carried out in the framework of a wide class of theories of
gravity in the metric-affine approach. The bound obtained represents an
improvement of several orders of magnitude to previous experimental
constraints.
