Phenomenology of space-time imperfection. II. Local defects

We propose a phenomenological model for the scattering of particles on space-time defects in a treatment that maintains Lorentz invariance on the average. The local defects considered here cause a stochastic violation of momentum conservation. The scattering probability is parametrized in the density of defects and the distribution of the momentum that a particle can obtain when scattering on the defect. We identify the most promising observable consequences and derive constraints from existing data.

Figure 1

Assignment of momentum notation. Left: Simple vertex for scattering on local defect (dotted line). Right: Photon (wavy line) decays into a fermion pair (solid line) enabled by scattering on local defect (dotted line).

Figure 2

Left: Contribution to photon mass from twice scattering on a defect. Right: Vacuum Cherenkov radiation, enabled by scattering on a defect.

Figure 3

Summary of constraints. The coral (dark) shaded region is excluded. The peachpuff (light) shaded region indicates the stronger constraint from photon decay with the ad-hoc assumption that the typical distance between defects increases with the cosmological scale factor. The dotted (black) line indicates the length scale associated with the cosmological constant. The dashed (blue) line is the case $LM=1$ and the solid (green) line is the case $LM=1/ϵ$.