  We present measurements of the reduction of light output by plastic
scintillators irradiated in the CMS detector during the 8 TeV run of the Large
Hadron Collider and show that they indicate a strong dose rate effect. The
damage for a given dose is larger for lower dose rate exposures. The results
agree with previous measurements of dose rate effects, but are stronger due to
the very low dose rates probed. We show that the scaling with dose rate is
consistent with that expected from diffusion effects.
