  We investigate "hot" regions with anomalous high field dissipation in bulk
niobium superconducting radio frequency cavities for particle accelerators by
using low energy muon spin rotation (LE-$\mu$SR) on corresponding cavity
cutouts. We demonstrate that superconducting properties at the hot region are
well described by the non-local Pippard/BCS model for niobium in the clean
limit with a London penetration depth $\lambda_\mathrm{L} = 23 \pm 2$ nm. In
contrast, a cutout sample from the 120$^\circ$C baked cavity shows a much
larger $\lambda > 100$ nm and a depth dependent mean free path, likely due to
gradient in vacancy concentration. We suggest that these vacancies can
efficiently trap hydrogen and hence prevent the formation of hydrides
responsible for rf losses in hot regions.
