  Much progress has been made recently in the study of the effects of
electron-phonon (el-ph) coupling in doped insulators using angle resolved
photoemission (ARPES), yielding evidence for the dominant role of el-ph
interactions in underdoped cuprates. As these studies have been limited to
doped Mott insulators, the important question arises how this compares with
doped band insulators where similar el-ph couplings should be at work. The
archetypical case is the perovskite SrTiO$_3$ (STO), well known for its giant
dielectric constant of 10000 at low temperature, exceeding that of
La$_2$CuO$_4$ by a factor of 500. Based on this fact, it has been suggested
that doped STO should be the archetypical bipolaron superconductor. Here we
report an ARPES study from high-quality surfaces of lightly doped SrTiO$_3$.
Comparing to lightly doped Mott insulators, we find the signatures of only
moderate electron-phonon coupling: a dispersion anomaly associated with the low
frequency optical phonon with a $\lambda'\sim0.3$ and an overall bandwidth
renormalization suggesting an overall $\lambda'\sim0.7$ coming from the higher
frequency phonons. Further, we find no clear signatures of the large pseudogap
or small polaron phenomena. These findings demonstrate that a large dielectric
constant itself is not a good indicator of el-ph coupling and highlight the
unusually strong effects of the el-ph coupling in doped Mott insulators.
