  We present a refined and improved study of the influence of screening on the
effective fine structure constant of graphene, $\alpha^*$, as measured in
graphite using inelastic x-ray scattering. This follow-up to our previous study
[J. P. Reed, et al., Science 330, 805 (2010)] was carried out with two times
better energy resolution, five times better momentum resolution, and improved
experimental setup with lower background. We compare our results to RPA
calculations and evaluate the relative importance of interlayer hopping,
excitonic corrections, and screening from high energy excitations involving the
$\sigma$ bands. We find that the static, limiting value of $\alpha^*$ falls in
the range 0.25 to 0.35, which is higher than our previous result of 0.14, but
still below the value expected from RPA. We show the reduced value is not a
consequence of interlayer hopping effects, which were ignored in our previous
analysis, but of a combination of excitonic effects in the $\pi \rightarrow
\pi^*$ particle-hole continuum, and background screening from the
$\sigma$-bonded electrons. We find that $\sigma$-band screening is extremely
strong at distances of the order of a few nm, and should be highly effective at
screening out short-distance, Hubbard-like interactions in graphene, as well as
other carbon allotropes.
