  We present a fully perturbative calculation of the quartet-channel
proton--deuteron scattering length up to next-to-next-to-leading order in
pionless effective field theory. We use a framework that consistently extracts
the Coulomb-modified effective range function for a screened Coulomb potential
in momentum space and allows for a clear linear extrapolation back to the
physical limit without screening. Our result of (10.9 +/- 0.4) fm agrees with
older experimental determinations of this quantity but deviates from
potential-model calculations and a more recent result from Black et al., which
find larger values around 14 fm. As a possible resolution to this discrepancy,
we discuss the scheme dependence of Coulomb subtractions in a three-body
system.
