The proton--deuteron scattering length in pionless EFT

We present a fully perturbative calculation of the quartet-channel proton--deuteron scattering length up to next-to-next-to-leading order (NNLO) in pionless effective field theory. In particular, 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. We find a natural convergence pattern as we go to higher orders in the EFT expansion. Our NNLO result of $(10.9\pm0.4)$~fm agrees with older experimental determinations but deviates from more recent results around $14$~fm. As a resolution of this discrepancy, we discuss the scheme dependence of Coulomb subtractions in a three-body system.