  We present a fully differential and spin-dependent $t$-channel
single-top-quark calculation at next-to-leading order (NLO) in QCD including
off-shell effects by using the complex mass scheme in the Standard Model (SM)
and in the Standard Model Effective Field Theory (SMEFT). We include all
relevant SMEFT operators at $1/\Lambda^2$ that contribute at NLO in QCD for a
fully consistent comparison to the SM at NLO. In addition, we include chirality
flipping operators that do not interfere with the SM amplitude and contribute
only at $1/\Lambda^4$ with a massless $b$-quark. Such higher order effects are
usually captured by considering anomalous right-handed $Wtb$ and left-handed
$Wtb$ tensor couplings. Despite their formal suppression in the SMEFT, they
describe an important class of models for new physics. Our calculation and
analysis framework is publicly available in MCFM.
