  The production of single top-quarks in the t-channel at hadron colliders
imposes strong analytic constraints on parton distribution functions (PDFs)
through its double deeply inelastic scattering (DDIS) form. We exploit this to
provide novel consistency checks between LO, NLO and NNLO PDF fits and propose
to include it as a constraint in future PDF fits. Furthermore, while it is
well-known that the b-quark PDF is highly sensitive to the b-quark mass, we
show that the treatment of this systematic uncertainty is still incomplete,
fragmented or outright missing at the moment. Consequently, we conclude that
the b-quark mass uncertainty is the dominant but so far broadly neglected
theory uncertainty for this process.
