On the positivity of $$\overline{\textrm{MS}}$$ MS ¯ parton distributions

Abstract We revisit our argument that shows that parton distribution functions (PDFs) in the $$\overline{\textrm{MS}}$$ MS ¯ scheme are non-negative in the perturbative region, with the dual goals of clarifying its theoretical underpinnings and elucidating its domain of validity. We specifically discuss recent results proving that PDFs can turn negative at sufficiently low scale, we clarify quantitatively various aspects of our derivation of positivity in the perturbative region, and we provide an estimate for the scale above which PDF positivity holds.