Nucleon and pion PDFs: large-x asymptotics meets functional mimicry

We review strategies to unveil the primordial large-$x$ structure of the nucleons as well as the pion from hard-scattering experiments. Ideas are presented for learning about the $x\to 1$ limit of nonperturbative QCD dynamics at energy scales of order 1 GeV from collider experiments at much higher scales. The behavior of parton distributions at $x\to 1$ predicted by the quark counting rules and other low-energy theoretical approaches is contrasted with phenomenological PDFs. Polynomial mimicry of PDF parametrizations is one of many factors that influence the apparent power of the $(1-x)$ falloff. We discuss implications of the mimicry for the large-$x$ falloff of the pion PDFs.