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Exploiting an evolution scheme for parton distribution functions (DFs) that is all-orders exact, contemporary lattice-QCD (lQCD) results for low-order Mellin moments of the pion valence quark DF are shown to be mutually consistent. The analysis introduces a means by which key odd moments can be obtained from the even moments in circumstances where only the latter are available. Combining these elements, one arrives at parameter-free lQCD-based predictions for the pointwise behaviour of pion valence, glue, and sea DFs, with sound uncertainty estimates. The behaviour of the pion DFs at large light-front momentum fraction, x≳0.85, is found to be consistent with QCD expectations and continuum analyses of pion structure functions, i.e., damping like (1−x)βparton, with βvalence≈2.4, βglue≈3.6, βsea≈4.6. It may be possible to test these predictions using data from forthcoming experiments.

Working with proton and pion valence distribution functions (DFs) determined consistently at the same, unique hadron scale and exploiting the possibility that there is an effective charge which defines an evolution scheme for DFs that is all-orders exact, we obtain a unified body of predictions for all proton and pion DFs – valence, glue, and four-flavour-separated sea. Whilst the hadron light-front momentum fractions carried by identifiable parton classes are the same for the proton and pion at any scale, the pointwise behaviour of the DFs is strongly hadron-dependent. All calculated distributions comply with quantum chromodynamics constraints on low- and high-x scaling behaviour and, owing to emergent hadron mass, pion DFs are the most dilated. These results aid in elucidating the sources of similarities and differences between proton and pion structure.

The impulse-approximation expression used hitherto to define the pion's valence-quark distribution function is flawed because it omits contributions from the gluons which bind quarks into the pion. A corrected leading-order expression produces the model-independent result that quarks dressed via the rainbow–ladder truncation, or any practical analogue, carry all the pion's light-front momentum at a characteristic hadronic scale. Corrections to the leading contribution may be divided into two classes, responsible for shifting dressed-quark momentum into glue and sea-quarks. Working with available empirical information, we use an algebraic model to express the principal impact of both classes of corrections. This enables a realistic comparison with experiment that allows us to highlight the basic features of the pion's measurable valence-quark distribution, qπ(x); namely, at a characteristic hadronic scale, qπ(x)∼(1−x)2 for x≳0.85; and the valence-quarks carry approximately two-thirds of the pion's light-front momentum.