We describe expressions for pion and kaon dressed-quark distribution functions that incorporate contributions from gluons which bind quarks into these mesons and hence overcome a flaw of the commonly used handbag approximation. The distributions therewith obtained are purely valence in character, ensuring that dressed quarks carry all the meson’s momentum at a characteristic hadronic scale and vanish as $(1-x{)}^2$ when Bjorken-$x\to 1$. Comparing such distributions within the pion and kaon, it is apparent that the size of $SU(3)$-flavor symmetry breaking in meson parton distribution functions is modulated by the flavor dependence of dynamical chiral symmetry breaking. Corrections to these leading-order formulas may be divided into two classes, responsible for shifting dressed-quark momentum into glue and sea quarks. Working with available empirical information, we build an algebraic framework that is capable of expressing the principal impact of both classes of corrections. This enables a realistic comparison with experiment which allows us to identify and highlight basic features of measurable pion and kaon valence-quark distributions. We find that whereas roughly two thirds of the pion’s light-front momentum is carried by valence dressed quarks at a characteristic hadronic scale; this fraction rises to 95% in the kaon; evolving distributions with these features to a scale typical of available Drell-Yan data produces a kaon-to-pion ratio of $u$-quark distributions that is in agreement with the single existing data set, and predicts a $u$-quark distribution within the pion that agrees with a modern reappraisal of $\pi N$ Drell-Yan data. Precise new data are essential in order to validate this reappraisal and because a single modest-quality measurement of the kaon-to-pion ratio cannot be considered definitive.

Using a confining, symmetry-preserving regularization of a $\mathrm{vector}\times \mathrm{vector}$ contact interaction, we compute the spectra of ground-state pseudoscalar and vector $(f\overline{g})$ mesons, scalar and axial-vector $(fg)$ diquarks, and $J^P=1/2^{+},3/2^{+}$ $(fgh)$ baryons, where $f,g,h\in \{u,d,s,c,b\}$. The diquark correlations are essentially dynamical and play a key role in formulating and solving the three-valence-quark baryon problems. The baryon spectrum obtained from this largely algebraic approach reproduces the 22 known experimental masses with an accuracy of 2.9(2.4)%. It also possesses the richness of states typical of constituent-quark models, predicting many heavy-quark baryons not yet observed. This study indicates that diquark correlations are an important component of all baryons; and owing to the dynamical character of the diquarks, it is typically the lightest allowed diquark correlation that defines the most important component of a baryon’s Faddeev amplitude.

We compute all kaon and pion parton distribution amplitudes (PDAs) to twist three and find that only the pseudotensor PDA can reasonably be approximated by its conformal limit expression. At terrestrially accessible energy scales, the twist-two and pseudoscalar twist-three PDAs differ significantly from those functions commonly associated with their forms in QCD’s conformal limit. In all amplitudes studied, $SU(3)$ flavor-symmetry breaking is typically a 13% effect. This scale is determined by nonperturbative dynamics; namely, the current-quark-mass dependence of dynamical chiral symmetry breaking. The heavier quark is favored by this distortion; for example, support is shifted to the $s$-quark in the negative kaon. It appears, therefore, that at energy scales accessible with existing and foreseeable facilities, one may obtain reliable expectations for experimental outcomes by using these “strongly dressed” PDAs in formulas for hard exclusive processes. Following this procedure, any discrepancies between experiment and theory will be significantly smaller than those produced by using the conformal-limit PDAs. Moreover, the magnitude of any disagreement will either be a better estimate of higher-order, higher-twist effects or provide more realistic constraints on the Standard Model.