Beginning with results for the leading-twist two-particle distribution amplitudes of $$\pi $$ π - and K-mesons, each of which exhibits dilation driven by the mechanism responsible for the emergence of hadronic mass, we develop parameter-free predictions for the pointwise behaviour of all $$\pi $$ π and K distribution functions (DFs), including glue and sea. The large-x behaviour of each DF meets expectations based on quantum chromodynamics; the valence-quark distributions match extractions from available data, including the pion case when threshold resummation effects are included; and at $$\zeta _5=5.2\,$$ ζ 5 = 5.2 GeV, the scale of existing measurements, the light-front momentum of these hadrons is shared as follows: $$\langle x_{\mathrm{valence}} \rangle ^\pi = 0.41(4)$$ ⟨ x valence ⟩ π = 0.41 ( 4 ) , $$\langle x_{\mathrm{glue}} \rangle ^\pi = 0.45(2)$$ ⟨ x glue ⟩ π = 0.45 ( 2 ) , $$\langle x_{\mathrm{sea}} \rangle ^\pi = 0.14(2)$$ ⟨ x sea ⟩ π = 0.14 ( 2 ) ; and $$\langle x_{\mathrm{valence}} \rangle ^K = 0.42(3)$$ ⟨ x valence ⟩ K = 0.42 ( 3 ) , $$\langle x_{\mathrm{glue}} \rangle ^K = 0.44(2)$$ ⟨ x glue ⟩ K = 0.44 ( 2 ) , $$\langle x_{\mathrm{sea}} \rangle ^K = 0.14(2)$$ ⟨ x sea ⟩ K = 0.14 ( 2 ) . The kaon’s glue and sea distributions are similar to those in the pion, although the inclusion of mass-dependent splitting functions introduces some differences on the valence-quark domain. This study should stimulate improved analyses of existing data and motivate new experiments sensitive to all $$\pi $$ π and K DFs. With little known empirically about the structure of the Standard Model’s (pseudo-) Nambu-Goldstone modes and analyses of existing, limited data being controversial, it is likely that new generation experiments at upgraded and anticipated facilities will provide the information needed to resolve the puzzles and complete the picture of these complex bound states.

A symmetry-preserving approach to the two valence-body continuum bound-state problem is used to calculate the valence, glue and sea distributions within the pion; unifying them with, inter alia, the electromagnetic pion elastic and transition form factors. The analysis reveals the following light-front momentum fractions at the scale ζ = 2 GeV: x valence = 0.48(3), x glue = 0.41 (2), xsea = 0.11(2); and despite hardening induced by the emergent phenomenon of dynamical chiral symmetry breaking, the valence-quark distribution function, q π (x), exhibits the x 1 behaviour predicted by quantum chromodynamics (QCD). After evolution to ζ = 5.2 GeV, the prediction for q π (x) matches that obtained using lattice-regularised QCD; hence two disparate treatments are now seen to yield the same prediction. This confluence should both stimulate improved analyses of existing data and aid in motivating and supporting efforts to obtain new data on the pion distribution functions at existing and anticipated facilities. arXiv:1905.05208v1 [nucl-th]