Clear windows onto emergent hadron mass (EHM) and modulations thereof by Higgs boson interactions are provided by observable measures of pion and kaon structure, many of which are accessible via generalised parton distributions (GPDs). Beginning with algebraic GPD Ansätze, constrained entirely by hadron-scale and K valence-parton distribution functions (DFs), in whose forms both EHM and Higgs boson influences are manifest, numerous illustrations are provided. They include the properties of electromagnetic form factors, impact parameter space GPDs, gravitational form factors and associated pressure profiles, and the character and consequences of all-orders evolution. The analyses predict that mass-squared gravitational form factors are stiffer than electromagnetic form factors; reveal that K pressure profiles are tighter than profiles, with both mesons sustaining near-core pressures at magnitudes similar to that expected at the core of neutron stars; deliver parameter-free predictions for and K valence, glue, and sea GPDs at the resolving scale GeV; and predict that at this scale the fraction of meson mass-squared carried by glue and sea combined matches that lodged with the valence degrees-of-freedom, with a similar statement holding for mass-squared radii.

Analyses of the pion valence-quark distribution function (DF), "Equation missing", which explicitly incorporate the behaviour of the pion wave function prescribed by quantum chromodynamics (QCD), predict "Equation missing", $$\beta (\zeta \gtrsim m_p)>2$$ β ( ζ ≳ m p ) > 2 , where $$m_p$$ m p is the proton mass. Nevertheless, more than forty years after the first experiment to collect data suitable for extracting the $$x\simeq 1$$ x ≃ 1 behaviour of "Equation missing", the empirical status remains uncertain because some methods used to fit existing data return a result for "Equation missing" that violates this constraint. Such disagreement entails one of the following conclusions: the analysis concerned is incomplete; not all data being considered are a true expression of qualities intrinsic to the pion; or QCD, as it is currently understood, is not the theory of strong interactions. New, precise data are necessary before a final conclusion is possible. In developing these positions, we exploit a single proposition, viz. there is an effective charge which defines an evolution scheme for parton DFs that is all-orders exact. This proposition has numerous corollaries, which can be used to test the character of any DF, whether fitted or calculated.

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