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Constrained by solutions of the continuum three-valence-body bound-state equations, we use perturbation theory integral representations (PTIRs) to develop algebraic Ansätze for the Faddeev wave functions of the proton and its first radial excitation, delivering therewith a quantum field theory calculation of the pointwise behaviour of their leading-twist parton distribution amplitudes (PDAs). The proton's PDA is a broad, concave function, with its maximum shifted relative to the peak in QCD's conformal limit expression for this PDA. The size and direction of this shift signal the presence of both scalar and pseudovector diquark correlations in the nucleon, with the scalar generating around 60% of the proton's normalisation. The radial-excitation is constituted similarly, and the pointwise form of its PDA, which is negative on a material domain, is the result of marked interferences between the contributions from both types of diquark; particularly, the locus of zeros that highlights its character as a radial excitation. These features originate with the emergent phenomenon of dynamical chiral-symmetry breaking in the Standard Model. [ABSTRACT FROM AUTHOR]

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, q π ( x ) ; namely, at a characteristic hadronic scale, q π ( x ) ∼ ( 1 − x ) 2 for x ≳ 0.85 ; and the valence-quarks carry approximately two-thirds of the pion's light-front momentum. [ABSTRACT FROM AUTHOR]