Abstract
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.
Highlights
With the advent of the constituent-quark model, the pion came to be considered as a two-body problem
Growing in parallel was an appreciation that the pion occupies a special place in nuclear and particle physics; viz., as the archetype for meson-exchange forces, and plays a critical role as an elementary field in the nuclear structure Hamiltonian [1,2]. These conflicting views are reconciled in the modern paradigm [3], which simultaneously describes the pion as a conventional bound-state in quantum field theory and the Goldstone mode associated with dynamical chiral symmetry breaking (DCSB)
We argued that the impulse-approximation expression used hitherto to define the pion’s dressed-quark distribution function is incorrect owing to omission of contributions from the gluons which bind dressed-quarks into the pion
Summary
With the advent of the constituent-quark model, the pion came to be considered as a two-body problem. Growing in parallel was an appreciation that the pion occupies a special place in nuclear and particle physics; viz., as the archetype for meson-exchange forces, and plays a critical role as an elementary field in the nuclear structure Hamiltonian [1,2] These conflicting views are reconciled in the modern paradigm [3], which simultaneously describes the pion as a conventional bound-state in quantum field theory and the Goldstone mode associated with dynamical chiral symmetry breaking (DCSB). As described elsewhere [6], conclusions drawn from a leading-order analysis of these experiments proved controversial, producing [7] qπ (x) ∼ (1 − x) and an apparent disagreement with QCD
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