Basic features of the pion valence-quark distribution function

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.