Valence-quark distributions in the pion

We calculate the pion’s valence-quark momentum-fraction probability distribution using a Dyson-Schwinger equation model. Valence quarks with an active mass of 0.30 GeV carry 71% of the pion’s momentum at a resolving scale $q_0=0.54\mathrm{}\hspace{0.5em}\mathrm{GeV}=1/\left(0.37\mathrm{}\hspace{0.5em}\mathrm{fm}\right).\mathrm{}$ The shape of the calculated distribution is characteristic of a strongly bound system and, evolved from $q_0$ to $q=2\mathrm{}\hspace{0.5em}\mathrm{GeV},$ it yields first, second, and third moments in agreement with lattice and phenomenological estimates, and valence-quarks carrying 49% of the pion’s momentum. However, pointwise there is a discrepancy between our calculated distribution and that hitherto inferred from parametrizations of extant pion-nucleon Drell-Yan data.