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Valence-quark distributions in the pion

M. B. Hecht·C. D. Roberts·S. M. Schmidt
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Abstract

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 GeV = 1/(0.37 fm). The shape of the calculated distribution is characteristic of a strongly bound system and, evolved from q_0 to q=2 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 parametrisations of extant pion-nucleon Drell-Yan data.

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M. B. Hecht, C. D. Roberts, S. M. Schmidt. 2000-11-29. Valence-quark distributions in the pion. https://doi.org/10.1103/physrevc.63.025213

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