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Symmetry, symmetry breaking, and pion parton distributions

Minghui Ding, Khepani Raya, Daniele Binosi, Lei Chang, C. D. Roberts, S. M. Schmidt
A symmetry-preserving approach to the two valence-body continuum bound-state problem is used to calculate the valence, glue and sea distributions within the pion; unifying them with, inter alia, the electromagnetic pion elastic and transition form factors. The analysis reveals the following light-front momentum fractions at the scale ζ=2GeV: ⟨xvalence⟩=0.48(3), ⟨xglue⟩=0.41(2), ⟨xsea⟩=0.11(2); and despite hardening induced by the emergent phenomenon of dynamical chiral symmetry breaking, the valence-quark distribution function, qπ(x), exhibits the x≃1 behaviour predicted by quantum chromodynamics (QCD). After evolution to ζ=5.2GeV, the prediction for qπ(x) matches that obtained using lattice-regularised QCD; hence two disparate treatments are now seen to yield the same prediction. This confluence should both stimulate improved analyses of existing data and aid in motivating and supporting efforts to obtain new data on the pion distribution functions at existing and anticipated facilities.