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Semi-Inclusive Charged-Pion Electroproduction off Protons and Deuterons: Cross Sections, Ratios and Access to the Quark-Parton Model at Low Energies

A large set of cross sections for semi-inclusive electroproduction of charged pions ($π^\pm$) from both proton and deuteron targets was measured. The data are in the deep-inelastic scattering region with invariant mass squared $W^2$ > 4 GeV$^2$ and range in four-momentum transfer squared $2 < Q^2 < 4$ (GeV/c)$^2$, and cover a range in the Bjorken scaling variable 0.2 < x < 0.6. The fractional energy of the pions spans a range 0.3 < z < 1, with small transverse momenta with respect to the virtual-photon direction, $P_t^2 < 0.2$ (GeV/c)$^2$. The invariant mass that goes undetected, $M_x$ or W', is in the nucleon resonance region, W' < 2 GeV. The new data conclusively show the onset of quark-hadron duality in this process, and the relation of this phenomenon to the high-energy factorization ansatz of electron-quark scattering and subsequent quark --> pion production mechanisms. The x, z and $P_t^2$ dependences of several ratios (the ratios of favored-unfavored fragmentation functions, charged pion ratios, deuteron-hydrogen and aluminum-deuteron ratios for $π^+$ and $π^-$) have been studied. The ratios are found to be in good agreement with expectations based upon a high-energy quark-parton model description. We find the azimuthal dependences to be small, as compared to exclusive pion electroproduction, and consistent with theoretical expectations based on tree-level factorization in terms of transverse-momentum-dependent parton distribution and fragmentation functions. In the context of a simple model, the initial transverse momenta of $d$ quarks are found to be slightly smaller than for $u$ quarks, while the transverse momentum width of the favored fragmentation function is about the same as for the unfavored one, and both fragmentation widths are larger than the quark widths.