A large set of cross sections for semi-inclusive electroproduction of charged pions (${\pi }^{\pm }$) 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${}^2$ (up to $\approx$7 GeV${}^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 $W^{\prime }$, is in the nucleon resonance region, $W^{\prime }<2$ 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 $\mathrm{quark}\to \mathrm{pion}$ 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 ${\pi }^{+}$ and ${\pi }^{-}$) 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.

• Received 7 March 2011

DOI:https://doi.org/10.1103/PhysRevC.85.015202