Onset of Quark-Hadron Duality in Pion Electroproduction

A large data set of charged-pion (${\pi }^{\pm }$) electroproduction from both hydrogen and deuterium targets has been obtained spanning the low-energy residual-mass region. These data conclusively show the onset of the quark-hadron duality phenomenon, as predicted for high-energy hadron electroproduction. We construct several ratios from these data to exhibit the relation of this phenomenon to the high-energy factorization ansatz of electron-quark scattering and subsequent $\mathrm{\text{quark}}\to \mathrm{\text{pion}}$ production mechanisms.

Figure 1

The ${}^{1,2}\mathrm{H}(e,e^{\prime }{\pi }^{\pm })X$ cross sections at $x=0.32$ as a function of $z$ in comparison with Monte Carlo simulations (dashed curves) starting from a fragmentation ansatz (see text). The various cross sections have been multiplied as indicated for the purpose of plotting.

Figure 2

The ratio of proton to deuterium results of the sum (top) and difference (bottom) of ${\pi }^{+}$ and ${\pi }^{-}$ cross sections as a function of $z$, at $x=0.32$. Solid (open) symbols reflect data after (before) events from coherent $\rho$ production are subtracted (see text). The symbols have been slightly offset in $z$ for clarity. The hatched areas in the bottom indicate the systematic uncertainties, whereas the shaded bands represent a variety of calculations, at both leading order and next-to-leading-order of ${\alpha }_s$, of the shown ratio [14, 28].

Figure 3

Top: The ratio of unfavored to favored fragmentation function $D^{-}/D^{+}$ as a function of $x$ at $z=0.55$, evaluated at leading order of ${\alpha }_s$ from the deuterium data. The triangles (squares) reflect HERMES (EMC) data [18, 29], with the solid curve a fit to HERMES data. Further symbols and the hatched area are as in Fig. 2. Bottom: Same as the top, but now as a function of $z$ for $x=0.32$. The dashed curve represents the expectation [27] under the independent fragmentation hypothesis.