$Q^2$ Dependence of Nuclear Transparency for Exclusive ${\rho }^0$ Production

Exclusive coherent and incoherent electroproduction of the ${\rho }^0$ meson from ${}^{\mathrm{1}}\mathrm{H}$ and ${}^{\mathrm{14}}\mathrm{N}$ targets has been studied at the HERMES experiment as a function of coherence length ($l_c$), corresponding to the lifetime of hadronic fluctuations of the virtual photon, and squared four-momentum of the virtual photon ($-Q^2$). The ratio of ${}^{\mathrm{14}}\mathrm{N}$ to ${}^{\mathrm{1}}\mathrm{H}$ cross sections per nucleon, called nuclear transparency, was found to increase (decrease) with increasing $l_c$ for coherent (incoherent) ${\rho }^0$ electroproduction. For fixed $l_c$, a rise of nuclear transparency with $Q^2$ is observed for both coherent and incoherent ${\rho }^0$ production, which is in agreement with theoretical calculations of color transparency.

Figure 1

Nuclear transparency as a function of coherence length for coherent (top panel) and incoherent (bottom panel) ${\rho }^0$ production on nitrogen, compared to predictions with CT effects included (curves) [21]. The inner error bars include only statistical uncertainties, while the outer error bars present the statistical and systematic uncertainties added in quadrature.

Figure 2

Distribution of $Q^2$ versus coherence length for exclusive ${\rho }^0$ production on hydrogen and nitrogen. The region surrounded by the rectangle represents the subset that was used for the two-dimensional analysis of the nuclear transparency.

Figure 3

Nuclear transparency as a function of $Q^2$ in specific coherence length bins (as indicated in each panel) for coherent ${\rho }^0$ production on nitrogen. The straight line is the result of the common fit of the $Q^2$ dependence. The error bars include only statistical uncertainties.

Figure 4

As for Fig. 3, except here for incoherent production.