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We present measurements of $\nu_{\mu}$ charged-current cross section ratioson carbon, iron, and lead relative to a scintillator (CH) using thefine-grained MINERvA detector exposed to the NuMI neutrino beam at Fermilab.The measurements utilize events of energies $2<E_{\nu}<20~GeV$, with $\left<E_{\nu}\right>=8~GeV$, which have a reconstructed $\mu^{-}$ scattering angleless than $17^\circ$ to extract ratios of inclusive total cross sections as afunction of neutrino energy $E_{\nu}$ and flux-integrated differential crosssections with respect to the Bjorken scaling variable $x$. These resultsprovide the first high-statistics direct measurements of nuclear effects inneutrino scattering using different targets in the same neutrino beam. Measuredcross section ratios exhibit a relative depletion at low $x$ and enhancement atlarge $x$. Both become more pronounced as the nucleon number of the targetnucleus increases. The data are not reproduced by GENIE, a conventionalneutrino-nucleus scattering simulation, or by the alternative models for thenuclear dependence of inelastic scattering that are considered.

Measurement of Ratios of $\nu_{\mu}$ Charged-Current Cross Sections on C, Fe, and Pb to CH at Neutrino Energies 2-20 GeV