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

We present measurements of ${\nu }_{\mu }$ charged-current cross section ratios on carbon, iron, and lead relative to a scintillator (CH) using the fine-grained MINERvA detector exposed to the NuMI neutrino beam at Fermilab. The measurements utilize events of energies $2<E_{\nu }<20GeV$, with $\left< E_{\nu}\right>=8~GeV$,whichhaveareconstructed$\mu^{-}$ scattering angle less than ${17}^{\circ }$ to extract ratios of inclusive total cross sections as a function of neutrino energy $E_{\nu }$ and flux-integrated differential cross sections with respect to the Bjorken scaling variable $x$. These results provide the first high-statistics direct measurements of nuclear effects in neutrino scattering using different targets in the same neutrino beam. Measured cross section ratios exhibit a relative depletion at low $x$ and enhancement at large $x$. Both become more pronounced as the nucleon number of the target nucleus increases. The data are not reproduced by GENIE, a conventional neutrino-nucleus scattering simulation, or by the alternative models for the nuclear dependence of inelastic scattering that are considered.