Measurement of the A dependence of the muon neutrino charged-current quasielastic-like cross section as a function of muon and proton kinematics at $<$E$_{\nu}>\sim$6 GeV

The first simultaneous measurements of the $\nu_{\mu}$ quasielastic-like cross section on C, CH, H$_2$0, Fe, and Pb targets as a function of kinematic imbalance variables in the plane transverse to the incoming neutrino direction are presented. These variables combine the muon and proton information to provide a new way to disentangle the effects of the nucleus in quasielastic-like processes. The data were obtained using a wide-band $\nu_{\mu}$ beam with $<$E$_{\nu}>\sim$6 GeV. Cross-section ratios of the different target materials to CH are also shown. These measurements are used to explore the nature of the cross-section $A$-scaling, as well as initial and final state interaction effects. Comparisons are made to predictions from a number of commonly used neutrino Monte Carlo event generators. The range of predictions of the different models tends to cover the data but the degree and consistency of the agreement suffers in regions, and on higher $A$ targets, where the final state interactions are expected to be more pronounced.