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We have measured new observables based on the final state kinematicimbalances in the mesonless production of $\nu_\mu+A\rightarrow\mu^-+p+X$ inthe $\text{MINER}\nu\text{A}$ tracker. Components of the muon-proton momentumimbalances parallel ($\delta p_\mathrm{Ty}$) and perpendicular($\deltap_\mathrm{Tx}$) to the momentum transfer in the transverse plane are found tobe sensitive to the nuclear effects such as Fermi motion, binding energy andnon-QE contributions. The QE peak location in $\delta p_\mathrm{Ty}$ isparticularly sensitive to the binding energy. Differential cross sections arecompared to predictions from different neutrino interaction models. The Fermigas models presented in this study cannot simultaneously describe features suchas QE peak location, width and the non-QE events contributing to the signalprocess. Correcting the GENIE's binding energy implementation according totheory causes better agreement with data. Hints of proton left-right asymmetryare observed in $\delta p_\mathrm{Tx}$. Better modeling of the binding energycan reduce bias in neutrino energy reconstruction and these observables can beapplied in current and future experiments to better constrain nuclear effects.

Nuclear binding energy and transverse momentum imbalance in neutrino-nucleus reactions