Nuclear binding energy and transverse momentum imbalance in neutrino-nucleus reaction.

Observables based on the final state kinematic imbalances are measured in the mesonless production of $\nu_\mu+A\rightarrow\mu^-+p+X$ in the MINERvA tracker. Components of the muon-proton momentum imbalances parallel ($\delta p_{Ty}$) and perpendicular($\delta p_{Tx}$) to the momentum transfer in the transverse plane are found to be sensitive to the nuclear effects such as Fermi motion, binding energy and non-QE contributions. The QE peak location in $\delta p_{Ty}$ is particularly sensitive to the binding energy. Differential cross sections are compared to predictions from different neutrino interaction models. None of the Fermi gas models simultaneously describe every feature of the QE peak width, location, and non-QE contribution to the signal process. Correcting the GENIE's binding energy implementation according to theory causes better agreement with data. Hints of proton left-right asymmetry is observed in $\delta p_{Tx}$. Better modelling of the binding energy can reduce bias in neutrino energy reconstruction and these observables can be applied in current and future experiments to better constrain nuclear effects.