  We have measured new observables based on the final state kinematic
imbalances in the mesonless production of $\nu_\mu+A\rightarrow\mu^-+p+X$ in
the $\text{MINER}\nu\text{A}$ tracker. Components of the muon-proton momentum
imbalances parallel ($\delta p_\mathrm{Ty}$) and perpendicular($\delta
p_\mathrm{Tx}$) 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 $\delta p_\mathrm{Ty}$ is
particularly sensitive to the binding energy. Differential cross sections are
compared to predictions from different neutrino interaction models. The Fermi
gas models presented in this study cannot simultaneously describe features such
as QE peak location, width and the non-QE events contributing 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
are observed in $\delta p_\mathrm{Tx}$. Better modeling 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.
