  Global fits to moments of kinematic distributions measured in inclusive
semileptonic $B\rightarrow X_c l \nu_l$ enable the determination of the
Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ together with
non-perturbative matrix elements of the heavy quark expansion. In current fits,
only two distinct kinematic distributions are employed and, as a consequence,
higher moments of these distributions need to be taken into account to extract
the relevant non-perturbative matrix elements. The moments of a given
distribution are highly correlated and experimental uncertainties increase for
higher moments. To address these issues, Turczyk suggested the inclusion of the
charged lepton forward-backward asymmetry $\mathcal{A}_{FB}$ in global fits,
since it provides information on non-perturbative parameters beyond the
commonly used moments.
  It is possible to construct differences of partial moments of kinematic
distributions, which can provide additional information on the non-perturbative
parameters beyond $\mathcal{A}_{FB}$ and are studied in this work for the first
time. Further, experimental cuts on the four-momentum transfer square are
studied and are shown to preserve the shape of the angular distribution, in
contrast to commonly used cuts on the lepton energy. Finally, the impact of
final-state radiation and experimental lepton identification requirements on
measurements of $\mathcal{A}_{FB}$ and differences of partial moments are
discussed.
