  In practice the asymmetry, which is defined based on the angular distribution
of the final states in scattering or decay processes, can be utilized to
scrutinize underlying dynamics in and/or beyond the standard model (BSM). As
one of the possible BSM physics which might be discovered early at the LHC,
extra neutral gauge bosons $Z^\prime$s are theoretical well motivated. Once
$Z^\prime$s are discovered at the LHC, it is crucial to discriminate different
$Z^\prime$s in various BSM. In principle such task can be accomplished by
measuring the angular distribution of the final states which are produced via
$Z^\prime$-mediated processes. In the real data analysis, asymmetry is always
adopted. In literature several asymmetries have been proposed at the LHC. Based
on these works, we stepped further on to study how to optimize the asymmetries
in the left-right model and the sequential standard model, as the examples of
BSM. In this paper, we examined four kinds of asymmetries, namely
rapidity-dependent forward-backward asymmetry, one-side forward-backward
asymmetry, central charge asymmetry and edge charge asymmetry (see text for
details), with $\ell^+\ell^-$ ($\ell=e,\mu$), $b\bar b$ and $t\bar t$ as the
final states. In the calculations with $b\bar b$ and $t\bar t$ final states,
the QCD-induced higher order contributions to the asymmetric cross section were
also included. For each kind of final states, we estimated the four kinds of
asymmetries and especially the optimal cut usually associated with the
definition of the asymmetry. Our numerical results indicated that the capacity
to discriminate $Z^\prime$ models can be improved by imposing the optimal cuts.
