  In this paper a pair of observables are proposed as alternative ways, by
examining the fluctuation of net momentum-ordering of charged pairs, to study
the charge separation induced by the Chiral Magnetic Effect (CME) in
relativistic heavy ion collisions. They are, the out-of-plane to in-plane ratio
of fluctuation of the difference between signed balance functions measured in
pair's rest frame, and the ratio of it to similar measurement made in the
laboratory frame. Both observables have been studied with simulations including
flow-related backgrounds, and for the first time, backgrounds that are related
to resonance's global spin alignment. The two observables have similar positive
responses to signal, and opposite, limited responses to identifiable
backgrounds arising from resonance flow and spin alignment. Both observables
have also been tested with two realistic models, namely, a multi-phase
transport (AMPT) model and the anomalous-viscous fluid dynamics (AVFD) model.
These two observables, when cross examined, will provide useful insights in the
study of CME-induced charge separation.
