  In this paper, we investigate the time-dependent angular analysis of $B_s^0
\rightarrow \phi \phi$ decay to search for new physics signals via CP-violating
observables. We work with a new physics Hamiltonian containing both left- and
right-handed Chromomagnetic dipole operators. The hierarchy of the helicity
amplitudes in this model gives us a new scheme of experimental search, which is
different from the ones LHCb has used in its analysis. To illustrate this new
scheme, we perform a sensitivity study using two pseudo datasets generated
using LHCb's measured values. We find the sensitivity of CP-violating
observables to be of the order of $5-7\%$ with the current LHCb statistics.
Moreover, we show that Belle(II)'s $B^0_d \rightarrow \phi K_s$ and LHCb's
$B_s^0 \rightarrow \phi \phi$ measurements could be coupled within our model to
obtain the chirality of the new physics.
