$B_s \to \phi l^+ l^-$ decays in the topcolor-assisted technicolor model

Using the updated form factors within the light-cone QCD sum rule approach, we calculate the new physics contributions to rare semileptonic $\bar{B}_s \to \phi\mu^+\mu^-, \phi \tau^+\tau^-$ decays from the new particles appearing in the topcolor-assisted technicolor (TC2) model. In our evaluations, we find that: (i) the branching ratio, normalized forward-backward asymmetry and lepton polarization show highly sensitivity to charged top-pions contributions and little sensitivity to $Z'$ contributions. The TC2 enhancements to the branching ratios of these decays can reach a factor of $2 \sim 4$; (ii) the NP enhancement to the forward-backward asymmetry of the decay $B_s\to \phi \mu^+\mu^-$ is in the range -9% to 22%, but -10% to 0% for decay $B_s\to \phi \tau^+\tau^-$ compared to the SM predictions; (iii) the TC2 model provide an enhancement of more than 30% to the longitudinal polarization asymmetry $P_L$ for decay $B_s\to \phi \mu^+\mu^-$, but a decrease of about 20% to the transverse polarization asymmetry $P_T$ for the decay $B_s\to \phi \tau^+\tau^-$.