Exclusive rare B_s → (K, η, η′) ℓ⁺ℓ^- decays in the light-front quark model

Using the light-front quark model, we calculate the transition form factors, decay rates and longitudinal lepton polarization asymmetries for the exclusive rare B_s → (K, η(′)) (ℓ⁺ℓ ^-, ?_ℓ?^̄_ℓ)(ℓ = e, μ, τ ) decays within the standard model, taking into account the η-η mixing angle. For the mixing angle θ =-20° (-10°) in the octet-singlet basis, we obtain BR B_s → η σ? _ℓ?^̄ = 1.1(1.7)×10^-6, BR(B _s → ημ⁺μ^-) = 1.5(2.4)×10-7 , BR(B_s → ητ⁺τ^-) = 3.8(5.8) × 10^-8, BR(B^s → η′ σ? _η ?′_η) = 1.8(1.3) × 10^-6 , BR(B_s → ηprime; μ⁺μ^-) = 2.4(1.8) × 10^-7 and BR(Bs → η′ τ⁺τ ^-) = 3.4(2.6) × 10^-8, respectively. The branching ratios for the B_s → K(?_ℓ ?macr;_ℓ, ℓ⁺ℓ^-) decays are at least an order of magnitude smaller than those for the B_s → η(prime;) (?_ℓ ?macr;_ℓ, ℓ⁺ℓ^-) decays. The averaged values of the lepton polarization asymmetries for B_s → (K, η(prime;) )ℓ⁺ℓ^- are obtained as (P ^K _L) _μ = (P^η _L) _μ = (P^η′ _L) _μ μ =-0.98, (P^k _L) _τ =-0.24, (P^η _L) _τ =-0.20 and (P^ηprime; _L) _τ =-0.14, respectively.