New physics contributions to $$\bar{B}_s \rightarrow \pi ^0(\rho ^0 )\,\eta ^{(')} $$ B ¯ s → π 0 ( ρ 0 ) η ( ′ ) decays

Abstract The decay modes $$\bar{B}_s \rightarrow \pi ^0(\rho ^0 )\,\eta ^{(')} $$ B ¯ s → π 0 ( ρ 0 ) η ( ′ ) are dominated by electroweak penguins that are small in the standard model. In this work we investigate the contributions to these penguins from a model with an additional $$U(1)'$$ U ( 1 ) ′ gauge symmetry and show there effects on the branching ratios of $$\bar{B}_s \rightarrow \pi ^0(\rho ^0 )\,\eta ^{(')} $$ B ¯ s → π 0 ( ρ 0 ) η ( ′ ) . In a scenario of the model, where $$Z^\prime $$ Z ′ couplings to the left-handed quarks vanish, we show that the maximum enhancement occurs in the branching ratio of $$\bar{B}^0_s\rightarrow \,\pi ^0\,\eta '$$ B ¯ s 0 → π 0 η ′ where it can reach 6 times the SM prediction. On the other hand, in a scenario of the model where $$Z^\prime $$ Z ′ couplings to both left-handed and right-handed quarks do not vanish, we find that $$Z^\prime $$ Z ′ contributions can enhance the branching ratio of $$B^0_s\rightarrow \,\rho ^0\,\eta $$ B s 0 → ρ 0 η up to one order of magnitude comparing to the SM prediction for several sets of the parameter space where both $$ \Delta M_{B_s}$$ Δ M B s and $$S_{\psi \phi }$$ S ψ ϕ constraints are satisfied. This kind of enhancement occurs for a rather fine-tuned point where the $$ \Delta M_{B_s}$$ Δ M B s constraint on $$\mid S_\mathrm{SM} (B_s) + S_{Z'} (B_s)\mid $$ ∣ S SM ( B s ) + S Z ′ ( B s ) ∣ is fulfilled by overcompensating the SM via $$S_{Z'} (B_s) \simeq -2 S_\mathrm{SM} (B_s)$$ S Z ′ ( B s ) ≃ - 2 S SM ( B s )