How to tame penguins: advancing to high-precision measurements of d and ₛ

Abstract The complex phases d ϕ d and ₛ ϕ s, associated with the mixing between neutral Bq⁰ B q 0 and Bq⁰ B ¯ q 0 mesons (q \d, s\ q ∈ d, s), are key observables to test the Standard Model and search for contributions from new physics. They are conventionally determined from the measurements of mixing-induced CP violation in the decays Bd⁰ J/ K⁰ B d 0 → J / ψ K 0, Bₛ⁰ J/ B s 0 → J / ψ ϕ and Bₛ⁰ Dₛ^+Dₛ^- B s 0 → D s + D s -. To reach the highest possible precision on d ϕ d and ₛ ϕ s, it is crucial that corrections from next-to-leading order effects – primarily associated with penguin decay topologies – are accounted for. The strategy adopted in this paper uses the SU (3) flavour symmetry of QCD to relate the unknown contributions from penguin topologies to their counterparts in suitably-chosen control modes, where their effects are enhanced. Utilising new CP asymmetry measurements from LHCb on the decays Bₛ⁰ Dₛ^+Dₛ^- B s 0 → D s + D s -, Bd⁰ D^+D^- <mm