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

The complex phases φ d ϕ d and φ ₛ ϕ s , associated with the mixing between neutral Bq⁰ B q 0 and B̄q⁰ B ¯ q 0 mesons ( q∈ ,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/ψ K⁰ B d 0 → J / ψ K 0 , Bₛ⁰→ J/ψ φ B s 0 → J / ψ ϕ and Bₛ⁰→ Dₛ⁺Dₛ⁻ B s 0 → D s + D s - . To reach the highest possible precision on φ d ϕ d and φ 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