Prediction of the CP asymmetry C ₀₀ in B⁰→ D⁰D⁰¯ decay

Of all B→ DD¯ decays, the B⁰→ D⁰D⁰¯ decay has the smallest observed branching ratio as it takes place primarily via the suppressed W-exchange diagram. The CP asymmetry for this mode is yet to be measured experimentally. By exploiting the relationship among the decay amplitudes of B→ DD¯ decays (using isospin and topological amplitudes) we are able to relate the CP asymmetries and branching ratios by a simple expression. This enables us to predict the CP asymmetry C₀₀ in B⁰→ D⁰D⁰¯. While the predicted central values of C₀₀ are outside the physically allowed region, they are currently associated with large uncertainties owing to the large errors in the measurements of the B⁰→ D⁰D⁰¯ branching ratio (B₀₀), the other CP asymmetries C₊₋ (of B⁰ → D⁺D⁻) and A_CP (of B⁺→ D⁺D⁰¯). With a precise determination of B₀₀, C₊₋ and A_CP, one can use our analytical result to predict C₀₀ with a reduced error and compare it with the experimental measurement when it becomes available. The correlation between B₀₀ and C₀₀ is an interesting aspect that can be probed in ongoing and future particle physics experiments such as LHCb and Belle II.