Prediction of the CP asymmetry C00 in $$ {B}^0\to {D}^0\overline{D^0} $$ decay

Abstract

Abstract Of all $$ B\to D\overline{D} $$ B → D D ¯ decays, the $$ {B}^0\to {D}^0\overline{D^0} $$ B 0 → D 0 D 0 ¯ 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 $$ B\to D\overline{D} $$ B → D D ¯ 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 C 00 in $$ {B}^0\to {D}^0\overline{D^0} $$ B 0 → D 0 D 0 ¯ . While the predicted central values of C 00 are outside the physically allowed region, they are currently associated with large uncertainties owing to the large errors in the measurements of the $$ {B}^0\to {D}^0\overline{D^0} $$ B 0 → D 0 D 0 ¯ branching ratio (B 00), the other CP asymmetries C +− (of B 0 → D + D −) and A CP (of $$ {B}^{+}\to {D}^{+}\overline{D^0} $$ B + → D + D 0 ¯ ). With a precise determination of B 00, C +− and A CP, one can use our analytical result to predict C 00 with a reduced error and compare it with the experimental measurement when it becomes available. The correlation between B 00 and C 00 is an interesting aspect that can be probed in ongoing and future particle physics experiments such as LHCb and Belle II.