Correction to CP-asymmetry in ϒ (4S) Decays due to the Admixture of B0{ {B}^0} in a C-even State

BB pairs from ϒ(4 S ) → BB decays are in C -odd state. However, there is a small admixture of the C -even state and it modifies the time dependent CP -asymmetry. The C -even component appears due to soft photon emission, breaking the pure C -odd nature of the initial state. Using the two-particle wave function formalism, we derive analytical expressions for CP -asymmetry in both pure and mixed C -parity states. We emphasize the strong energy dependence of the admixture magnitude.