Re-examining sin⁡2βsin⁡2β and ΔmdΔmd from evolution of Bd0 mesons with decoherence

In the time evolution of neutral meson systems, a perfect quantum coherence is usually assumed. The important quantities of the Bd0 system, such as sin⁡2βsin⁡2β and ΔmdΔmd, are determined under this assumption. However, the meson system interacts with its environment. This interaction can lead to decoherence in the mesons even before they decay. In our formalism this decoherence is modelled by a single parameter λ  . It is desirable to re-examine the procedures of determination of sin⁡2βsin⁡2β and ΔmdΔmd in meson systems with decoherence. We find that the present values of these two quantities are modulated by λ  . Re-analysis of Bd0 data from B-factories and LHCb can lead to a clean determination of λ  , sin⁡2βsin⁡2β and ΔmdΔmd.