Precise discussion on T-asymmetry with B-meson decays

Through $B\bar{B}$ mixing system, one can construct an asymmetry which naively seems to be a time reversal (T) odd quantity. In this article, the two processes $(\mathrm{a})\: B_-\rightarrow \bar{B^0}$ and $(\mathrm{b})\: \bar{B^0}\rightarrow B_-$ are used to construct the event number asymmetry. The CP violation of Kaon system denoted as $\epsilon_K$ contributes to observables and we evaluate the contribution from $\epsilon_K$ explicitly. The asymmetry is formulated with phase convention independent parameters which are invariant under redefinition of phase of quark fields. The overall factors of the time dependent decay rates are taken into account in this article. Furthermore, we suggest conditions for the asymmetry to be a T-odd quantity. The one of such conditions arises due to the difference of overall factors which form the asymmetry.