On Indirect CP Violation and Implications for D0-\overline{D0} and Bs -\overline{Bs} mixing

Abstract

The two kinds of indirect CP violation in neutral meson systems are related, in the absence of new weak phases in decay. The result is a model-independent expression relating CP violation in mixing, CP violation in the interference of decays with and without mixing, and the meson mass and width differences. It relates the semileptonic and time-dependent CP asymmetries; and CP-conjugate pairs of time-dependent $D^0$ CP asymmetries. CP violation in the interference of decays with and without mixing is related to the mixing parameters of relevance to model building: the off-diagonal mixing matrix elements |M12|, |Gamma12|, and phi12 = arg(M12 /Gamma12). Incorporating this relation into a fit to the D0 -\overline{D0} mixing data implies a level of sensitivity to |phiD12| of 0.10 [rad] at 1 sigma. The formalism is extended to include new weak phases in decay, and in Gamma12. The phases are highly constrained by direct CP violation measurements. Consequently, the bounds on |phiD12| are not significantly altered, and the effects of new weak phases in decay could be difficult to observe at a high luminosity flavor factory (D0) or at the LHC (Bs) via violations of the above relations, unlike in direct CP violation.