IndirectCPviolation and implications forD0−D¯0andBs−B¯smixing

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 pairs of time-dependent $CP$ asymmetries in ${D}^{0}$ decays to non-$CP$ eigenstates. $CP$ 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 $|{M}_{12}|$, $|{\ensuremath{\Gamma}}_{12}|$, and ${\ensuremath{\phi}}_{12}\ensuremath{\equiv}\mathrm{arg}({M}_{12}/{\ensuremath{\Gamma}}_{12})$. Incorporating this relation into a fit to the ${D}^{0}\ensuremath{-}{\overline{D}}^{0}$ mixing data implies a level of sensitivity to $|{\ensuremath{\phi}}_{12}^{D}|$ of 0.10 (rad) at $1\ensuremath{\sigma}$. The formalism is extended to include new weak phases in decay, and in ${\ensuremath{\Gamma}}_{12}$. The phases are highly constrained by direct $CP$ violation measurements. Consequently, the bounds on $|{\ensuremath{\phi}}_{12}^{D}|$ are not significantly altered, and the effects of new weak phases in decay could be difficult to observe at a high luminosity flavor factory (${D}^{0}$) or at the LHC (${B}_{s}$) via violations of the above relations, unlike in direct $CP$ violation.