Measurement of the Angle $\phi_1(\beta)$ and $B \bar B$ Mixing (Recent Results from BaBar and Belle)

Abstract

Recent results from BaBar and Belle experiments on $B \bar B$ mixing and $\sin 2\phi_1$ are presented. Accuracy of $\Delta m_d$ measurements has reached 1.2%. Higher order effects within the Standard Model or possible new physics effect that might appear in the $B \bar B$ mixing through non-zero $\Delta \Gamma/\Gamma$, CP violation, or $CPT$ violation have been explored. The BaBar and Belle results on $\sin 2\phi_1$ from the $b \to c \bar{c} s$ modes are in good agreement with each other and a combined result with an accuracy of 8% is in good agreement with a global CKM fit. A simple average of the $\sin 2\phi_1$ values that were measured in the penguin-loop dominated decay modes, $\phi K_S$, $\eta^{\prime} K_S$, and $K^+ K^- K_S$, shows about 2.5$\sigma$ deviation from the Standard Model.