Implication of $\sin 2β$ from global fit and $B\to J/ψK_S$
The measurement of $\sin 2 β$ is discussed within and beyond the standard model. In the presence of new physics, the angle $β$ extracted from the global fit(denoted by $β^{SM}_{fit}$) and the one extracted from $B\to J/ψK_S$ (denoted by $β_{J/ψ}$) are in general all different from the 'true' angle $β$ which is the weak phase of CKM matrix element $V^*_{td}$. Possible new physics effects on the ratio $R_β=\sin2β_{J/ψ}/\sin 2β^{SM}_{fit}$ is studied and parameterized in a most general form. It is shown that the ratio $R_β$ may provide a useful tool in probing new physics. The experimental value of $R_β$ is obtained through an update of the global fit of the unitarity triangle with the latest data and found to be less than unity at 1$σ$ level. The new physics effects on $R_β$ from the models with minimum flavor violation (MFV) and the standard model with two-Higgs-doublet (S2HDM) are studied in detail. It is found that the MFV models seem to give a relative large value $R_β\geq 1$. With the current data, this may indicate that this kind of new physics may be disfavored and alternative new physics with additional phases appears more relevant. As an illustration for models with additional phase beyond CKM phase, the S2HDM effects on $R_β$ are studied and found to be easily coincide with the data due to the flavor changing neutral Higgs interaction.