We present results of unitary triangle fits based on the scan method. This frequentist approach employs Gaussian uncertainties for experimental quantities, but avoids assumptions about the distribution of theoretical errors. Instead, we perform a large number of fits, scanning over regions of plausible theory errors for each quantity. We retain those fits meeting a specific confidence level criterion, thereby constructing a region in the $\overline{\rho }-\overline{\eta }$ plane using the “standard” measurements (Cabibbo-Kobayashi-Maskawa matrix elements, $\sin 2\beta$, $B_{d,s}^0$ mixing, ${\epsilon }_K$). In addition we use branching fraction and $CP$ asymmetry measurements of $B$ decays to pseudoscalar pseudoscalar, pseudoscalar vector, vector vector, and $a_1$ pseudoscalar final states to determine $\alpha$, $D^{(*)}{K}^{(*)}$ modes to determine $\gamma$, and $D^{(*)}\pi$ and $D\rho$ modes to determine $2\beta +\gamma$. We parametrize individual decay amplitudes in terms of color-allowed tree, color-suppressed tree, penguin, singlet penguin, electroweak penguin, as well as $W$-exchange and $W$-annihilation amplitudes. With this parametrization, we obtain a good fit to the measured branching fractions and $CP$ asymmetries within the standard model ansatz, with no new physics contributions. This simultaneous fit allows us to determine, for the first time in a global fit, the correlation between $\alpha$ and $\beta$, as well as between $\gamma$ and $\beta$.

Close

PrevNext

View figure in article

• 
• 
• 
• 
• 
• 
•