Global CKM Fits with the Scan Method

Abstract

We present results of a unitary triangle fit based on the scan method. This frequentist approach employs Gaussian uncertainties for experimental quantities, but makes no arbitrary 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, and retain those fits meeting a specific confidence level criterion, thereby constraining the $\bar \rho - \bar \eta $ plane using the standard input measurements (CKM matrix elements, $\sin2 \beta, B^0_{d,s}$ mixing, $\epsilon_K$) as well as branching fraction and \CP asymmetry measurements of B decays to $PP, PV, VV$, and $a_1 P$ final states to determine $\alpha$, $D^{(*)}K^{(*)}$ modes to determine $\gamma$, and $D^{(*)}\pi$ and $D\rho$ modes to determine $2\beta +\gamma$. We parameterize 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 parameterization, we obtain a good fit to the measured branching fractions and \CP asymmetries within the Standard Model {\it ansatz}, with no new physics contributions. This simultaneous fit allows us to determine the correlation between $\alpha$ and $\beta$ as well as between $\gamma$ and $\beta$.