Global CKM Fits with the Scan Method

TL;DR

This paper introduces a scan method for CKM matrix fits that accounts for theoretical uncertainties without arbitrary assumptions, providing a comprehensive analysis of the unitarity triangle and related CP violation parameters within the Standard Model.

Contribution

It presents a novel frequentist scan approach for CKM fits that handles theoretical errors systematically and constrains the unitarity triangle using diverse experimental measurements.

Findings

Good fit to measured branching fractions and CP asymmetries within the Standard Model

Determines correlations between CKM angles alpha, beta, gamma

No evidence for new physics contributions in the analyzed data

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 $\beta$.