# Isospin analysis of charmless B-meson decays

## TL;DR

This paper analyzes charmless B-meson decays to precisely determine the CKM angle alpha, using latest data, isospin methods, and assessing uncertainties, with implications for understanding QCD dynamics and future measurements.

## Contribution

It provides a comprehensive extraction of the CKM angle alpha from multiple decay channels and evaluates uncertainties and theoretical assumptions involved.

## Key findings

- Determined alpha with combined data: (86.2^{+4.4}_{-4.0} or 178.4^{+3.9}_{-5.1}) degrees.
- Assessed uncertainties from isospin symmetry breaking and statistical choices.
- Compared hadronic amplitude results with theoretical expectations.

## Abstract

We discuss the determination of the CKM angle $\alpha$ using the non-leptonic two-body decays $B\to \pi\pi$, $B\to \rho\rho$ and $B\to \rho\pi$ using the latest data available. We illustrate the methods used in each case and extract the corresponding value of $\alpha$. Combining all these elements, we obtain the following determination of $\alpha_{\rm dir}=( 86.2^{+4.4}_{-4.0}~~ \cup~~ 178.4^{+3.9}_{-5.1})^\circ$. We assess the uncertainties associated to the breakdown of the isospin hypothesis and the choice of statistical framework in detail. We also determine the hadronic amplitudes (tree and penguin) describing the QCD dynamics involved in these decays, briefly comparing our results with theoretical expectations. For each observable of interest in the $B\to \pi\pi$, $B\to \rho\rho$ and $B\to \rho\pi$ systems, we perform an indirect determination based on the constraints from all the other observables available and we discuss the compatibility between indirect and direct determinations. Finally, we review the impact of future improved measurements on the determination of $\alpha$.