Abstract
We discuss the determination of the CKM angle alpha using the non-leptonic two-body decays Brightarrow pi pi , Brightarrow rho rho and Brightarrow 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 determination alpha _mathrm{dir}={({86.2}_{-4.0}^{+4.4} cup {178.4}_{-5.1}^{+3.9})}^{circ }. We assess the uncertainties associated to the breakdown of the isospin hypothesis and the choice of the 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 Brightarrow pi pi , Brightarrow rho rho and Brightarrow 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 .
Highlights
Over the last few decades, our understanding of C P violation has made great progress, with many new constraints from BaBar, Belle and LHCb experiments among others [1,2]
An accurate knowledge of the Cabibbo– Kobayashi–Maskawa matrix is essential for these studies and it requires the combination of many precise constraints
We have focussed on the determination of the α angle, which can be extracted with a high accuracy from two-body charmless B-meson decays extensively studied at B-factories and LHCb
Summary
Over the last few decades, our understanding of C P violation has made great progress, with many new constraints from BaBar, Belle and LHCb experiments among others [1,2]. This discrepancy affects only marginally the combination Eq (1), which is dominated by the results from ρρ decays, and to a lesser extent π π decays, whereas ρπ modes play only a limited role At this level of accuracy, it proves interesting to assess uncertainties neglected up to now, namely the sources of violation of the assumptions underlying these determinations (ΔI = 3/2 electroweak penguins, π 0–η–η mixing, ρ width) and the role played by the statistical framework used to extract the confidence intervals. Dedicated appendices gather additional numerical results for observables in three modes, separate analyses using either the BaBar or Belle inputs only, and a brief discussion of the quasi-two-body analysis of the charmless B0 → a1±π ∓ that may provide some further information on α
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