Improved Determination of the CKM Angle alpha from B to pi pi decays

Motivated by a recent paper that compares the results of the analysis of the CKM angle α in the frequentist and in the Bayesian approaches, we have reconsidered the information on the hadronic amplitudes, which helps in constraining the value of α in the standard model. We find that the Bayesian method gives consistent results irrespective of the parametrization of the hadronic amplitudes and that the results of the frequentist and Bayesian approaches are equivalent when comparing meaningful probability ranges or confidence levels. We also find that from B→ππ decays alone the 95% probability region for α is the interval [80°, 170°], well consistent with recent analyses of the unitarity triangle where, by using all the available experimental and theoretical information, one gets α=(93±4)°. Last but not least, by using simple arguments on the hadronic matrix elements, we show that the unphysical region α∼0, present in several experimental analyses, can be eliminated.