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

Abstract : Motivated by a recent paper that compares the results of the analysis of the CKM angle alpha in the frequentist and in the Bayesian approaches, we have reconsidered the information on the hadronic amplitudes, which helps constraining the value of alpha in the Standard Model. We find that the Bayesian method gives consistent results irrespective of the parametrisation 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 to pi pi decays alone the 95% probability region for alpha is the interval [80^o,170^o], well consistent with recent analyses of the unitarity triangle where, by using all the available experimental and theoretical information, one gets alpha = (93 +- 4)^o. Last but not least, by using simple arguments on the hadronic matrix elements, we show that the unphysical region alpha ~ 0, present in several experimental analyses, can be eliminated.
Document type :
Journal articles

http://hal.in2p3.fr/in2p3-00157703
Contributor : Sabine Starita <>
Submitted on : Tuesday, June 26, 2007 - 5:29:13 PM
Last modification on : Friday, November 20, 2020 - 5:38:01 PM

### Citation

M. Bona, M. Ciuchini, E. Franco, V. Lubicz, G. Martinelli, et al.. Improved Determination of the CKM Angle $\alpha$ from $B \to \pi\pi$ decays. Physical Review D, American Physical Society, 2007, 76, pp.014015. ⟨10.1103/PhysRevD.76.014015⟩. ⟨in2p3-00157703⟩

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