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Isospin constraints from/on $B \to \pi\pi$

Authors:	Email author" target="_blank">M?Pivk Email author F?R?Le?Diberder

Institution:	(1) PH-EP Department, CERN, 1211 Geneva 23, Switzerland;(2) Laboratoire de lAccélérateur Linéaire, IN2P3-CNRS et Université de Paris-Sud, 91898 Orsay, France

Abstract:	The Standard Model constraints on $\alpha$ which can be derived from the $B\rightarrow\pi\pi$ decays are revisited in some depth. As experimental inputs, the $B^0\rightarrow\pi^ + \pi^-$ , $B^ + \rightarrow\pi^ + \pi^0$ decays complemented by the $B^0\rightarrow\pi^0\pi^0$ decays, the CP parameters $S_{\pi\pi}$ and $C_{\pi\pi}$ , and/or the value of $\alpha$ as determined by the global CKM fit are used. The constraints discussed here are model independent in the sense that they rely only on Isospin symmetry, following the Gronau-London proposal. A new bound on $\mathcal{B}^{00}$ and the function $C_{00}(\mathcal{B}^{00})$ are introduced. While another bound applied to BABAR results is shown to imply that $\cos(2\alpha_{\rm eff})$ is negative. The Grossman-Quinn bound is rediscussed. A close form expression is given for $\alpha$ as a function of the measurements. Various scenarios for the future of the isospin analysis are explored. To probe the Standard Model the $(\mathcal{B}^{00},C_{00})$ plane is introduced.Received: 17 December 2004, Published online: 25 January 2005

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