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Author: S. Gardner (Kentucky)

Title: Isospin Violation in ${\bf B\rightarrow \pi\pi}$ Decays

Abstract: An isospin analysis of $B\rightarrow \pi\pi$ decays yields $\sin 2\alpha$, where $\alpha$ is the usual CKM angle $\alpha\equiv {\rm arg} [-V_{td} V_{tb}^\ast/(V_{ud}V_{ub}^\ast)]$without hadronic uncertainty if isospin is a perfect symmetry.Yet isospin symmetry is broken not only by electroweak effects but also by the $u$ and $d$ quark mass difference --- the latter drives$\pi^0-\eta,\eta'$ mixing and converts the isospin-perfect triangle relation between the $B\rightarrow \pi\pi$ amplitudes to a quadrilateral. The error incurred in $\sin 2\alpha$ through the neglect of theresulting isospin-violating effects can be significant, particularly if $\sin 2\alpha$ is small.

Comments: 6 pages, REVTeX, epsf, 1 eps figureReport-no.: gardner0418


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