How Isospin Violation Mocks ``New'' Physics: $π^0-η,η'$ Mixing in $B\to ππ$ Decays

Details How Isospin Violation Mocks ``New'' Physics: $π^0-η,η'$ Mixing in $B\to ππ$ Decays How Isospin Violation Mocks ``New'' Physics: $π^0-η,η'$ Mixing in $B\to ππ$ Decays

1998-06-19

arxiv.org/abs/hep-ph/9806423v2

Phys.Rev.D59:077502,1999

Physics

High Energy Physics

High Energy Physics - Phenomenology

9 pages, 1 figure, REVTeX, epsfig; major revisions; num. error corrected

Scientific paper

10.1103/PhysRevD.59.077502

An isospin analysis of $B\to\pi\pi$ decays yields $\sin 2\alpha$, where $\alpha$ is the usual CKM angle $\alpha\equiv arg [-V_{td}V_{tb}^\ast /(V_{ud}V_{ub}^\ast)]$, without hadronic uncertainty if isospin is a perfect symmetry. Isospin, however, is broken not only by electroweak effects but also by the u and d quark mass difference. The latter generates $\pi^0-\eta, \eta'$ mixing and converts the isospin-perfect triangle relation between the $B\to\pi\pi$ amplitudes to a quadrilateral. The combined isospin-violating effects impact the extracted value of $\sin 2\alpha$ in a significant manner, particularly if the latter is small.

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