Isospin Structure of Penguins And Their Consequences in $B$ Physics

Isospin structure of gluon mediated or strong penguin is significantly altered when the full electroweak corrections are included. This has the consequence that some previous analyses which relied on a simple isospin structure in charmless $B$ decays become inapplicable. We present the general Hamiltonian in next-to-leading order QCD, and illustrate our conclusion quantitatively for $B\rightarrow \pi\pi$ and $B\rightarrow K\pi$ decays in the factorization approximation. Some remarks on CP asymmetries in $B$ decays are also made.