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

Abstract

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 $B\rightarrow ππ$ and $B\rightarrow Kπ$ decays in the factorization approximation. Some remarks on CP asymmetries in $B$ decays are also made.