A useful approximate isospin equality for charmless strange B Decays

A useful inequality is obtained if charmless strange B decays are assumed to be dominated by a ∆I = 0 transition like that from the gluonic penguin diagram and the contributions of all other diagrams including the tree, electroweak penguin and annihilation diagrams are small but not negligible. The interference contributions which are linear in these other amplitudes are included but the direct contributions which are quadratic are neglected. It is now believed that charmless strange B decays are dominated by the gluonic penguin diagram. If all other diagrams are negligible, the branching ratios for sets of decays to states in the same isospin multiplets are uniquely related by isospin because the gluonic penguin leads to a pure I=1/2 final state, and there is no simple mechanism in the standard model that can give CP violation. Supported in part by The German-Israeli Foundation for Scientific Research and Development (GIF) and by the U.S. Department of Energy, Division of High Energy Physics, Contract W-31109-ENG-38.