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We perform an isospin analysis of $B$ decays to two pseudoscalars. Theanalysis extracts appropriate CKM and short distance loop factors to allow forcomparison of non-perturbative QCD effects in the reduced matrix elements ofthe amplitudes. In decays where penguin diagrams compete with tree-leveldiagrams we find that the reduced matrix elements of the penguin diagrams,which are singlets or doublets under isospin, are significantly enhancedcompared with the triplet and fourplet contributions of the weak Hamiltonian.This similarity to the $\Delta I =\frac{1}{2}$ rule in $K \to \pi \pi$ decayssuggests that, more generally, processes mediated by Hamiltonians inlower-dimensional isospin representations see enhancement overhigher-dimensional ones in QCD.

$B$ decays to two pseudoscalars and a generalized $\Delta I = \frac{1}{2}$ rule