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We describe a new method for obtaining the CP phase alpha via measurements of B_{d,s} -> K() Kbar() decays. This method is particularly appropriate for hadron colliders since some of the branching ratios are small [O(10^{-6})], and since B_s decays are involved. By comparing the value of alpha extracted from this method with that obtained in B -> pi pi or B -> rho pi decays, one can detect the presence of new physics in the b -> d penguin amplitude. The method does require theoretical input, but model calculations suggest that the theoretical uncertainty is at most 5%, and might well be even smaller. These estimates can be tested experimentally. The method is therefore quite clean.

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