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We investigate the pure penguin decays in the Standard Model(SM) and in the Constrained Minimal Supersymmetric Standard Model (CMSSM) using the QCD factorization approach and consider the Sudakov effects in the twist-3 contribution. We find ${\rm Br}(B^-\to \pi^-\phi) = (1.95-5.70)\times 10^{-9}(1.1-2.4)\times 10^{-8}\tan\beta $ which is about one order of magnitude larger than that in SM.

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