Implication of the B -> rho rho data on the B -> pi pi puzzle

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Abstract
We point out that the B -> rho rho data have seriously constrained the possibility of resolving the B -> pi pi puzzle from the large observed B^0 -> pi^0 pi^0 branching ratio in the available theoretical approaches. The next-to-leading-order (NLO) contributions from the vertex corrections, the quark loops, and the magnetic penguin evaluated in the perturbative QCD (PQCD) approach have saturated the experimental upper bound of the B^0 -> rho^0 rho^0 branching ratio, and do not help. The NLO PQCD predictions for the B^0 -> rho^\mp rho^\pm and B^\pm -> rho^\pm rho^0 branching ratios are consistent with the data. The inclusion of the NLO jet function from the soft-collinear effective theory into the QCD-improved factorization approach, though enhancing the B^0 -> pi^0 pi^0 branching ratio sufficiently, overshoots the bound of the B^0 -> rho^0 rho^0 branching ratio, and deteriorates the predictions for the B^\pm -> pi^0 K^\pm and B^0 -> pi^\mp K^\pm direct CP asymmetries.

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