On the B -> pi pi puzzle

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  • 23 February 2006
Abstract
We investigate the resolutions in the literature to the B -> pi pi puzzle arising from the large observed B^0 -> pi^0 pi^0 branching ratio, and conclude that the puzzle still stands. The next-to-leading-order (NLO) contributions from the vertex corrections, the quark loops, and the magnetic penguin evaluated in the perturbative QCD approach, having saturated the experimental upper bound of the B^0 -> rho^0 rho^0 branching ratio, do not help. 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, deteriorates the predictions for the B^\pm -> pi^0 K^\pm and B^0 -> pi^\mp K^\pm direct CP asymmetries, and overshoots the bound of the B^0 -> rho^0 rho^0 branching ratio. The effect of final-state interaction through either elastic or inelastic channels has been constrained by the B -> pi K data, and is not enough to resolve the B -> pi pi puzzle.

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