B→M 1 M 2 : Factorization, charming penguins, strong phases, and polarization

By Christian W. Bauer, D. Pirjol, I. Rothstein, Iain W. Stewart. 2004

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Using the soft-collinear effective theory we derive the factorization theorem for the decays $B\ensuremath{\rightarrow}{M}_{1}{M}_{2}$ with ${M}_{1,2}=\ensuremath{\pi},K,\ensuremath{\rho},{K}^{*}$, at leading order in $\ensuremath{\Lambda}/{E}_{M}$ and $\ensuremath{\Lambda}/{m}_{b}$. The results derived here apply even if ${\ensuremath{\alpha}}_{s}({E}_{M}\ensuremath{\Lambda})$ is not perturbative, and we prove that the physics sensitive to the $E\ensuremath{\Lambda}$ scale is the same in $B\ensuremath{\rightarrow}{M}_{1}{M}_{2}$ and $B\ensuremath{\rightarrow}M$ form factors. We argue that $c\overline{c}$ penguins could give long-distance effects at leading order. Decays to two transversely polarized vector mesons are discussed. Analyzing $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ we find predictions for ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ and $|{V}_{ub}|{f}_{+}^{B\ensuremath{\rightarrow}\ensuremath{\pi}}(0)$ as a function of $\ensuremath{\gamma}$.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/7153babda807dd94c8409c038d4aebdadd60d35d