<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo>โ</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>M</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>: Factorization, charming penguins, strong phases, and polarization
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo>โ</mml:mo><mml:msub><mml:mi>M</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>M</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>: Factorization, charming penguins, strong phases, and polarization
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 $B\ensuremath{\rightarrow}{M}_{1}{M}_{2}$ โฆ