Factorization of<i>B</i>decays into two light mesons in soft-collinear effective theory
Factorization of<i>B</i>decays into two light mesons in soft-collinear effective theory
We show that the amplitudes for B decays into two light mesons at leading order in soft-collinear effective theory are factorized to all orders in ${\ensuremath{\alpha}}_{s}.$ We construct gauge-invariant four-quark operators by employing the effective theories ${\mathrm{SCET}}_{\mathrm{I}}$ for $\sqrt{{m}_{b}\ensuremath{\Lambda}}<\ensuremath{\mu}<{m}_{b},$ and ${\mathrm{SCET}}_{\mathrm{II}}$ for $\ensuremath{\mu}<\sqrt{{m}_{b}\ensuremath{\Lambda}}$ with $\ensuremath{\Lambda}\ensuremath{\sim}0.5$ GeV. These operators do not …