No abstract

We consider a collinear effective theory of highly energetic quarks with energy E, interacting with collinear and soft gluons by integrating out collinear degrees of freedom to subleading order. The collinear effective theory offers a systematic expansion in power series of a small parameter ϳp Ќ /E, where p Ќ is the transverse momentum of a collinear particle. We construct the effective Lagrangian to first order in and discuss its features, including additional symmetries such as collinear gauge invariance and reparametrization invariance. Heavy-light currents can be matched from the full theory onto the operators in the collinear effective theory at one loop and to order . We obtain heavy-light current operators in the effective theory, calculate their Wilson coefficients at this order, and the renormalization group equations for the Wilson coefficients are solved. As an application, we calculate the form factors for decays of B mesons to light energetic mesons to order and at leading-logarithmic order in ␣ s .

We consider rare radiative B decays such as B → K * γ or B → ργ in soft-collinear effective theory, and show that the decay amplitudes are factorized to all orders in α s and at leading order in Λ QCD /m b . By employing two-step matching, we classify the operators for radiative B decays in powers of a small parameter λ(∼ Λ QCD /m b ) and obtain the relevant operators to order λ in SCET I . These operators are constructed with or without spectator quarks including the four-quark operators contributing to annihilation and W -exchange channels. And we employ SCET II where the small parameter becomes of order Λ QCD /m b , and evolve the operators in order to compute the decay amplitudes for rare radiative decays in soft-collinear effective theory. We show explictly that the contributions from the annihilation channels and the W -exchange channels vanish at leading order in SCET. We present the factorized result for the decay amplitudes in rare radiative B decays at leading order in SCET, and at next-to-leading order in α s .

We compute the decay rates for the exclusive decays B ± → (η ′ , η)(K ± , K * ± ) and B 0 → (η ′ , η)(K 0 , K * 0 ) in a QCD-improved factorization framework by including the contribution from the process b → sgg → s(η ′ , η) through the QCD anomaly. This method provides an alternative estimate of the contribution b → scc → s(η, η ′ ) to these decays as compared to the one using the intrinsic charm content of the η ′ and η mesons determined through the decays J/ψ → (η, η ′ , η c )γ. The advantage of computing the relevant matrix elements via the QCD anomaly governing the transition gg → (η ′ , η) is that there is no sign ambiguity in these contributions relative to the matrix elements from the rest of the operators in the weak effective Hamiltonian. Numerically, the QCD anomaly method and the one using the radiative decays J/ψ → (η, η ′ , η c )γ give similar branching ratios for the decays of interest here. The resulting branching ratios are compared with the CLEO data on B ± → η ′ K ± and B 0 → η ′ K 0 and predictions are made for the rest.