QCD Factorization in B Decays into ρπ

Based on the QCD factorization approach we analyse the branching ratios for the channel B → ρπ. From the comparisons with experimental data provided by CLEO, BELLE and BABAR we constrain the form factor F B→π (m 2 ρ) and propose boundaries for this form factor depending on the CKM matrix element parameters ρ and η. The investigation of B decays requires a knowledge of both the soft and hard interactions which control the dynamics of quarks and gluons. Because the energy involved in B decays covers a large range, from m b down to Λ QCD , it is necessary to describe the phenomenon with accuracy. Recently, the BELLE, BABAR, and CLEO facilities have been providing more and more data which can be compared with theoretical results and hence increase our knowledge in this area. In any phenomenological treatment of the weak decays of hadrons, the starting point is the weak effective Hamiltonian at low energy [1, 2, 3, 4, 5]. It is obtained by integrating out the heavy fields (e.g. the top quark, W and Z bosons) from the Standard Model Lagrangian. It can be written as, H e f f = G F √ 2 ∑ i V CKM C i (µ)O i (µ) , (1) where G F is the Fermi constant, V CKM is the CKM matrix element, C i (µ) are the Wilson coefficients, O i (µ) are the operators entering the Operator Product Expansion and µ represents the renormalization scale. In the present case, since we analyse direct CP