Isospin Analysis of Two-body B Decays and Test of Factorization

It is shown that the existing data on two-body B decays, some of them only upper limits, are precise enough to perform an isospin analysis to extract the phase shifts due to final state interaction. Unlike charm decays, no significant final state interaction is observed in decays B → Dπ,Dρ, and Dπ supporting the factorization hypothesis in these decays. From the isospin amplitudes obtained, we extract the ratio a2/a1, where a1 and a2 are the coefficients in the factorized effective Hamiltonian. The idea of factorization has been used for evaluating non-leptonic weak decays ever since Schwinger employed it to show that the ∆I = 3/2 kaon decay rate is consistent with the corresponding semileptonic decay rate [1, 2]. Even though the method was originally thought to be useful only for order of magnitude estimations, it has been extensively applied to heavy hadron decays [3, 4, 5, 6] with results varying from mixed to reasonable. Since factorization is thus far virtually the only way to quantitatively calculate exclusive non-leptonic rates, it is important to test the validity of the hypothesis whenever possible; in fact, it has been a subject of a number of studies [7]. We take the decay B 0 → Dπ as an example which can occur by the 4-fermion operator [5] a1(du)μ(cb) μ + a2(cu)μ(db) μ (1) where the notation is (qq′)μ ≡ qγμ(1−γ5)q and a1,2 are real coefficients which are related to the Wilson coefficients C1 and C2 by a1 = C1 + ξC2 a2 = C2 + ξC1. (2)