Estimates of Flavoured Scalar Production in B -decays

Estimates are presented for the branching ratios of several two-particle B-meson decays into flavoured scalar mesons. It seems that there are no estimates of B-meson decays into scalar mesons. The purpose of this short note is to present such estimates. As will be shown, some two-particle decays of B-mesons into scalar mesons have sufficiently large branchings to be of current interest. 1. Having in mind B → K̄o(1430)π− and B → K̄π decays, the main contributions in the factorization approximation which looks reliable for these decays, and in the standard notation, come from two terms in the effective Hamiltonian: Heff = GF √ 2 (−VtbV ∗ ts) { a4 [ s̄γμ(1 + γ5)d ]⊗ [ d̄γμ(1 + γ5)b ]− − 2 a6 [ s̄(1− γ5)d ]⊗ [ d̄(1 + γ5)b ] } . (1) The effective coefficients ai in (1) can be expressed either explicitly through the original coefficients Ci(μ) of the effective Hamiltonian [1], plus perturbative one loop corrections: Ci(μ) → C i ; this cancels the main scale dependence of Ci(μ), see e.g. [2] and references therein. Or they can be calculated in ”the QCD improved factorization approximation” [3], which is not much different.