Penguin Amplitudes: Charming Contributions *

We briefly introduce the Wick-contraction parametrization of hadronic matrix elements and discuss some applications to B and K physics. In spite of the progresses in non-perturbative techniques, the computation of hadronic matrix elements is still an open problem, particularly when the final state contains more than one meson. In this case, methods based on Euclidean field theory, such as QCD sum rules or lattice QCD, have serious difficulties in computing physical amplitudes [1, 2]. Besides the standard parametrization of hadronic matrix elements in terms of B parameters, it is useful for phenomenological studies to introduce a different parametrization based on the contractions of quark fields inside the matrix element. In the following, we briefly discuss the Wick-contraction parametrization introduced within the framework of non-leptonic B decays in ref. [3]. To be concrete, let us illustrate how this parametrization works in few examples taken from B physics. Consider the Cabibbo-allowed decay B → D̄π. Only two operators of the ∆B = 1 effective weak Hamiltonian contribute to this amplitude, namely 〈D̄π|Q 1 |B 〉 = 〈D̄0π+|b̄γμ(1− γ5)d ūγ (1− γ5)c|B 〉 , 〈D̄π|Q 2 |B 〉 = 〈D̄0π+|b̄γμ(1− γ5)c ūγ (1− γ5)d|B 〉 . (1) ∗Talk given by M. Ciuchini at KAON ‘99, June 21–26, 1999, University of Chicago, Chicago, IL, USA.