Light-quark loops in image Original Research Article

We present a comprehensive analysis of the contributions to image decays not described by the leading dimension-six effective Hamiltonian. These include both dimension-eight four-fermion operators generated at the charm scale, and genuine long-distance contributions which can be described within the framework of chiral perturbation theory. We show that a consistent treatment of the latter contributions, which turn out to be the dominant effect, requires the introduction of new chiral operators already at image. Using this new chiral Lagrangian, we analyze the long-distance structure of image amplitudes at the one-loop level, and discuss the role of the dimension-eight operators in the matching between short- and long-distance components. From the numerical point of view, we find that these image corrections enhance the SM prediction of image by about ≈6%.