Charm mass dependence of the weak hamiltonian in chiral perturbation theory -: art. no. 018

Suppose that the weak interaction hamiltonian of four-flavour SU(4) chiral effective theory is known, for a small charm quark mass m(c). We study how the weak hamiltonian changes as the charm quark mass increases, by integrating it out within chiral perturbation theory to obtain a three-flavour SU(3) chiral theory. We find that the ratio of the SU(3) low-energy constants which mediate DeltaI = 1/2 and DeltaI = 3/2 transitions, increases rather rapidly with m(c), as similar to m(c) ln(1/m(c)). The logarithmic effect originates from "penguin-type" charm loops, and could represent one of the reasons for the DeltaI = 1/2 rule.