Quark-Hadron Duality in Decays of Heavy Hadrons

Quark-hadron duality is often used to calculate rates of hadronic processes. For heavy mesons duality predicts small differences in lifetimes of the B±, B0 and Λb, in sharp disagreement with experimental results. We embark in a study of quark-hadron duality in heavy meson decays. Using the 't Hooft model as a laboratory, we discover violations to duality that scale as one inverse power of the heavy quark mass. In contrast, we find that the heavy quark mass smeared meson and quark widths differ by two inverse powers of the heavy quark mass. In 3 + 1 dimensions an analogous result holds, namely, the heavy meson hadronic decay widths satisfy quark-hadron duality when smeared over the heavy quark mass to an accuracy of order 1/M2