Lifetime Differences of Charmed Mesons in the ’t Hooft Model

In this report I will be showing how to use meson wave functions and masses to find the decay width difference between the two mass eigenstates of the D0 meson. Due to a large coupling at small energies in QCD, perturbation theory unfortunately does us no good. However, there does exist a model that attempts to keep as much of the QCD Lagrangian as possible. The model was developed by Gerard t’ Hooft and is, not surprisingly, called the t’ Hooft model. In this study, we explore the different solutions to the ’t Hooft equation for bound state mesons. This model is very useful in that we are able to compute the masses and wave functions for all the mesons necessary to calculate the decay width difference (and therefore the lifetime difference) of the two mass eigenstates of the D0 meson. We hope to show that the width difference is proportional to the square of the mass of the strange quark.