Charming Decays And How To Calculate Them

Abstract

In this work we focus on the phenomenology of the charm system, more specifically the description of D-mixing and the lifetimes of the $D^0$, $D^+$ and $D_s^+$ meson. We start with a brief introduction of flavour physics and the role the charm quark plays in the Standard Model (SM). Then, we focus on more specialised techniques like the Weak Effective Theory (WET) and the Heavy Quark Effective theory (HQET) as well as the Heavy Quark Expansion (HQE), a framework built to express inclusive decays of heavy hadrons as a series of local operators. We continue with the description of the neutral meson mixing system in general before focusing on the $D^0$ case and discuss the peculiarities arising that make its theoretical description more difficult than the B system. We propose two different methods of tackling these issues and show that we can get results in the ballpark of the experimental measurements. Then, we move to the calculations of the D mesons lifetimes. Including the recently calculated Darwin operator contribution and $D_s^+$ Bag parameters, we present updated results for the total and semi-leptonic decay rates and their ratios. We conclude that after comparing our results with experimental measurements by the LHCb, Belle II and BESIII collaborations we can describe inclusive decays of charm mesons in the HQE framework albeit with large theoretical uncertainties. Finally, we suggest how this work could continue in the future and what new measurements would be needed to get more precise results