Calculation Of Heavy-flavor Mesons Decay Constants And Phenomenological Studies

The Standard Model (SM) of elementary particle is the most successful theoretical model of the ones describing the strong and electroweak interactions between the fundamental particles. In the SM, the leptonic decay of heavy-flavor meson is a theoretical clean decay mode which is free from hadronic final states interaction and transition form factors. The decay constant fP is a measure of the quark-antiquark attraction inside the bound state. At present about the decay constants of B, BS,D and DS, there are agreement between experiment and theoretical estimations for fB and fD. Recent measurements of the branching fraction for Ds→(?)v deviate from the Standard Model estimation by around 2σ, i.e., theoretical predictions are 2σlower than the experiment. The current update weighted average of HPQCD and Fermilab/MILC is 2.3σlower than the average of measurements. The above discrepancy is sometimes called the 'fDS puzzle" in the literature.In this thesis, we point out a method of calculating fDS in "fDS puzzle". We can find a relation fB/fD=fBS/fDS of the decay constants of B, BS, D and DS according Heavy-Quark Effective theory. Using the values of fB, fBS and fD from Lattice QCD and QCD sum rules, we can obtain the values of fDS with the above equation. Then comparing our results for fDS with Lattice QCD, QCD sum rules and the update experiment, we find that they are higher than both Lattice QCD and the update experiment averages, but in good agreement with QCD sum rule estimations. Next, we use the values of fB+ and fD+ from the update experiment, and fBS from Lattice QCD, we find our results for fDS is lower than Lattice QCD.