Search

The inclusion of heavy quarks, such as the charm quark, poses difficulties in Lattice QCD simulations. These need to be overcome in order to make predictions of hadronic observables including a charm quark such as the decay constants fD and fDs. We first establish the region of validity of simulating heavy quarks with domain wall fermions (DWFs) in a feasibility study. We then carry out dynamical simulations with RBC/UKQCD’s Nf = 2+1f ensembles at three lattice spacings (a −1 = 1.73 − 2.77 GeV) including two physical pion mass ensembles. From this we make a prediction for the decay constants fD and fDs and, using experimental input, the corresponding CKM matrix elements. In the first part of this work we investigate the suitability of domain wall fermions (DWF) as a lattice regularisation for heavy quarks. We generate four quenched QCD gauge ensembles with the tree-level improved Symanzik gauge action and inverse lattice spacings in the range 2.0 − 5.7 GeV. On these we carry out an exploratory study to identify a region in the DWF parameter space that displays minimal cut-off effects. We find this region for the domain wall height M5 = 1.6 allowing for bare heavy quark masses satisfying amh <∼ 0.4, independent of the lattice spacing. Below this limit we maintain desirable features of DWF such as approximate chiral symmetry and O(a)-improvement. Based on this, we carry out a detailed scaling study of the decay constants of heavy-strange pseudoscalar mesons and the dispersion relation of heavy-heavy and heavy-strange pseudoscalar mesons. We find mild a2 discretisation effects for the heavy-strange decay constants and the heavy-strange dispersion relation. The cut-off effects for the heavy-heavy pseudoscalar dispersion relation are somewhat more pronounced. On our ensembles we find a 4 effects for heavy masses beyond the charm quark mass and large momenta (|p| ∼ 1.6 GeV). The findings of the pilot study establish the basis for simulations of charm quarks with domain wall fermions. In the second part of the presented work we simulate heavy-light and heavy-strange pseudoscalar mesons on RBC/UKQCD’s 2 + 1f ensembles with pion masses as low as 139 MeV and inverse lattice spacings ranging from 1.73 GeV to 2.77 GeV. From this data we extract the decay constants fD and fDs. We devise two different fit ansatze to process this data and carry out a full systematic error analysis. We find fD = 208.7(2.8)stat (+2.1−1.8)sys MeV, fDs = 246.4(1.9)stat (+1.3−1.9)sys MeV and fDs/fD = 1.1667(77)stat (+60−46)sys. Finally, using experimental input we extract the corresponding CKM matrix elements. We find |V|cd = 0.2185(50)exp. (+35−37)lat and |V |cs = 1.011(16)exp. (+11− 9)lat where the first error comes from the experimental input and the second from our determination of the decay constants. We compare our results with the existing literature and find good agreement between our central values and competitive errors. This work constitutes the basis of RBC/UKQCD’s wider charm physics program.