The decay constants fDs and fD+ form lattice QCD

Recent calculations of the decay constants in lattice QCD are reviewed and compared to experiment. The decay constants are tabulated in Table 2 and plotted in Figure 2. The most precise fDs value is from HPQCD. It is about 2σ higher than their previous result. The change is due to a more precise determination of the lattice spacing and better tuning of the quark masses. They have updated fD+ using the new fDs and their older fDs/fD+ ratio which is expected to be less sensitive to mistuning of the lattice spacing and masses. The preliminary FNAL/MILC fDs value is about 1.4σ higher than the HPQCD result but with a larger error. The fD+ values, however, are in better agreement. FNAL/MILC expect to finalize their results once the charm quark mass tuning is complete. The two flavor ETM fD+ value is about 1.6σ lower than the HPQCD value while fDs is in better agreement. It is not clear how much of the difference is from neglecting the strange sea quark, given the errors. Lattice and experiment differ most significantly for fDs. Figure 3 shows Kronfeld's (updated) history of fDs. The yellow bands depict the evolution of the experimental average while the three-flavor lattice average is shown in grey. The right-hand scale and green lines show the differences in sigmas. The 3.8σ discrepancy around t ∼ 2 provoked the 'fDs puzzle'. That discrepancy has now shrunk to 1.6σ. Future lattice and experiment will be decisive.