The decay constants ${\mathbf{f}}_{\mathbf{D}}$ and ${\mathbf{f}}_{{\mathbf{D}}_{\mathbf{s}}}$ in the continuum limit of ${\mathbf{N}}_{\mathbf{f}}=2+1$ domain wall lattice QCD

Abstract

We present results for the decay constants of the $D$ and $D_s$ mesons computed in lattice QCD with $N_f=2+1$ dynamical flavours. The simulations are based on RBC/UKQCD's domain wall ensembles with both physical and unphysical light-quark masses and lattice spacings in the range 0.11--0.07fm. We employ the domain wall discretisation for all valence quarks. The results in the continuum limit are $f_D=208.7(2.8{)}_{\mathrm{stat}}{\left({}_{-1.8}^{+2.1}\right)}_{\mathrm{sys}}\mathrm{MeV}$ and $f_{D_s}=246.4(1.3{)}_{\mathrm{stat}}{\left({}_{-1.9}^{+1.3}\right)}_{\mathrm{sys}}\mathrm{MeV}$ and $f_{D_s}/f_D=1.1667(77{)}_{\mathrm{stat}}{\left({}_{-43}^{+57}\right)}_{\mathrm{sys}}$. Using these results in a Standard Model analysis we compute the predictions $|V_{cd}|=0.2185(50{)}_{\exp }{\left({}_{-37}^{+35}\right)}_{\mathrm{lat}}$ and $|V_{cs}|=1.011(16{)}_{\exp }{\left({}_{-9}^{+4}\right)}_{\mathrm{lat}}$ for the CKM matrix elements.