Charmed and $\varphi$ meson decay constants from 2+1-flavor lattice QCD

Abstract

On a lattice with 2+1-flavor dynamical domain-wall fermions at the physical pion mass, we calculate the decay constants of $D_s^{(\ast )}$, $D^{(\ast )}$ and $\varphi$. The lattice size is $48^3\times 96$, which corresponds to a spatial extension of $\sim 5.5$ fm with the lattice spacing $a\approx 0.114$ fm. For the valence light, strange and charm quarks, we use overlap fermions at several mass points close to their physical values. Our results at the physical point are $f_D=213(5)$ MeV, $f_{D_s}=249(7)$ MeV, $f_{D^{\ast }}=234(6)$ MeV, $f_{D_s^{\ast }}=274(7)$ MeV, and $f_{\varphi }=241(9)$ MeV. The couplings of $D^{\ast }$ and $D_s^{\ast }$ to the tensor current ($f_V^T$) can be derived, respectively, from the ratios $f_{D^{\ast }}^T/f_{D^{\ast }}=0.91(4)$ and $f_{D_s^{\ast }}^T/f_{D_s^{\ast }}=0.92(4)$, which are the first lattice QCD results. We also obtain the ratios $f_{D^{\ast }}/f_D=1.10(3)$ and $f_{D_s^{\ast }}/f_{D_s}=1.10(4)$, which reflect the size of heavy quark symmetry breaking in charmed mesons. The ratios $f_{D_s}/f_D=1.16(3)$ and $f_{D_s^{\ast }}/f_{D^{\ast }}=1.17(3)$ can be taken as a measure of SU(3) flavor symmetry breaking.

Comments: 20 pages, 5 figures, 10 tables; references and acknowledgements added; minor changes, version to be published in Chinese Physics C