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

TL;DR

This study uses 2+1-flavor lattice QCD with domain-wall and overlap fermions to precisely calculate decay constants of various charmed and $$ mesons, providing new lattice results for tensor current couplings and symmetry breaking ratios.

Contribution

First lattice QCD calculation of $D^*$ and $D_s^*$ tensor decay constants and detailed ratios reflecting heavy quark and SU(3) flavor symmetry breaking.

Findings

Decay constants: $f_D=213(5)$ MeV, $f_{D_s}=249(7)$ MeV, $f_{D^*}=234(6)$ MeV, $f_{D_s^*}=274(7)$ MeV, $f_=241(9)$ MeV.

First lattice results for $f_{D^*}^T/f_{D^*}$ and $f_{D_s^*}^T/f_{D_s^*}$ ratios.

Heavy quark symmetry breaking ratios: $f_{D^*}/f_D=1.10(3)$, $f_{D_s^*}/f_{D_s}=1.10(4)$.

Abstract

On a lattice with 2+1-flavor dynamical domain-wall fermions at the physical pion mass, we calculate the decay constants of $D_{s}^{(*)}$, $D^{(*)}$ and $\phi$. The lattice size is $48^3\times96$, which corresponds to a spatial extension of $\sim5.5$ 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, $f_{D^*}=234(6)$ MeV, $f_{D_s^*}=274(7)$ MeV, and $f_\phi=241(9)$ MeV. The couplings of $D^*$ and $D_s^*$ to the tensor current ($f_V^T$) can be derived, respectively, from the ratios $f_{D^*}^T/f_{D^*}=0.91(4)$ and $f_{D_s^*}^T/f_{D_s^*}=0.92(4)$, which are the first lattice QCD results. We also obtain the ratios $f_{D^*}/f_D=1.10(3)$ and $f_{D_s^*}/f_{D_s}=1.10(4)$, which reflect the size of heavy quark symmetry breaking in charmed mesons. The ratios $f_{D_s}/f_{D}=1.16(3)$ and $f_{D_s^*}/f_{D^*}=1.17(3)$ can be taken as a measure of SU(3) flavor symmetry breaking.