A precise determination of the charm quark's mass in quenched QCD

Abstract

We present a lattice determination of the charm quark's mass, using the mass of the Ds meson as experimental input. All errors are under control with the exception of the quenched approximation. Setting the scale with FK = 160 MeV, our final result for the renormalization group invariant (RGI) quark mass is Mc = 1.654(45) GeV, which translates to m̄c̄MS(m̄c) = 1.301(34) GeV for the running mass in the MS̄ scheme. A 6 percent increase of the RGI quark mass is observed when the scale is set by the nucleon mass. This is a typical quenched scale ambiguity, which is reduced to about 3 percent for m̄c(m̄c), and to 4 percent for the mass ratio Mc/Ms. In contrast, the mass splitting mDs+ - mDs changes from 117(11) MeV to 94(11) MeV, which is significantly smaller than the experimental value of 144 MeV. © SISSA/ISAS 2003.