High-precisioncandbmasses, and QCD coupling from current-current correlators in lattice and continuum QCD

We extend our earlier lattice-QCD analysis of heavy-quark correlators to smaller lattice spacings and larger masses to obtain new values for the c mass and QCD coupling, and, for the first time, values for the b mass: mc(3 GeV,nf=4)=0.986(6) GeV, αMS̄(MZ,nf=5)=0.1183(7), and mb(10 GeV,nf=5)=3.617(25) GeV. These are among the most accurate determinations by any method. We check our results using a nonperturbative determination of the mass ratio mb(μ,nf)/mc(μ,nf); the two methods agree to within our 1% errors and taken together imply mb/mc=4.51(4). We also update our previous analysis of αMS̄ from Wilson loops to account for revised values for r₁ and r₁/a, finding a new value αMS̄(MZ,nf=5)=0.1184(6); and we update our recent values for light-quark masses from the ratio mc/mₛ. Finally, in the Appendix, we derive a procedure for simplifying and accelerating complicated least-squares fits.