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We extend our earlier lattice-QCD analysis of heavy-quark correlators tosmaller lattice spacings and larger masses to obtain new values for the c massand QCD coupling, and, for the first time, values for the b mass:m_c(3GeV,n_f=4)=0.986(6)GeV, alpha_msb(M_Z,n_f=5)=0.1183(7), andm_b(10GeV,n_f=5)=3.617(25)GeV. These are among the most accurate determinationsby any method. We check our results using a nonperturbative determination ofthe mass ratio m_b(mu,n_f)/m_c(mu,n_f); the two methods agree to within our 1%errors and taken together imply m_b/m_c=4.51(4). We also update our previousanalysis of alpha_msb from Wilson loops to account for revised values for r_1and r_1/a, finding a new value alpha_\msb(M_Z,n_f=5)=0.1184(6); and we updateour recent values for light-quark masses from the ratio m_c/m_s. Finally, inthe Appendix, we derive a procedure for simplifying and acceleratingcomplicated least-squares fits.

High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD