High-precision<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>c</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>b</mml:mi></mml:math>masses, and QCD coupling from current-current correlators in lattice and continuum QCD

Abstract

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: ${m}_{c}(3\text{ }\text{ }\mathrm{GeV},{n}_{f}=4)=0.986(6)\text{ }\text{ }\mathrm{GeV}$, ${\ensuremath{\alpha}}_{\overline{\mathrm{MS}}}({M}_{Z},{n}_{f}=5)=0.1183(7)$, and ${m}_{b}(10\text{ }\text{ }\mathrm{GeV},{n}_{f}=5)=3.617(25)\text{ }\text{ }\mathrm{GeV}$. These are among the most accurate determinations by any method. We check our results using a nonperturbative determination of the mass ratio ${m}_{b}(\ensuremath{\mu},{n}_{f})/{m}_{c}(\ensuremath{\mu},{n}_{f})$; the two methods agree to within our 1% errors and taken together imply ${m}_{b}/{m}_{c}=4.51(4)$. We also update our previous analysis of ${\ensuremath{\alpha}}_{\overline{\mathrm{MS}}}$ from Wilson loops to account for revised values for ${r}_{1}$ and ${r}_{1}/a$, finding a new value ${\ensuremath{\alpha}}_{\overline{\mathrm{MS}}}({M}_{Z},{n}_{f}=5)=0.1184(6)$; and we update our recent values for light-quark masses from the ratio ${m}_{c}/{m}_{s}$. Finally, in the Appendix, we derive a procedure for simplifying and accelerating complicated least-squares fits.