New high-precision <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>b</mml:mi> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>c</mml:mi> </mml:math> , and <mml:math x

We extend an earlier lattice QCD analysis of heavy-quark current-current correlators to obtain new values for the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mover accent="true"> <a:mi>MS</a:mi> <a:mo stretchy="true">¯</a:mo> </a:mover> </a:math> masses of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>b</e:mi> </e:math> , <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>c</g:mi> </g:math> , and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>s</i:mi> </i:math> quarks. The analysis uses gluon configurations from the MILC Collaboration with vacuum polarization contributions from <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>u</k:mi> </k:math> , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>d</m:mi> </m:math> , <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>s</o:mi> </o:math> , and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>c</q:mi> </q:math> quarks ( <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msub> <s:mi>n</s:mi> <s:mi>f</s:mi> </s:msub> <s:mo>=</s:mo> <s:mn>4</s:mn> </s:math> ), and lattice spacings down to 0.032 fm. We find that <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msub> <u:mover accent="true"> <u:mi>m</u:mi> <u:mo stretchy="false">¯</u:mo> </u:mover> <u:mi>b</u:mi> </u:msub> <u:mo stretchy="false">(</u:mo> <u:msub> <u:mover accent="true"> <u:mi>m</u:mi> <u:mo stretchy="false">¯</u:mo> </u:mover> <u:mi>b</u:mi> </u:msub> <u:mo>,</u:mo> <u:msub> <u:mi>n</u:mi> <u:mi>f</u:mi> </u:msub> <u:mo>=</u:mo> <u:mn>5</u:mn> <u:mo stretchy="false">)</u:mo> <u:mo>=</u:mo> <u:mrow> <u:mn>4.1923</u:mn> <u:mo stretchy="false">(</u:mo> <u:mn>63</u:mn> <u:mo stretchy="false">)</u:mo> </u:mrow> <u:mtext> </u:mtext> <u:mtext> </u:mtext> <u:mi>GeV</u:mi> </u:math> , <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:msub> <eb:mover accent="true"> <eb:mi>m</eb:mi> <eb:mo stretchy="false">¯</eb:mo> </eb:mover> <eb:mi>c</eb:mi> </eb:msub> <eb:mo stretchy="false">(</eb:mo> <eb:mn>3</eb:mn> <eb:mtext> </eb:mtext> <eb:mtext> </eb:mtext> <eb:mi>GeV</eb:mi> <eb:mo>,</eb:mo> <eb:msub> <eb:mi>n</eb:mi> <eb:mi>f</eb:mi> </eb:msub> <eb:mo>=</eb:mo> <eb:mn>4</eb:mn> <eb:mo stretchy="false">)</eb:mo> <eb:mo>=</eb:mo> <eb:mspace linebreak="goodbreak"/> <eb:mrow> <eb:mn>0.9813</eb:mn> <eb:mo stretchy="false">(</eb:mo> <eb:mn>34</eb:mn> <eb:mo stretchy="false">)</eb:mo> </eb:mrow> <eb:mtext> </eb:mtext> <eb:mtext> </eb:mtext> <eb:mi>GeV</eb:mi> </eb:math> , and <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"> <nb:msub> <nb:mover accent="true"> <nb:mi>m</nb:mi> <nb:mo stretchy="false">¯</nb:mo> </nb:mover> <nb:mi>s</nb:mi> </nb:msub> <nb:mo stretchy="false">(</nb:mo> <nb:mn>3</nb:mn> <nb:mtext> </nb:mtext> <nb:mtext> </nb:mtext> <nb:mi>GeV</nb:mi> <nb:mo>,</nb:mo> <nb:msub> <nb:mi>n</nb:mi> <nb:mi>f</nb:mi> </nb:msub> <nb:mo>=</nb:mo> <nb:mn>4</nb:mn> <nb:mo stretchy="false">)</nb:mo> <nb:mo>=</nb:mo> <nb:mrow> <nb:mn>83.39</nb:mn> <nb:mo stretchy="false">(</nb:mo> <nb:mn>26</nb:mn> <nb:mo stretchy="false">)</nb:mo> </nb:mrow> <nb:mtext> </nb:mtext> <nb:mtext> </nb:mtext> <nb:mi>MeV</nb:mi> </nb:math> . These results are corrected for QED by including (quenched) QED in the simulations. They are among the most accurate values by any method to date. We give a detailed analysis of finite-lattice-spacing errors that shows why the highly improved staggered quark discretization of the quark action is particularly useful for <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"> <vb:mi>b</vb:mi> </vb:math> -quark simulations even for lattices where <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"> <xb:mi>a</xb:mi> <xb:msub> <xb:mi>m</xb:mi> <xb:mi>b</xb:mi> </xb:msub> <xb:mo>≈</xb:mo> <xb:mn>1</xb:mn> </xb:math> . We also calculate QED and isospin corrections to the (fictitious) <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"> <zb:msub> <zb:mi>η</zb:mi> <zb:mi>s</zb:mi> </zb:msub> </zb:math> -meson mass, which is used to tune <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"> <bc:mi>s</bc:mi> </bc:math> -quark masses in lattice simulations.