Determination of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mover accent="true"><mml:mi>m</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mi>b</mml:mi></mml:msub><mml:mo stretchy="false">/</mml:mo><mml:msub><mml:mover accent="true"><mml:mi>m</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mi>c</mml:mi></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mover accent="true"><mml:mi>m</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mi>b</mml:mi></mml:msub></mml:math> from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>n</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math> lattice <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>QCD</mml:mi><mml:mo>+</mml:mo><mml:mtext>QED</mml:mtext></mml:mrow></mml:math>
D. Hatton, C. T. H. Davies, J. Koponen, G. Peter Lepage, Andrew Lytle
Abstract
We extend HPQCD's earlier ${n}_{f}=2+1+1$ lattice-QCD analysis of the ratio of $\overline{\mathrm{MS}}$ masses of the $b$ and $c$ quark to include results from finer lattices (down to 0.03 fm) and a new calculation of QED contributions to the mass ratio. We find that ${\overline{m}}_{b}(\ensuremath{\mu})/{\overline{m}}_{c}(\ensuremath{\mu})=4.586(12)$ at renormalization scale $\ensuremath{\mu}=3\text{ }\text{ }\mathrm{GeV}$. This result is nonperturbative. Combining it with HPQCD's recent lattice $\mathrm{QCD}+\mathrm{QED}$ determination of ${\overline{m}}_{c}(3\text{ }\text{ }\mathrm{GeV})$ gives a new value for the $b$-quark mass: ${\overline{m}}_{b}(3\text{ }\text{ }\mathrm{GeV})=4.513(26)\text{ }\text{ }\mathrm{GeV}$. The $b$-mass corresponds to ${\overline{m}}_{b}({\overline{m}}_{b},{n}_{f}=5)=4.202(21)\text{ }\text{ }\mathrm{GeV}$. These results are the first based on simulations that include QED.