ϒ and ϒ ′ leptonic widths, a μ b , and m b from full lattice QCD
2015
We determine the decay rate to leptons of the ground-state ϒ meson and its first radial excitation in lattice
QCD for the first time. We use radiatively improved nonrelativistic QCD for the b quarks and include u, d,
s and c quarks in the sea with u=d masses down to their physical values. We find Γðϒ → eþe−Þ ¼
1.19ð11Þ keV and Γðϒ0 → eþe−Þ ¼ 0.69ð9Þ keV, both in good agreement with experimental results. The
decay constants we obtain are included in a summary plot of meson decay constants from lattice QCD
given in the Conclusions. We also test time moments of the vector current-current correlator against values
determined from the b-quark contribution to σðeþe− → hadronsÞ and calculate the b-quark piece of the
hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon,
ab
μ ¼ 0.271ð37Þ × 10−10. Finally we determine the b-quark mass, obtaining in the MS scheme, ¯
m¯ bðm¯ b; nf ¼ 5Þ ¼ 4.196ð23Þ GeV, the most accurate result from lattice QCD to date.
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