The $\hat{I}\yen$ and $\hat{I}{\yen }^{\prime }$ Leptonic Widths, $a_{\hat{I}}{¼}^b$ and $m_b$ from full lattice QCD

Abstract

We determine the decay rate to leptons of the ground-state $\hat{I}\yen$ meson and its first radial excitation in lattice QCD for the first time. We use radiatively-improved NRQCD 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 $\hat{I}“(\hat{I}\yen \to e^{+}{e}^{-})$ = 1.19(11) keV and $\hat{I}“(\hat{I}{\yen }^{\prime }\to e^{+}{e}^{-})$ = 0.69(9) keV, both in good agreement with experiment. 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 $\ddot{I}ƒ(e^{+}{e}^{-}\to \mathrm{hadrons})$ and calculate the $b$-quark piece of the hadronic vacuum polarisation contribution to the anomalous magnetic moment of the muon, $a_{\hat{I}}{¼}^b=0.271(37)\times 10^{-10}$. Finally we determine the $b$-quark mass, obtaining in the $\overline{MS}$ scheme, ${\overline{m}}_b({\overline{m}}_b,n_f=5)$ = 4.196(23) GeV, the most accurate result from lattice QCD to date.

21 pages, 15 figures