Bottomonium precision tests from full lattice QCD: hyperfine splitting, $Υ$ leptonic width and $b$ quark contribution to $e^+e^- \rightarrow$ hadrons

Abstract

We calculate the mass difference between the Υ and η b and the Υ leptonic width from lattice QCD using the Highly Improved Staggered Quark formalism for the b quark and including u, d, s and c quarks in the sea. We have results for lattices with lattice spacing as low as 0.03 fm and multiple heavy quark masses, enabling us to map out the heavy quark mass dependence and determine values at the b quark mass. Our results are: MΥ − Mη b = 57.5(2.3)(1.0) MeV (where the second uncertainty comes from neglect of quark-line disconnected correlation functions) and decay constants, fη b = 724(12) MeV and fΥ = 677.2(9.7) MeV, giving Γ(Υ → e + e − ) = 1.292(37)(3) keV. The hyperfine splitting and leptonic width are both in good agreement with experiment, and provide the most accurate lattice QCD results to date for these quantities by some margin. At the same time results for the time moments of the vector-vector correlation function can be compared to values for the b quark contribution to σ(e + e − → hadrons) determined from experiment. Moments 4-10 provide a 2% test of QCD and yield a b quark contribution to the anomalous magnetic moment of the muon of 0.300(15)×10 −10 . Our results, covering a range of heavy quark masses, may also be useful to constrain QCD-like composite theories for beyond the Standard Model physics.

Charm-quark mass effects in NRQCD matching coefficients and the leptonic decay of the $Υ(1S)$ meson

“…We oberserve a notable discrepancy to the experimental result which is given by Γ(Υ(1S) → e + e − )| exp = 1.340 (18) keV. We also want to mention a recent lattice evaluation [37] where the value Γ(Υ(1S) → e + e − ) = 1.292 (37)(3) keV has been reported.…”

Determination of m¯b/m¯c and Hatton1, Davies2, Koponen3 et al. 2021Phys. Rev. DSelf Cite140230View full textAdd to dashboardCite

“…This is expected to be the dominant contribution in O(α QED ) and is much less costly to analyze. The techniques we use for introducing QED into simulations are standard and are described in [5,10]. The R factor for the c mass (Eq.…”

“…This relationship between the MS and lattice quark masses is nonperturbative and independent of the MS renormalization scale µ. Pseudoscalar and vector meson masses from our simulations are listed in Table II for a variety of (valence) heavyquark masses, ranging on the finest lattices (Sets 5 and 6) approximately from the c mass to the b mass. The analysis methods for extracting these masses (and most of the results) come from [5,10].…”

“…This correction should be small because of heavy-quark decoupling [4] -the momentum transfers in the heavy-quark mesons are too small to produce cc pairs efficiently. We include the correction (10). The lines, which vary in thickness, show results from the best-fit values for the functions f P/V hh ; the line thickness shows the 1σ uncertainty in these functions.…”

“…Lattice (without QED) results for m h /mc plotted versus the hh meson masses. Values for m h /mc are corrected as in Eq (10)…”