An accurate calculation of the nucleon axial charge with lattice QCD

We report on a lattice QCD calculation of the nucleon axial charge, $g_A$, using M\"{o}bius Domain-Wall fermions solved on the dynamical $N_f=2+1+1$ HISQ ensembles after they are smeared using the gradient-flow algorithm. The calculation is performed with three pion masses, $m_\pi\sim\{310,220,130\}$ MeV. Three lattice spacings ($a\sim\{0.15,0.12,0.09\}$ fm) are used with the heaviest pion mass, while the coarsest two spacings are used on the middle pion mass and only the coarsest spacing is used with the near physical pion mass. On the $m_\pi\sim220$ MeV, $a\sim0.12$ fm point, a dedicated volume study is performed with $m_\pi L \sim \{3.22,4.29,5.36\}$. Using a new strategy motivated by the Feynman-Hellmann Theorem, we achieve a precise determination of $g_A$ with relatively low statistics, and demonstrable control over the excited state, continuum, infinite volume and chiral extrapolation systematic uncertainties, the latter of which remains the dominant uncertainty. Our final determination at 2.6\% total uncertainty is $g_A = 1.278(21)(26)$, with the first uncertainty including statistical and systematic uncertainties from fitting and the second including model selection systematics related to the chiral and continuum extrapolation. The largest reduction of the second uncertainty will come from a greater number of pion mass points as well as more precise lattice QCD results near the physical pion mass.Comment: 17 pages + 11 pages of references and appendices. 15 figures. Interested readers can download the Python analysis scripts and an hdf5 data file at https://github.com/callat-qcd/project_gA_v

Production of Propylene from 1-Butene on Highly Active “Bi-Functional Single Active Site” Catalyst: Tungsten Carbene-Hydride Supported on Alumina

1-Butene is transformed in a continuous flow reactor over tungsten hydrides precursor W–H/Al₂O₃, <b>1</b>, giving a promising yield into propylene at 150 °C and different pressures. Tungsten carbene-hydride single active site operates as a “bi-functional catalyst” through 1-butene isomerization on W-hydride and 1-butene/2-butenes cross-metathesis on W-carbene. This active moiety is generated in situ at the initiation steps by insertion of 1-butene on tungsten hydrides precursor W–H/Al₂O₃, <b>1</b> followed by α-H and β-H abstraction