The axial coupling of the nucleon, gA, is the strength of its coupling to the weak axial current of the standard model of particle physics, in much the same way as the electric charge is the strength of the coupling to the electromagnetic current. This axial coupling dictates the rate at which neutrons decay to protons, the strength of the attractive long-range force between nucleons and other features of nuclear physics. Precision tests of the standard model in nuclear environments require a quantitative understanding of nuclear physics that is rooted in quantum chromodynamics, a pillar of the standard model. The importance of gA makes it a benchmark quantity to determine theoretically—a difficult task because quantum chromodynamics is non-perturbative, precluding known analytical methods. Lattice quantum chromodynamics provides a rigorous, non-perturbative definition of quantum chromodynamics that can be implemented numerically. It has been estimated that a precision of two per cent would be possible by 2020 if two challenges are overcome1,2: contamination of gA from excited states must be controlled in the calculations and statistical precision must be improved markedly2,3,4,5,6,7,8,9,10. Here we use an unconventional method11 inspired by the Feynman–Hellmann theorem that overcomes these challenges. We calculate a gA value of 1.271 ± 0.013, which has a precision of about one per cent.
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We thank C. Bernard, A. Bernstein, P. J. Bickel, C. Detar, A. X. El-Khadra, W. Haxton, Y. Hsia, V. Koch, A. S. Kronfeld, W. T. Lee, G. P. Lepage, E. Mereghetti, G. Miller, A. E. Raftery, D. Toussaint and F. Yuan for discussions. We thank E. Mereghetti for the updated Extended Data Fig. 729. We thank the MILC Collaboration for providing their highly improved staggered quark configurations30 without restriction. Computer time was awarded to CalLat (2016) by the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) programme, as well as by the Lawrence Livermore National Laboratory (LLNL) Multiprogrammatic and Institutional Computing programme through a Tier-1 Grand Challenge award. This research used the NVIDIA GPU-accelerated Titan supercomputer at the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the US Department of Energy under contract number DE-AC05-00OR22725, the GPU-enabled Surface and RZHasGPU clusters, and Vulcan, a BG/Q supercomputer, all at LLNL. This work was supported by the NVIDIA Corporation (M.A.C.), the DFG and the NSFC Sino-German CRC110 (E.B.), an LBNL LDRD (A.W.-L.), the RIKEN Special Postdoctoral Researcher Program (E.R.), the Leverhulme Trust (N.G.), the US Department of Energy, Office of Science: Office of Nuclear Physics (E.B., C.B., D.A.B., C.C.C., T.K., C.J.M., H.M.-C., A.N.N., E.R., B.J., K.O., P.V. and A.W.-L.); Office of Advanced Scientific Computing (E.B., B.J., T.K. and A.W.-L.); Nuclear Physics Double Beta Decay Topical Collaboration (D.A.B., H.M.-C. and A.W.-L.); and the DOE Early Career Award Program (D.A.B., C.C.C., H.M.-C. and A.W.-L.). This work (E.B., E.R. and P.V.) was performed under the auspices of the US Department of Energy by LLNL under contract number DE-AC52-07NA27344. Part of this work was performed at the Kavli Institute for Theoretical Physics, supported by NSF grant number PHY-1748958.