The axial coupling of the nucleon from Quantum Chromodynamics*

The axial coupling of the nucleon, $g_A$, is a fundamental property of neutrons and protons. The long-range nuclear force between nucleons and the $\beta$-decay rate of a free neutron both depend on $g_A^2$. This coupling therefore underpins all of low-energy nuclear physics, controlling, for example, the primordial composition of the universe. While the value of $g_A$ is, in principle, determined by the fundamental theory of nuclear strong interactions, Quantum Chromodynamics (QCD), it is daunting to compute, as QCD is non-perturbative and has evaded an analytic solution. Lattice QCD provides a rigorous, non-perturbative definition of the theory through a discretised formulation which can be numerically implemented. Using an innovative computational method, we resolve the two outstanding challenges identified by the lattice QCD community for determining $g_A$: we demonstrably control excited state lattice artefacts and are able to utilise exponentially more precise numerical data resulting in the determination $g_A^{QCD} = 1.275\pm 0.012$, compatible with the experimentally measured value and with unprecedented precision of 0.95\%. Prior to the work presented here, it was estimated, using standard methods of the field, that a 2\% precision would only be achievable with the next-generation of leadership computing facilities by 2020. This calculation signals a new era of precision lattice QCD applications to high-impact experimental searches for physics beyond the Standard Model in nuclear environments.