The axial coupling of the nucleon, g, 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 g 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 overcome: contamination of g from excited states must be controlled in the calculations and statistical precision must be improved markedly. Here we use an unconventional method inspired by the Feynman-Hellmann theorem that overcomes these challenges. We calculate a g value of 1.271 ± 0.013, which has a precision of about one per cent.

Observation of neutrinoless double beta decay, a lepton number violating process that has been proposed to clarify the nature of neutrino masses, has spawned an enormous world-wide experimental effort. Relating nuclear decay rates to high-energy, beyond the Standard Model (BSM) physics requires detailed knowledge of non-perturbative QCD effects. Using lattice QCD, we compute the necessary matrix elements of short-range operators, which arise due to heavy BSM mediators, that contribute to this decay via the leading order π − → π + exchange diagrams. Utilizing our result and taking advantage of effective field theory methods will allow for model-independent calculations of the relevant two-nucleon decay, which may then be used as input for nuclear many-body calculations of the relevant experimental decays. Contributions from short-range operators may prove to be equally important to, or even more important than, those from long-range Majorana neutrino exchange.Introduction.-Neutrinoless double beta decay (0νββ) is a process that, if observed, would reveal violations of symmetries fundamental to the Standard Model, and would guarantee that neutrinos have nonzero Majorana mass [1, 2]. Such decays can probe physics beyond the electroweak scale and expose a source of leptonnumber (L) violation which may explain the observed matter-antimatter asymmetry in the universe [3,4]. Existing and planned experiments will constrain this novel nuclear decay [5][6][7][8][9][10][11][12][13][14][15][16], but the interpretation of the resulting decay rates or limits as constraints on new physics poses a tremendous theoretical challenge.The most widely discussed mechanism for 0νββ is that of a light Majorana neutrino, which can propagate a long distance within a nucleus. However, if the mechanism involves a heavy scale, Λ ββ , the resulting L-violating process can be short-ranged. While naïvely short-range operators are suppressed compared to long-range interactions due to the heavy mediator propagator, in the case of 0νββ, the long-range interaction requires a helicity flip and is proportional to the mass of the light neutrino. In a standard seesaw scenario [17][18][19][20][21], this light neutrino mass is similarly suppressed by the same large mass scale, so the relative importance of long-versus short-range contributions is dependent upon the particle physics model under consideration and in general cannot be determined until the nuclear matrix elements for both types of processes are computed.Both long-and short-range mechanisms present substantial theoretical challenges if we hope to connect high energy physics with experimentally observed decay rates. The former case is difficult because one must understand long-distance nuclear correlations. In the latter case the short-distance physics is masked by QCD effects, requiring non-perturbative methods to match few-nucleon matrix elements to Standard Model operators.Effective field theory (EFT) arguments show that at leading order (LO) in the Standard Model, there are nine local four-...