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.

We present a determination of nucleon-nucleon scattering phase shifts for ≥ 0. The S, P, D and F phase shifts for both the spin-triplet and spin-singlet channels are computed with lattice Quantum ChromoDynamics. For > 0, this is the first lattice QCD calculation using the Lüscher finitevolume formalism. This required the design and implementation of novel lattice methods involving displaced sources and momentum-space cubic sinks. To demonstrate the utility of our approach, the calculations were performed in the SU(3)-flavor limit where the light quark masses have been tuned to the physical strange quark mass, corresponding to mπ=mK ≈800 MeV. In this work, we have assumed that only the lowest partial waves contribute to each channel, ignoring the unphysical partial wave mixing that arises within the finite-volume formalism. This assumption is only valid for sufficiently low energies; we present evidence that it holds for our study using two different channels. Two spatial volumes of V ≈ (3.5fm) 3 and V ≈ (4.6fm) 3 were used. The finite-volume spectrum is extracted from the exponential falloff of the correlation functions. Said spectrum is mapped onto the infinite volume phase shifts using the generalization of the Lüscher formalism for two-nucleon systems. T + 1 n (t/b) J = 1, = 2, S = 1 J = 3, = 2, S = 1 J = 1, = 0, S = 1 J = 1, = 0, S = 1, |r| = 0 J = 1, = 0, S = 1 J = 1, = 0, S = 1, |r| = 0 FIG. 1: Effective masses for the energy splitting, ∆En = 2 m 2 N + q 2 n − 2mN , in lattice units for the second excited state in the spin triplet T + 1 channel at L/b = 32, showing operators having different [J S] labels (Eq.(1)): J = 1, = 2, S = 1 (black), J = 3, = 2, S = 1 (blue), J = 1, = 0, S = 1 (red), J = 1, = 0, S = 1, r = 0 (green). The dashed horizontal lines represent the energy levels of the nearest non-interacting two-nucleon states.

One intriguing beyond-the-Standard-Model particle is the QCD axion, which could simultaneously provide a solution to the Strong CP problem and account for some, if not all, of the dark matter density in the universe. This particle is a pseudo-Nambu-Goldstone boson of the conjectured Peccei-Quinn (PQ) symmetry of the Standard Model. Its mass and interactions are suppressed by a heavy symmetry breaking scale, f a , whose value is roughly greater than 10 9 GeV (or, conversely, the axion mass, m a , is roughly less than 10 4 µeV). The density of axions in the universe, which cannot exceed the relic dark matter density and is a quantity of great interest in axion experiments like ADMX, is a result of the early-universe interplay between cosmological evolution and the axion mass as a function of temperature. The latter quantity is proportional to the second derivative of the temperature-dependent QCD free energy with respect to the CP-violating phase, θ. However, this quantity is generically non-perturbative and previous calculations have only employed instanton models at the high temperatures of interest (roughly 1 GeV). In this and future works, we aim to calculate the temperature-dependent axion mass at small θ from firstprinciple lattice calculations, with controlled statistical and systematic errors. Once calculated, this temperature-dependent axion mass is input for the classical evolution equations of the axion density of the universe, which is required to be less than or equal to the dark matter density. Due to a variety of lattice systematic effects at the very high temperatures required, we perform a calculation of the leading small-θ cumulant of the theta vacua on large volume lattices for SU(3) Yang-Mills with high statistics as a first proof of concept, before attempting a full QCD calculation in the future. From these pure glue results, the misalignment mechanism yields the axion mass bound m a ≥ (14.6 ± 0.1) µeV when PQ-breaking occurs after inflation.

We perform a systematic, large-scale lattice simulation of D0-brane quantum mechanics. The large-N and continuum limits of the gauge theory are taken for the first time at various temperatures 0.4 ≤ T ≤ 1.0. As a way to test the gauge/gravity duality conjecture we compute the internal energy of the black hole as a function of the temperature directly from the gauge theory. We obtain a leading behavior that is compatible with the supergravity result E/N 2 = 7.41T 14/5 : the coefficient is estimated to be 7.4 ± 0.5 when the exponent is fixed and stringy corrections are included. This is the first confirmation of the supergravity prediction for the internal energy of a black hole at finite temperature coming directly from the dual gauge theory. We also constrain stringy corrections to the internal energy.

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-...

We study the thermodynamics of the 'ungauged' D0-brane matrix model by Monte Carlo simulation. Our results appear to be consistent with the conjecture by Maldacena and Milekhin. In this work, in order to test the Maldacena-Milekhin conjecture, we perform Monte Carlo calculations for the ungauged matrix model at small temperatures. First, we introduce the gauged and ungauged D0-brane matrix models in Sec. 2. The dual gravity descriptions are reviewed in Sec. 2.1. The lattice regularization used for the simulations is explained in Sec. 2.2. In Sec. 3, we study the bosonic analogue of the ungauged D0-brane matrix model numerically. Although the bosonic models do not admit dual gravity descriptions, they illuminate the numerical approach we have adopted. Sec. 4 is the main part of this paper, which tests the Maldacena-Milekhin conjecture. Gauged and ungauged D0-brane matrix modelThe Euclidean action of the original, 'gauged' D0-brane matrix model [3,[8][9][10] is given bywhere X M (M = 1, 2, · · · , 9) are N × N Hermitian matrices and D t X M is the covariant derivative given byBy doing so, the circumference of the Euclidean circle β is the inverse temperature: β = 1/T . The gamma matrices γ M αβ (M = 1, 2, · · · , 9) are the 16 × 16 left-handed part of the gamma matrices in (9 + 1)-dimensions. ψ α (α = 1, 2, · · · , 16) are N × N real fermionic matrices. This theory is the dimensional reduction of 4D N = 4 super Yang-Mills theory to (0 + 1)dimensions. We often set the 't Hooft coupling λ = g 2 Y M N to one, without losing generality. Equivalently, all dimensionful quantities are measured in units of the 't Hooft coupling; for example the temperature T actually refers to the dimensionless combinationT ≡ λ −1/3 T . It also means the energy scale is related to the strength of the interaction: low temperature (small T ) and strong coupling (large λ) are equivalent, in the sense thatT is small. In the same manner, long distance is strong coupling.The action and partition function are given byThe 'ungauged' theory is defined simply by dropping the gauge field A t , asIn the Hamiltonian language, the ungauging procedure we just described is equivalent to removing the gauge singlet constraint.

Is the evaporation of a black hole described by a unitary theory? In order to shed light on this question -especially aspects of this question such as a black hole's negative specific heat-we consider the real-time dynamics of a solitonic object in matrix quantum mechanics, which can be interpreted as a black hole (black zero-brane) via holography. We point out that the chaotic nature of the system combined with the flat directions of its potential naturally leads to the emission of D0-branes from the black brane, which is suppressed in the large N limit. Simple arguments show that the black zero-brane, like the Schwarzschild black hole, has negative specific heat, in the sense that the temperature goes up when it evaporates by emitting D0-branes. While the largest Lyapunov exponent grows during the evaporation, the Kolmogorov-Sinai entropy decreases. These are consequences of the generic properties of matrix models and gauge theory. Based on these results, we give a possible geometric interpretation of the eigenvalue distribution of matrices in terms of gravity.Applying the same argument in the M-theory parameter region, we provide a scenario to derive the Hawking radiation of massless particles from the Schwarzschild black hole. Finally, we suggest that by adding a fraction of the quantum effects to the classical theory, we can obtain a matrix model whose classical time evolution mimics the entire life of the black brane, from its formation to the evaporation.

We calculate the spin-independent scattering cross section for direct detection that results from the electromagnetic polarizability of a composite scalar baryon dark matter candidate -"Stealth Dark Matter", based on a dark SU(4) confining gauge theory. In the nonrelativistic limit, electromagnetic polarizability proceeds through a dimension-7 interaction leading to a very small scattering cross section for dark matter with weak-scale masses. This represents a lower bound on the scattering cross section for composite dark matter theories with electromagnetically charged constituents. We carry out lattice calculations of the polarizability for the lightest baryons in SU(3) and SU(4) gauge theories using the background field method on quenched configurations. We find the polarizabilities of SU(3) and SU(4) to be comparable (within about 50%) normalized to the baryon mass, which is suggestive for extensions to larger SU(N) groups. The resulting scattering cross sections with a xenon target are shown to be potentially detectable in the dark matter mass range of about 200-700 GeV, where the lower bound is from the existing LUX constraint while the upper bound is the coherent neutrino background. Significant uncertainties in the cross section remain due to the more complicated interaction of the polarizablity operator with nuclear structure, however the steep dependence on the dark matter mass, 1/m 6 B , suggests the observable dark matter mass range is not appreciably modified. We briefly highlight collider searches for the mesons in the theory as well as the indirect astrophysical effects that may also provide excellent probes of stealth dark matter.