Many low-energy, particle-physics experiments seek to reveal new fundamental physics by searching for very rare scattering events on atomic nuclei. The interpretation of their results requires quantifying the non-linear effects of the strong interaction on the spin-independent couplings of this new physics to protons and neutrons. Here we present a fully-controlled, ab-initio calculation of these couplings to the quarks within those constituents of nuclei. We use lattice quantum chromodynamics computations for the four lightest species of quarks and heavy-quark expansions for the remaining two. We determine each of the six quark contributions with an accuracy better than 15%. Our results are especially important for guiding and interpreting experimental searches for our universe's dark matter.

By using numerical stochastic perturbation theory, we carry out a quenched two-loop computation of the improvement coefficient c(A) associated to the isovector axial current. Within the Schrodinger functional formalism, we compute the bare partially conserved axial-vector current quark mass m and fix c(A) by requiring discretization corrections on m to be of order O(a(2)) in the lattice spacing a.

We present lattice QCD results by the Budapest-Marseille-Wuppertal (BMW) Collaboration for the leading-order contribution of the hadron vacuum polarization (LOHVP) to the anomalous magnetic moments of all charged leptons. Calculations are performed with u, d, s and c quarks at their physical masses, in volumes of linear extent larger than 6 fm, and at six values of the lattice spacing, allowing for controlled continuum extrapolations. All connected and disconnected contributions are calculated for not only the muon but also the electron and tau anomalous magnetic moments. Systematic uncertainties are thoroughly discussed and comparisons with other calculations and phenomenological estimates are made.

We compute the leading, strong-interaction contribution to the anomalous magnetic moment of the electron, muon, and tau using lattice quantum chromodynamics (QCD) simulations. Calculations include the effects of u, d, s, and c quarks and are performed directly at the physical values of the quark masses and in volumes of linear extent larger than 6 fm. All connected and disconnected Wick contractions are calculated. Continuum limits are carried out using six lattice spacings. We obtain a_{e}^{LO-HVP}=189.3(2.6)(5.6)×10^{-14}, a_{μ}^{LO-HVP}=711.1(7.5)(17.4)×10^{-10} and a_{τ}^{LO-HVP}=341.0(0.8)(3.2)×10^{-8}, where the first error is statistical and the second is systematic.

We compute the slope and curvature, at vanishing four-momentum transfer squared, of the disconnected contribution of the leading order hadron vacuum polarization function, using lattice QCD. Calculations are performed with $2+1+1$ flavors of staggered fermions directly at the physical values of the quark masses and in volumes of linear extent larger than $6$~fm. The continuum limit is carried out using five different lattice spacings.

The low, euclidean momentum behavior of the hadron vacuum polarization (HVP) is critical for determining, amongst other quantities, the anomalous magnetic moments of the muon. Here we present lattice QCD results for the first two derivatives of the HVP function at vanishing virtuality [1]. Computations are performed with 2+1+1 flavors of staggered quarks around the physical mass point, in volumes of linear extent larger than 6 fm, and at six values of the lattice spacing, allowing for a fully controlled continuum extrapolation.. We further consider possible uncertainties which stem from finite-volume and isospin-breaking effects. After adding to our connected contributions the disconnected terms presented in [2], we compare the resulting derivatives of the full HVP with phenomenological estimates.

We compute the slope and curvature, at vanishing four-momentum transfer squared, of the leading order hadron vacuum polarization function, using lattice QCD. Calculations are performed with 2+1+1 flavors of staggered fermions directly at the physical values of the quark masses and in volumes of linear extent larger than 6fm. The continuum limit is carried out using six different lattice spacings. All connected and disconnected contributions are calculated, up to and including those of the charm.

We present a QCD calculation of the u, d, and s scalar quark contents of nucleons based on 47 lattice ensembles with N_{f}=2+1 dynamical sea quarks, 5 lattice spacings down to 0.054 fm, lattice sizes up to 6 fm, and pion masses down to 120 MeV. Using the Feynman-Hellmann theorem, we obtain f_{ud}^{N}=0.0405(40)(35) and f_{s}^{N}=0.113(45)(40), which translates into σ_{πN}=38(3)(3)  MeV, σ_{sN}=105(41)(37)  MeV, and y_{N}=0.20(8)(8) for the sigma terms and the related ratio, where the first errors are statistical and the second errors are systematic. Using isospin relations, we also compute the individual up and down quark contents of the proton and neutron (results in the main text).

After a detailed analysis of possible sources of systematic uncertainty, ab-initio N f = 2 + 1 results for the up-down and strange quark content -with pion masses all the way down to the physical point -are presented and discussed.

Nucleon sigma terms are quantities that play an important role in various areas: among others, they connect the pion-nucleon and the kaon-nucleon amplitudes to the hadron spectrum and they are also relevant for the direct detection of Dark Matter. We present preliminary results for the up-down and strange sigma terms obtained from $N_f=2+1$ lattice simulations that are performed at five lattice spacings and for pion masses all the way down to its physical value.

We propose an efficient method to compute the so-called residual phase that appears when performing Monte Carlo calculations on a Lefschetz thimble. The method is stochastic and its cost scales linearly with the physical volume, linearly with the number of stochastic estimators and quadratically with the length of the extra dimension along the gradient flow. This is a drastic improvement over previous estimates of the cost of computing the residual phase. We also report on basic tests of correctness and scaling of the code.

We determine the infinite volume coefficients of the perturbative expansions of the self-energies of static sources in the fundamental and adjoint representations in SU(3) gluodynamics to order \alpha^{20} in the strong coupling parameter \alpha. We use numerical stochastic perturbation theory, where we employ a new second order integrator and twisted boundary conditions. The expansions are obtained in lattice regularization with the Wilson action and two different discretizations of the covariant time derivative within the Polyakov loop. Overall, we obtain four different perturbative series. For all of them the high order coefficients display the factorial growth predicted by the conjectured renormalon picture, based on the operator product expansion. This enables us to determine the normalization constants of the leading infrared renormalons of heavy quark and heavy gluino pole masses and to translate these into the modified minimal subtraction scheme (MS). We also estimate the four-loop \beta-function coefficient of the lattice scheme.

By means of Numerical Stochastic Perturbation Theory (NSPT), we calculate the lattice gluon propagator up to three loops of perturbation theory in the limits of infinite volume and vanishing lattice spacing. Based on known anomalous dimensions and a parametrization of both the hypercubic symmetry group H(4) and finite-size effects, we calculate the non-leading-log and non-logarithmic contributions iteratively, starting with the first-loop expression.

This is the first of a series of two papers on the perturbative computation of the ghost and gluon propagators in SU(3) Lattice Gauge Theory. Our final aim is to eventually compare with results from lattice simulations in order to enlight the genuinely non-perturbative content of the latter. By means of Numerical Stochastic Perturbation Theory we compute the ghost propagator in Landau gauge up to three loops. We present results in the infinite volume and a → 0 limits, based on a general strategy that we discuss in detail.

We complete our high-accuracy studies of the lattice ghost propagator in Landau gauge in Numerical Stochastic Perturbation Theory up to three loops. We present a systematic strategy which allows to extract with sufficient precision the non-logarithmic parts of logarithmically divergent quantities as a function of the propagator momentum squared in the infinite-volume and $a\to 0$ limits. We find accurate coincidence with the one-loop result for the ghost self-energy known from standard Lattice Perturbation Theory and improve our previous estimate for the two-loop constant contribution to the ghost self-energy in Landau gauge. Our results for the perturbative ghost propagator are compared with Monte Carlo measurements of the ghost propagator performed by the Berlin Humboldt university group which has used the exponential relation between potentials and gauge links.

Within the framework of the Schr\"odinger Functional (SF), we outline how to combine Numerical Stochastic Perturbation Theory (NSPT) and PCAC relations to determine the two-loop contributions to the improvement coefficients $c_A$ and $c_{SW}$ for Sheikholeslami-Wohlert-Wilson fermions.

We outline a strategy to compute the second-loop contribution to the Csw coefficient of the Sheikoleslami-Wohlert-Wilson fermion action by means of NSPT. We also present preliminary results for higher-order integrators for the Langevin evolution within NSPT. At fixed numerical accuracy, these integrators considerably reduce the required computer-time.

We present higher loop results for the gluon and ghost propagator in Landau gauge on the lattice calculated in numerical stochastic perturbation theory. We make predictions for the perturbative content of those propagators as function of the lattice momenta for finite lattices. To find out their nonperturbative contributions, the logarithmic definition of the gauge fields and the corresponding Faddeev-Popov operator have to be implemented in the Monte Carlo simulations.

Thanks to dimensional reduction, the contributions to the hot QCD pressure coming from socalled soft modes can be studied via an effective three-dimensional theory named Electrostatic QCD (spatial Yang-Mills fields plus an adjoint Higgs scalar).The poor convergence of the perturbative series within EQCD suggests to perform lattice measurements of some of the associated gluon condensates.These turn out, however, to be plagued by large discretization artifacts.We discuss how Numerical Stochastic Perturbation Theory can be exploited to determine the full lattice spacing dependence of one of these condensates up to 4-loop order, and sharpen our tools on a concrete 2-loop example.