High Energy Physics Lattice

We discuss a gauged XY model aθ-term on an arbitrary lattice in 1+1 dimensions, and show that the theory reduces exactly to the 2d Ising model on the dual lattice in the limit of the strong gauge coupling, provided that the topological term is defined via the Villain action. We discuss the phase diagram by comparing the strong and weak gauge coupling limits, and perform Monte Carlo simulations at intermediate couplings. We generalize the duality to higher-dimensional Ising models using higher-form U(1) gauge field analogues.

Isospin-1/2D?scattering amplitudes are computed using lattice QCD, working in a single volume of approximately(3.6fm)3and with a light quark mass corresponding tom???39MeV. The spectrum of the elasticD?energy region is computed yielding 20 energy levels. Using the Lüscher finite-volume quantisation condition these energies are translated into constraints on the infinite volume scattering amplitudes. For the first time, we find a complexD??0resonance pole from lattice QCD, strongly coupled to theS-waveD?channel, with a massm??200MeV and a width???00MeV. Combined with earlier work investigating theD??s0, andD??0with heavier light quarks, similar couplings between each of these scalar states and their relevant meson-meson scattering channels are determined. The mass of theD??0is consistently found well below that of theD??s0, in contrast to the currently reported experimental result.

In this contribution we present a lattice calculation of the leading-order electromagnetic and strong isospin-breaking (IB) corrections to the quark-connected hadronic-vacuum-polarization (HVP) contribution to the anomalous magnetic moment of the muon. The results are obtained adopting the RM123 approach in the quenched-QED approximation and using the QCD gauge configurations generated by the ETM Collaboration withNf=2+1+1dynamical quarks, at three values of the lattice spacing (a≃0.062,0.082,0.089fm), at several lattice volumes and with pion masses between≃210and≃450MeV. After the extrapolations to the physical pion mass and to the continuum and infinite-volume limits the contributions of the light, strange and charm quarks are respectively equal toδaHVPμ(ud)=7.1 (2.5)⋅10−10,δaHVPμ(s)=−0.0053 (33)⋅10−10andδaHVPμ(c)=0.0182 (36)⋅10−10. At leading order inαemand(md−mu)/ΛQCDwe obtainδaHVPμ(udsc)=7.1 (2.9)⋅10−10, which is currently the most accurate determination of the IB corrections toaHVPμ.

We present results for the isovector electromagnetic form factors of the nucleon computed on the CLS ensembles withNf=2+1flavors ofO(a)-improved Wilson fermions and anO(a)-improved vector current. The analysis includes ensembles with four lattice spacings and pion masses ranging from 130 MeV up to 350 MeV and mainly targets the low-Q2region. In order to remove any bias from unsuppressed excited-state contributions, we investigate several source-sink separations between 1.0 fm and 1.5 fm and apply the summation method as well as explicit two-state fits. The chiral interpolation is performed by applying covariant chiral perturbation theory including vector mesons directly to our form factor data, thus avoiding an auxiliary parametrization of theQ2dependence. At the physical point, we obtainμ=4.71(11)stat(13)sysfor the nucleon isovector magnetic moment, in good agreement with the experimental value and??r2M??= 0.661(30)stat(11)sys fm2for the corresponding square-radius, again in good agreement with the value inferred from theep-scattering determination [Bernauer et~al., Phys. Rev. Lett., 105, 242001 (2010)] of the proton radius. Our estimate for the isovector electric charge radius,??r2E??0.800(25)stat(22)sys fm2, however, is in slight tension with the larger value inferred from the aforementionedep-scattering data, while being in agreement with the value derived from the 2018 CODATA average for the proton charge radius.

We study isovector unpolarized and helicity parton distribution functions (PDF) of the proton within the framework of Large Momentum Effective Theory. We use a gauge ensemble, generated by the MILC Collaboration, with a superfine lattice spacing of0.042fm and a pion mass of310MeV, enabling us to simultaneously reach sub-fermi spatial separations and larger nucleon momenta. We compare the spatial dependence of quasi-PDF matrix elements in different renormalization schemes with the corresponding results of the global fits, obtained using 1-loop perturbative matching. We present determinations of the first four moments of the unpolarized and helicity PDFs of proton from the Ioffe-time dependence of the isovector matrix elements, obtained by employing a ratio-based renormalization scheme.

We present the first calculation of the jet transport coefficientq^in (2+1)-flavor QCD on a 4-dimensional Euclidean lattice. Carried out in a factorized approach, the light-like propagation of a single hard parton within a jet is treated separately from the soft gluon field, off which it scatters. The mean square gain in momentum transverse to the direction of propagation is expressed in terms of the field-strength field-strength correlation function, which is then calculated on the lattice. Dispersion relations and the operator product expansion are used to relate theq^defined on the light-cone with the expectation of a diminishing series of local operators. Calculations of the local operator products are carried out at finite temperature, over a range of lattice sizes, and compared with the results from quenched calculations, perturbative and phenomenological extractions ofq^.

We present our results of theKl3form factors on the volume whose spatial extent is more thanL=10 fm, with the physical pion and kaon masses using the stout-smearing cloverNf=2+1quark action and Iwasaki gauge action ata−1≈2.3GeV. TheKl3form factor at zero momentum transfer is obtained from fit based on the next-to-leading (NLO) formula in SU(3) chiral perturbation theory. We estimate systematic errors of the form factor, mainly coming from the finite lattice spacing effect. We also determine the value of|Vus|by combining our result with the experiment and check the consistency with the standard model prediction. The result is compared with the previous lattice calculations.

We simulate4dSU(N)pure-gauge theories at largeNusing a parallel tempering scheme that combines simulations with open and periodic boundary conditions, implementing the algorithm originally proposed by Martin Hasenbusch for2dCPN??models. That allows to dramatically suppress the topological freezing suffered from standard local algorithms, reducing the autocorrelation time ofQ2up to two orders of magnitude. Using this algorithm in combination with simulations at non-zero imaginaryθwe are able to refine state-of-the-art results for the large-Nbehavior of the quartic coefficient of theθ-dependence of the vacuum energyb2, reaching an accuracy comparable with that of the large-Nlimit of the topological susceptibility.

We study latent heat and the pressure gap between the hot and cold phases at the first-order deconfining phase transition temperature of the SU(3) Yang-Mills theory. Performing simulations on lattices with various spatial volumes and lattice spacings, we calculate the gaps of the energy density and pressure using the small flow-time expansion (SFtX) method. We find that the latent heatΔϵin the continuum limit isΔϵ/T4=1.117±0.040for the aspect ratioNs/Nt=8and1.349±0.038forNs/Nt=6at the transition temperatureT=Tc. We also confirm that the pressure gap is consistent with zero, as expected from the dynamical balance of two phases atTc. From hysteresis curves of the energy density nearTc, we show that the energy density in the (metastable) deconfined phase is sensitive to the spatial volume, while that in the confined phase is insensitive. Furthermore, we examine the effect of alternative procedures in the SFtX method - the order of the continuum and the vanishing flow-time extrapolations, and also the renormalization scale and higher-order corrections in the matching coefficients. We confirm that the final results are all very consistent with each other for these alternatives.

The quantum link~\cite{Brower:1997ha} Hamiltonian was introduced two decades ago as an alternative to Wilson's Euclidean lattice QCD with gauge fields represented by bi-linear fermion/anti-fermion operators. When generalized this new microscopic representation of lattice field theories is referred as {\tt D-theory}~\cite{Brower:2003vy}. Recast as a Hamiltonian in Minkowski space for real time evolution, D-theory leads naturally to quantum Qubit algorithms. Here to explore digital quantum computing for gauge theories, the simplest example of U(1) compact QED on triangular lattice is defined and gauge invariant kernels for the Suzuki-Trotter expansions are expressed as Qubit circuits capable of being tested on the IBM-Q and other existing Noisy Intermediate Scale Quantum (NISQ) hardware. This is a modest step in exploring the quantum complexity of D-theory to guide future applications to high energy physics and condensed matter quantum field theories.