We calculate the thermal Euclidean correlators and the spectral functions of the energy-momentum tensor for pure gauge theories, including at non-zero spatial momentum, at leading order in perturbation theory. Our goal is to improve the extraction of transport properties from Euclidean correlators that are computable in lattice QCD. Based on our results and the predictions of hydrodynamics for the structure of the spectral functions at low frequencies, we show that the shear and bulk viscosities can advantageously be extracted from the Euclidean correlators of the conserved charges, energy and momentum, at small but non-vanishing spatial momentum. The spectral functions in these channels are free of the ultraviolet $ω^4$ term which represents a large background to the thermal physics encoded in the correlators of the fluxes.
We compute the Euclidean correlators of the stress tensor in pure $SU(3)$ Yang-Mills theory at finite temperature at zero and finite spatial momenta with lattice simulations. We perform continuum extrapolations using $N_τ=10,12,16,20$ lattices with renormalized anisotropy 2. We use these correlators to estimate the shear viscosity of the gluon plasma in the deconfined phase. For $T=1.5T_c$ we obtain $η/s=0.17(2)$.
We investigate the discretization errors affecting correlators of the energy-momentum tensor $T_{μν}$ at finite temperature in SU($N_c$) gauge theory with the Wilson action and two different discretizations of $T_{μν}$. We do so by using lattice perturbation theory and non-perturbative Monte-Carlo simulations. These correlators, which are functions of Euclidean time $x_0$ and spatial momentum ${\bf p}$, are the starting point for a lattice study of the transport properties of the gluon plasma. We find that the correlator of the energy $\int d^3x T_{00}$ has much larger discretization errors th…
In lattice simulations one generally projects correlators over zero spatial momentum to calculate masses and related spectral data. The sum over space lattice points, however, discards information which may be useful especially in the calculation of disconnected diagrams. By using momentum conservation, the calculation of non-zero momentum components of disconnected diagrams and other quantities related to space convolutions can be done with little additional computational cost and may be useful in the analysis of disconnected correlators.
We present analytical results both in momentum and position space for the massless correlators of the vector and scalar currents to order alpha_s^4 as well as for the tensor currents to order alpha_s^3. The evolution equations for the correlators together with all relevant anomalous dimensions are discussed in detail. As an application we present explicit conversion formulas relating the MSbar-renormalized vector, scalar and tensor currents to their counterparts renormalized in the X-space renormalization scheme more appropriate for lattice calculations.
We study spatial isovector meson correlators in $N_f=2$ QCD with dynamical domain-wall fermions on $32^3\times 8$ lattices at temperatures $T=220-380$ MeV. We measure the correlators of spin-one ($J=1$) operators including vector, axial-vector, tensor and axial-tensor. Restoration of chiral $U(1)_A$ and $SU(2)_L \times SU(2)_R$ symmetries of QCD implies degeneracies in vector--axial-vector ($SU(2)_L \times SU(2)_R$) and tensor--axial-tensor ($U(1)_A$) pairs, which are indeed observed at temperatures above $T_c$. Moreover, we observe an approximate degeneracy of all $J=1$ correlators with incre…
The thermal photon emission rate is determined by the spatially transverse, in-medium spectral function of the electromagnetic current. Accessing the spectral function using Euclidean data is, however, a challenging problem due to the ill-posed nature of inverting the Laplace transform. In this contribution, we present the first results on implementing the proposal of directly computing the analytic continuation of the retarded correlator at fixed, vanishing virtuality of the photon via the calculation of the appropriate Euclidean correlator at imaginary spatial momentum. We employ two dynamic…
We study hadronic two- and three-point correlators relevant for heavy to light pseudoscalar meson semi-leptonic decays, using Symanzik improved glue, D234 light quark and NRQCD heavy quark actions. Detailed comparisons are made between simulations on anisotropic and isotropic lattices involving finite momentum hadrons. We find evidence that having an anisotropy helps in extracting better signals at higher momenta. Initial results for the form factors f_+(q^2) and f_0(q^2) are presented with tree-level matching of the lattice heavy-light currents.
For the Lorentz gauge the influence of various Gribov gauge copies on the fermion propagator is investigated in quenched compact lattice QED. Within the Coulomb phase besides double Dirac sheets the zero-momentum modes of the gauge fields are shown to cause the propagator to deviate strongly from the perturbatively expected behaviour. The standard way to extract the fermion mass fails. The recently proposed zero-momentum Lorentz gauge is demonstrated to cure the problem.
Collective flow has been observed in heavy ion collisions, with a large anisotropic component, and ideal hydrodynamic calculations had significant successful in describing the distribution of produced particles at the RHIC experiments. In order to account for this near ideal fluid behavior, the shear and bulk viscosity of the quark gluon plasma (QGP) must be computed from first principles in a regime where the QGP is not weakly coupled. In this talk I describe recent progress in computing energy-momentum tensor correlators on the lattice from which the viscosities can be extracted via Kubo for…
The photon emission rate of a thermally equilibrated system is determined by the imaginary part of the in-medium retarded correlator of the electromagnetic current transverse to the spatial momentum of the photon. In a Lorentz-covariant theory, this correlator can be parametrized by a scalar function ${\cal G}_R(u\cdot {\cal K},{\cal K}^2)$, where $u$ is the fluid four-velocity and ${\cal K}$ corresponds to the momentum of the photon. We propose to compute the analytic continuation of ${\cal G}_R(u\cdot {\cal K},{\cal K}^2)$ at fixed, vanishing virtuality ${\cal K}^2$, to imaginary values of t…
Gradient flow has been proposed in the lattice community as a tool to reduce the sensitivity of operator correlation functions to noisy UV fluctuations. We test perturbatively under what conditions doing so may contaminate the results. To do so, we compute gradient-flowed electric field two-point correlators and stress tensor one- and two-point correlators at finite temperature in QCD. Gradient flow has almost no influence on the value of correlators until a (temperature- and separation-dependent) level of flow is reached, after which the correlator is rapidly compromised. We provide a prescri…
We present a study of gauge invariant density-density correlators. Density-density correlators probe hadron wave functions and thus can be used to study hadron deformation. Their zero momentum projection requires the computation of all-to-all propagators, which are evaluated with the standard stochastic technique, the dilution method and the stochastic sequential technique. We compare the results to a previous analysis that did not employ the zero momentum projection.
We calculate the small-momentum expansion of vector, axial-vector, scalar, and pseudo-scalar heavy-quark current correlators in the large-$β_0$ limit of QCD, extending the analysis of Grozin and Sturm beyond the vector current. Our results are used to study the higher-order behaviour of dimensionless ratios of vector and pseudo-scalar moments used for the precise extraction of the strong coupling, $α_s$, from relativistic quarkonium sum rules and lattice data, respectively. We show that these ratios benefit from a partial cancellation of the leading renormalon singularities. Our results can gu…
We study spatial isovector meson correlators in $N_f=2$ QCD with dynamical domain-wall fermions on $32^3\times 8$ lattices at temperatures up to 380 MeV with various quark masses. We measure the correlators of spin-one isovector operators including vector, axial-vector, tensor and axial-tensor. At temperatures above $T_c$ we observe an approximate degeneracy of the correlators in these channels, which is unexpected because some of them are not related under $SU(2)_L \times SU(2)_R$ nor $U(1)_A$ symmetries. The observed approximate degeneracy suggests emergent $SU(2)_{CS}$ (chiral-spin) and $SU…
The investigation of the scalar gluonium correlator is interesting because it carries the quantum numbers of the vacuum and the relevant hadronic current is related to the anomalous trace of the QCD energy-momentum tensor in the chiral limit. After reviewing the purely perturbative corrections known up to next-next-to-leading order, the behaviour of the correlator is studied to all orders by means of the large-beta_0 approximation. Similar to the QCD Adler function, the large-order behaviour is governed by the leading ultraviolet renormalon pole. The structure of infrared renormalon poles, bei…
This PhD dissertation is devoted to a non-perturbative study of QCD correlators. The main tool that we use is lattice QCD. We concentrated our efforts on the study of the main correlators of the pure Yang - Mills theory in the Landau gauge, namely the ghost and the gluon propagators. We are particularly interested in determining the $\Lqcd$ parameter. It is extracted by means of perturbative predictions available up to NNNLO. The related topic is the influence of non-perturbative effects that show up as appearance of power-corrections to the low-momentum behaviour of the Green functions. A new…
Chiral perturbation theory gives direct and unambiguous predictions for the form of various two-point hadronic correlators at low momentum in terms of a finite set of couplings in a chiral Lagrangian. In this paper we study the feasibility of extracting the couplings in the chiral Lagrangian (through 1-loop order) by fitting two-point correlators computed in lattice QCD to the predicted chiral form. The correlators are computed using a pseudofermion technique yielding all-point quark propagators which allows the computation of the full four-momentum transform of the two-point functions to be o…
Euclidean two-point correlators of the energy-momentum tensor (EMT) in SU(3) gauge theory on the lattice are studied on the basis of the Yang-Mills gradient flow. The entropy density and the specific heat obtained from the two-point correlators are shown to be in good agreement with those from the one-point functions of EMT. These results constitute a first step toward the first principle simulations of the transport coefficients with the gradient flow.
Partially twisted boundary conditions are widely used for improving the momentum resolution in lattice computations of hadronic correlation functions. The method is however expensive since every additional twist requires computing additional propagators. We propose a novel variance reduction technique that exploits statistical correlations to reduce the overall cost for computing correlators with additional twist angles. We explain and demonstrate the method for meson 2pt and 3pt functions.
Quantum simulation of real-time current correlators and DIS-inspired observables in the Schwinger model
University of Massachusetts Boston（马萨诸塞大学波士顿分校）；Stony Brook University（石溪大学）；University of California, Los Angeles（加州大学洛杉矶分校）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Central China Normal University（华中师范大学）；Universidade de Santiago de Compostela（圣地亚哥德孔波斯特拉大学）
We apply the gradient flow on a color-electric two-point function that encodes the heavy quark momentum diffusion coefficient. The simulations are done on fine isotropic lattices in the quenched approximation at $1.5\,T_c$. The continuum extrapolation is performed at fixed flow time followed by a second extrapolation to zero flow time. Perturbative calculations of this correlation function under Wilson flow are used to enhance the extrapolations of the non-perturbative lattice correlator. The final estimate for the continuum correlator at zero flow time largely agrees with one obtained from a …
We show that a recent interesting idea to circumvent the difficulties with the continuation of parton distribution functions to the Euclidean region, that consists in looking at equal time correlators between proton states of infinite momentum, encounters some problems related to the power divergent mixing pattern of DIS operators, when implemented within the lattice regularization.
