High Energy Physics Lattice

The mass components of charmoniumlike states are investigated through the decomposition of QCD energy-momentum tensor (EMT) on lattice. The quark mass contribution⟨Hm⟩and the momentum fraction⟨x⟩of valence charm quark and antiquark are calculated for conventional1S,1P,1Dcharmonia and the exotic1−+charmoniumlike state, based on theNf=2+1gauge configurations generated by the RBC/UKQCD collaboration. It is found that⟨Hm⟩is close to each other and around 2.0 to 2.2 GeV for these states, which implies that the mass splittings among these states come almost from the gluon contribution of QCD trace anomaly. The⟨x⟩of the1−+state is only around 0.55, while that in conventional charmonia is around 0.7 to 0.8. This difference manifests that the proportion of light quarks and gluons in the1−+charmoniumlike state is significantly larger than conventional states.

We calculate the step scaling function, the lattice analog of the renormalization groupβ-function, for an SU(3) gauge theory with ten fundamental flavors. We present a detailed analysis including the study of systematic effects of our extensive data set generated with ten dynamical flavors using the Symanzik gauge action and three times stout smeared Möbius domain wall fermions. Using up to324volumes, we calculate renormalized couplings for different gradient flow schemes and determine the step-scalingβfunction for a scale changes=2on up to five different lattice volume pairs. In an accompanying paper we discuss that gradient flow can promote lattice dislocations to instanton-like objects, introducing nonperturbative lattice artifacts to the step scaling function. Motivated by the observation that Wilson flow sufficiently suppresses these artifacts, we choose Wilson flow with the Symanzik operator as our preferred analysis. We study systematic effects by calculating the step-scaling function based on alternative flows (Zeuthen or Symanzik), alternative operators (Wilson plaquette, clover), and also explore the effects of the perturbative tree-level improvement. Further we investigate the effects due to the finite value ofLs.

We calculate the step scaling function, the lattice analog of the renormalization groupβ-function, for an SU(3) gauge theory with twelve flavors. The gauge coupling of this system runs very slowly, which is reflected in a small step scaling function, making numerical simulations particularly challenging. We present a detailed analysis including the study of systematic effects of our extensive data set generated with twelve dynamical flavors using the Symanzik gauge action and three times stout smeared Möbius domain wall fermions. Using up to324volumes, we calculate renormalized couplings for different gradient flow schemes and determine the step-scalingβfunction for a scale changes=2on up to five different lattice volume pairs. Our preferred analysis is fullyO(a2)Symanzik improved and uses Zeuthen flow combined with the Symanzik operator. We find an infrared fixed point within the range5.2≤g2c≤6.4in thec=0.250finite volume gradient flow scheme. We account for systematic effects by calculating the step-scaling function based on alternative flows (Wilson or Symanzik) as well as operators (Wilson plaquette, clover) and also explore the effects of the perturbative tree-level improvement.

The use of lattice tensor representations is explored to investigate the lattice Landau gauge gluon propagator for the pure SU(3) Yang-Mills gauge theory in 4D. The analysis of several tensor bases allows to quantify the completeness of the various tensor bases considered, the deviations of the lattice results from the continuum theory due to the lattice artefacts and estimate the theoretical uncertainty in the propagator. Furthermore, our analysis tests continuum based relations with the lattice data and show that the lattice Landau gauge gluon propagator is described by a unique form factor, as in the continuum formulation.

We perform a lattice QCD calculation of the hadronic light-by-light contribution to(g−2)μat the SU(3) flavor-symmetric pointmπ=mK≃420MeV. The representation used is based on coordinate-space perturbation theory, with all QED elements of the relevant Feynman diagrams implemented in continuum, infinite Euclidean space. As a consequence, the effect of using finite lattices to evaluate the QCD four-point function of the electromagnetic current is exponentially suppressed. Thanks to the SU(3)-flavor symmetry, only two topologies of diagrams contribute, the fully connected and the leading disconnected. We show the equivalence in the continuum limit of two methods of computing the connected contribution, and introduce a sparse-grid technique for computing the disconnected contribution. Thanks to our previous calculation of the pion transition form factor, we are able to correct for the residual finite-size effects and extend the tail of the integrand. We test our understanding of finite-size effects by using gauge ensembles differing only by their volume. After a continuum extrapolation based on four lattice spacings, we obtainahlblμ=(65.4±4.9±6.6)×10−11, where the first error results from the uncertainties on the individual gauge ensembles and the second is the systematic error of the continuum extrapolation. Finally, we estimate how this value will change as the light-quark masses are lowered to their physical values.

The gradient-flow operator product expansion for QCD current correlators including operators up to mass dimension four is calculated through NNLO. This paves an alternative way for efficient lattice evaluations of hadronic vacuum polarization functions. In addition, flow-time evolution equations for flowed composite operators are derived. Their explicit form for the non-trivial dimension-four operators of QCD is given through orderα3s.

We introduce a half-filled Hamiltonian of spin-half lattice fermions that can be studied with the efficient meron-cluster algorithm in any dimension. As with the usual bipartite half-filled Hubbard models, the naïveU(2)symmetry is enhanced toSO(4). On the other hand our model has a novel spin-charge flipZC2symmetry which is an important ingredient of free massless fermions. In this work we focus on one spatial dimension, and show that our model can be viewed as a lattice-regularized two-flavor chiral-mass Gross-Neveu model. Our model remains solvable in the presence of the Hubbard couplingU, which maps to a combination of Gross-Neveu and Thirring couplings in one dimension. Using the meron-cluster algorithm we find that the ground state of our model is a valence bond solid whenU=0. From our field theory analysis, we argue that the valence bond solid forms inevitably because of an interesting frustration between spin and charge sectors in the renormalization group flow enforced by theZC2symmetry. This state spontaneously breaks translation symmetry by one lattice unit, which can be identified with aZχ2chiral symmetry in the continuum. We show that increasingUinduces a quantum phase transition to a critical phase described by theSU(2)1Wess-Zumino-Witten theory. The quantum critical point between these two phases is known to exhibit a novel symmetry enhancement between spin and dimer. Here we verify the scaling relations of these correlation functions near the critical point numerically. Our study opens up the exciting possibility of numerical access to similar novel phase transitions in higher dimensions in fermionic lattice models using the meron-cluster algorithm.

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 at1.5Tc. 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 previous study using the multi-level algorithm. We perform a spectral reconstruction based on perturbative model fits to estimate the heavy quark momentum diffusion coefficient. The approach we present here yields high-precision data for the correlator and is also applicable for actions with dynamical fermions.

A formalism is given to hermitize the HAL QCD potential, which needs to be non-hermitian except the leading order (LO) local term in the derivative expansion as the Nambu-Bethe-Salpeter (NBS) wave functions for different energies are not orthogonal to each other. It is shown that the non-hermitian potential can be hermitized order by order to all orders in the derivative expansion. In particular, the next-to-leading order (NLO) potential can be exactly hermitized without approximation. The formalism is then applied to a simple case ofΞΞ(1S0)scattering, for which the HAL QCD calculation is available to the NLO. The NLO term gives relatively small corrections to the scattering phase shift and the LO analysis seems justified in this case. We also observe that the local part of the hermitized NLO potential works better than that of the non-hermitian NLO potential. The hermitian version of the HAL QCD potential is desirable for comparing it with phenomenological interactions and also for using it as a two-body interaction in many body systems.

We present lattice QCD calculations of higher order cumulants of electric charge distributions for small baryon chemical potentialsμBby using up to NNNLO Taylor expansions. Ratios of these cumulants are evaluated on the pseudo-critical line,Tpc(μB), of the chiral transition and compared to corresponding measurements in heavy ion collision experiments by the STAR and PHENIX Collaborations. We demonstrate that these comparisons give strong constraints on freeze-out parameters. Furthermore, we use strangeness fluctuation observables to compute the ratioμS/μBon the crossover line and compare it toμS/μBat freeze-out stemming from fits to strange baryon yields measured by the STAR Collaboration.