High Energy Physics Lattice

We present high statistics (O(2×105)measurements) preliminary results on (i) the isovector charges,gu−dA,S,T, and form factors,Gu−dE(Q2),Gu−dM(Q2),Gu−dA(Q2),G˜u−dP(Q2),Gu−dP(Q2), on six 2+1-flavor Wilson-clover ensembles generated by the JLab/W&M/LANL/MIT collaboration with lattice parameters given in Table 1. Examples of the impact of using different estimates of the excited state spectra are given for the clover-on-clover data, and as discussed in [1], the biggest difference on including the lower energy (close toNπandNππ) states is in the axial channel. (ii) Flavor diagonal axial, tensor and scalar charges,gu,d,sA,S,T, are calculated with the clover-on-HISQ formulation using nine 2+1+1-flavor HISQ ensembles generated by the MILC collaboration [2] with lattice parameters given in Table 2. Once finished, the calculations ofgu,d,sA,Twill update the results given in Refs.[3,4]. The estimates forgu,d,sSandσNπare new. Overall, a large part of the focus is on understanding the excited state contamination (ESC), and the results discussed provide a partial status report on developing defensible analyses strategies that include contributions of possible low-lying excited states to individual nucleon matrix elements.

The role of the strange quarks on the low-energy interactions of the proton can be probed through the strange electromagnetic form factors. Knowledge of these form factors provides essential input for parity-violating processes and contributes to the understanding of the sea quark dynamics. We determine the strange electromagnetic form factors of the nucleon within the lattice formulation of Quantum Chromodynamics using simulations that include light, strange and charm quarks in the sea all tuned to their physical mass values. We employ state-of-the-art techniques to accurately extract the form factors for values of the momentum transfer square up to 0.8~GeV2. We find that both the electric and magnetic form factors are statistically non-zero. We obtain for the strange magnetic momentμs=−0.017(4), the strange magnetic radius⟨r2M⟩s=−0.015(9)~fm2, and the strange charge radius⟨r2E⟩s=−0.0048(6)~fm2.

We study the Chiral Separation Effect (CSE) in finite-density SU(2) lattice gauge theory with dynamical fermions. We find that the strength of the CSE is close to that for free quarks in most regions of the phase diagram, including the high-temperature quark-gluon plasma phase, the low-temperature phase with spontaneously broken chiral symmetry, and the diquark condensation phase which is specific for the SU(2) gauge theory. The CSE is significantly suppressed only at low temperatures and low densities, where the chemical potential is roughly less than half of the pion mass. This suppression can be approximately described by assuming that the CSE current is proportional to the charge density, rather than to the chemical potential, as suggested in the literature [PRD 97 (2018) 085020, arXiv:1712.01256]. We also provide an upper bound on the contribution of disconnected fermionic diagrams to the CSE, which is consistent with zero within our statistical errors and small compared to that of the connected diagrams.

We investigate the implications of Nambu-Goto (NG), Lüscher-Weisz (LW) and Polyakov-Kleinert (PK) string actions for the Casimir energy of the QCD flux-tube at one and two loop order at finite temperature. We perform our numerical study on the 4-dim pure SU(3) Yang-Mills lattice gauge theory at finite temperatureβ=6.0. The static quark-antiquark potential is calculated using link-integrated Polyakov loop correlators. At a high temperature-close to the critical point- We find that the rigidity and self-interactions effects of the QCD string to become detectable. The remarkable feature of this model is that it retrieves a correct dependency of the renormalized string tension on the temperature. Good fit to static potential data at source separationsR≥0.5fm is obtained when including additional two-boundary terms of (LW) action. On the other-hand, at a lower temperature-near the QCD plateau- We detect signatures of two boundary terms of the Lüscher-Weisz (LW) string action. The (LW) string with boundary action is yielding a static potential which is in a good agreement with the lattice data, however, for color source separation as short asR=0.3fm.

One of the more important systematic effects affecting lattice computations of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon,aHVPμ, is the distortion due to a finite spatial volume. In order to reach sub-percent precision, these effects need to be reliably estimated and corrected for, and one of the methods that has been employed for doing this is finite-volume chiral perturbation theory. In this paper, we argue that finite-volume corrections toaHVPμcan, in principle, be calculated at any given order in chiral perturbation theory. More precisely, once all low-energy constants needed to define the Effective Field Theory representation ofaHVPμin infinite volume are known to a given order, also the finite-volume corrections can be predicted to that order in the chiral expansion.

We consider the chiral Lagrangian with nucleon, isobar, and pion degrees of freedom. The baryon masses and the axial-vector form factor of the nucleon are derived at the one-loop level. We explore the impact of using on-shell baryon masses in the loop expressions. As compared to results from conventional chiral perturbation theory we find significant differences. An application to QCD lattice data is presented. We perform a global fit to the available lattice data sets for the baryon masses and the nucleon axial-vector form factor, and determine the low-energy constants relevant at N3LO for the baryon masses and at N2LO for the form factor. Partial finite-volume effects are considered. We point out that the use of on-shell masses in the loops results in non-analytic behavior of the baryon masses and the form factor as function of the pion mass, which becomes prominent for larger lattice volumes than presently used.

We discuss the relation of three methods to determine energy levels in lattice QCD simulations: the generalised eigenvalue, the Prony and the generalised pencil of function methods. All three can be understood as special cases of a generalised eigenvalue problem. We show analytically that the leading corrections to an energyElin all three methods due to unresolved states decay asymptotically exponentially likeexp(−(En−El)t). Using synthetic data we show that these corrections behave as expected also in practice. We propose a novel combination of the generalised eigenvalue and the Prony method, denoted as GEVM/PGEVM, which helps to increase the energy gapEn−El. We illustrate its usage and performance using lattice QCD examples.

Lattice gauge theory results show the confinement for the quark potential in different Yang-Mills theories and even the G(2) gauge theory. LGT calculations show that quark potential should have the down concavity behavior. Confinement properties can be explained using the thick center vortex model. However an upward concavity is seen in the quark potential intervals using this model. After study the reason of this concavity, it is shown the non physical concavity can be reduced by taking an arbitrary symmetric vortex flux in the space time plane of the lattice.

Using non-relativistic effective field theory, we derive a three-particle analog of the Lellouch-Lüscher formula at the leading order. This formula relates the three-particle decay amplitudes in a finite volume with their infinite-volume counterparts and, hence, can be used to study the three-particle decays on the lattice. The generalization of the approach to higher orders is briefly discussed.

This work explores scattering amplitudes that couple two-particle systems via a single external current insertion,2+J??. Such amplitudes can provide structural information about the excited QCD spectrum. We derive an exact analytic representation for these reactions. From these amplitudes, we show how to rigorously define resonance and bound-state form-factors. Furthermore, we explore the consequences of the narrow-width limit of the amplitudes as well as the role of the Ward-Takahashi identity for conserved vector currents. These results hold for any number of two-body channels with no intrinsic spin, and a current with arbitrary Lorentz structure and quantum numbers. This work and the existing finite-volume formalism provide a complete framework for determining this class of amplitudes from lattice QCD.