High Energy Physics Lattice

TheSU(3)pure gauge theory exhibits a first-order thermal deconfinement transition due to spontaneous breaking of its globalZ3center symmetry. When heavy dynamical quarks are added, this symmetry is broken explicitly and the transition weakens with decreasing quark mass until it disappears at a critical point. We compute the critical hopping parameter and the associated pion mass for lattice QCD withNf=2degenerate standard Wilson fermions onNτ∈{6,8,10}lattices, corresponding to lattice spacingsa=0.12fm,a=0.09fm,a=0.07fm, respectively. Significant cut-off effects are observed, with the first-order region growing as the lattice gets finer. While current lattices are still too coarse for a continuum extrapolation, we estimatemcπ≈4GeVwith a remaining systematic error of∼20%. Our results allow to assess the accuracy of the LO and NLO hopping expanded fermion determinant used in the literature for various purposes. We also provide a detailed investigation of the statistics required for this type of calculation, which is useful for similar investigations of the chiral transition.

We study the deconfinement transition line in QCD for quark chemical potentials up toμq∼5T(μB∼15T). To circumvent the sign problem we use the complex Langevin equation with gauge cooling. The plaquette gauge action is used with two flavors of naive Wilson fermions at a relatively heavy pion mass of roughly 1.3 GeV. A quadratic dependence describes the transition line well on the whole chemical potential range.

We discuss a new strategy for treating the complex action problem of lattice field theories with aθ-term based on density of states (DoS) methods. The key ingredient is to use open boundary conditions where the topological charge is not quantized to integers and the density of states is sufficiently well behaved such that it can be computed precisely with recently developed DoS techniques. After a general discussion of the approach and the role of the boundary conditions, we analyze the method for 2-d U(1) lattice gauge theory with aθ-term, a model that can be solved in closed form. We show that in the continuum limit periodic and open boundary conditions describe the same physics and derive the DoS, demonstrating that only for open boundary conditions the density is sufficiently well behaved for a numerical evaluation. We conclude our proof of principle analysis with a small test simulation where we numerically compute the density and compare it with the analytical result.

From simulations on 2+1 flavor domain wall fermion ensembles at three lattice spacings with two of them at physical quark masses, we compute the spectrum of the Dirac operator up to the eigenvalueλ??100 MeV using the overlap fermion. The spectrum is close to a constant belowλ??20 MeV as predicted by the 2-flavor chiral perturbative theory (?PT) up to the finite volume correction, and then increases linearly due to the non-vainishing strange quark mass. Furthermore, one can extract the light and strange quark masses with??20\% uncertainties from the spectrum data with sub-percentage statistical uncertainty, using the next to leading order?PT. Using the non-perturbative RI/MOM renormalization, we obtain the chiral condensates atMS¯¯¯¯¯¯¯2GeV asΣ=(260.3(0.7)(1.3)(0.7)(0.8) MeV)3in theNf=2(keeping the strange quark mass at the physical point) chiral limit andΣ0=(232.6(0.9)(1.2)(0.7)(0.8) MeV)3in theNf=3chiral limit, where the four uncertainties come from the statistical fluctuation, renormalization constant, continuum extrapolation and lattice spacing determination. Note thatΣ/Σ0=1.40(2)(2)is much larger than 1 due to the strange quark mass effect.

We present a determination of the charm quark mass in lattice QCD with three active quark flavours. The calculation is based on PCAC masses extracted fromNf=2+1flavour gauge field ensembles at five different lattice spacings in a range from 0.087 fm down to 0.039 fm. The lattice action consists of theO(a)improved Wilson-clover action and a tree-level improved Symanzik gauge action. Quark masses are non-perturbativelyO(a)improved employing the Symanzik-counterterms available for this discretisation of QCD. To relate the bare mass at a specified low-energy scale with the renormalisation group invariant mass in the continuum limit, we use the non-pertubatively known factors that account for the running of the quark masses as well as for their renormalisation at hadronic scales. We obtain the renormalisation group invariant charm quark mass at the physical point of the three-flavour theory to beMc=1486(21)MeV. Combining this result with five-loop perturbation theory and the corresponding decoupling relations in theMS¯¯¯¯¯¯¯scheme, one arrives at a result for the renormalisation group invariant charm quark mass in the four-flavour theory ofMc(Nf=4)=1548(23)MeV. In theMS¯¯¯¯¯¯¯scheme, and at finite energy scales conventional in phenomenology, we quotemMS¯¯¯¯¯¯¯¯c(mMS¯¯¯¯¯¯¯¯c;Nf=4)=1296(19)MeVandmMS¯¯¯¯¯¯¯¯c(3GeV;Nf=4)=1007(16)MeVfor the renormalised charm quark mass

We extend HPQCD's earliernf=4lattice-QCD analysis of the ratio ofMSB¯¯¯¯¯¯¯¯¯¯¯masses of thebandcquark to include results from finer lattices (down to 0.03fm) and a new calculation of QED contributions to the mass ratio. We find thatm¯¯¯¯¯b(μ)/m¯¯¯¯¯c(μ)=4.586(12)at renormalization scaleμ=3\,GeV. This result is nonperturbative. Combining it with HPQCD's recent lattice QCD+QED determination ofm¯¯¯¯¯c(3GeV)gives a new value for theb-quark mass:m¯¯¯¯¯b(3GeV)=4.513(26)GeV. Theb-mass corresponds tom¯¯¯¯¯b(m¯¯¯¯¯b,nf=5)=4.202(21)GeV. These results are the first based on simulations that include QED.

Computing the gluon component of momentum in the nucleon is a difficult and computationally expensive problem, as the matrix element involves a quark-line-disconnected gluon operator which suffers from ultra-violet fluctuations. But also necessary for a successful determination is the non-perturbative renormalisation of this operator. As a first step we investigate here this renormalisation in the RI-MOM scheme. Using quenched QCD as an example, a statistical signal is obtained in a direct calculation using an adaption of the Feynman-Hellmann technique.

We perform a digital quantum simulation of a gauge theory with a topological term in Minkowski spacetime, which is practically inaccessible by standard lattice Monte Carlo simulations. We focus on1+1dimensional quantum electrodynamics with theθ-term known as the Schwinger model. We construct the true vacuum state of a lattice Schwinger model using adiabatic state preparation which, in turn, allows us to compute an expectation value of the fermion mass operator with respect to the vacuum. Upon taking a continuum limit we find that our result in massless case agrees with the known exact result. In massive case, we find an agreement with mass perturbation theory in small mass regime and deviations in large mass regime. We estimate computational costs required to take a reasonable continuum limit. Our results imply that digital quantum simulation is already useful tool to explore non-perturbative aspects of gauge theories with real time and topological terms.

New results are reported from tests of a low-energy effective field theory (EFT) that includes a dilaton field to describe the emergent light scalar with0++quantum numbers in the strongly coupled near-conformal gauge theory with a massless fermion flavor doublet in the two-index symmetric (sextet) representation of the SU(3) color gauge group. In the parlor of walking --- based on the observed light scalar, the smallβ-function at strong coupling, and the large anomalous scale dimension of the chiral condensate --- the dilaton EFT hypothesis is introduced to test if it explains the slowly changing nearly scale invariant physics that connects the asymptotically free UV fixed point and the far-infrared scale of chiral symmetry breaking. The characteristic dilaton EFT signatures of scale symmetry breaking are probed in this report in the small Compton wavelength limit of Goldstone bosons relative to the size of the lattice volume (p-regime) and in the limit when the Goldstone wavelength exceeds the size of the volume (ϵ-regime). Random matrix theory (RMT) analysis of the dilaton EFT is applied to the lowest part of the Dirac spectrum in theϵ-regime to directly test predictions for the fundamental EFT parameters. The predictions, sensitive to the choice of the dilaton potential, were limited before to the p-regime, using extrapolations from far above the chiral limit with untested uncertainties. The dilaton EFT analysis of theϵ-regime was first suggested in \cite{Fodor:2019vmw}, with some results presented at this conference and with our continued post-conference analysis added to stimulate discussions.

We utilize the eigenvalue filtering technique combined with the stochastic estimate of the mode number to determine the eigenvalue spectrum. Simulations of (2 + 1)-flavor QCD are performed using the Highly Improved Staggered Quarks (HISQ/tree) action onNτ= 8 lattices with aspect ratiosNσ/Nτranging from 5 to 7. The strange quark mass is fixed to its physical valuemphys, and the light quark massesmlare varied frommphys/40tomphys/160which correspond to pion massmπranging from 110 MeV to 55 MeV in the continuum limit. We compute the chiral condensate andχπ−χδthrough the eigenvalue spectrum obtained from the the eigenvalue filtering method. We compare these results with those obtained from a direct calculation of the observables which involves inversions of the fermion matrix using the stochastic "noise vector" method. We find that these approaches yield consistent results. Furthermore, we also investigate the quark mass and temperature dependences of the Dirac eigenvalue density at zero eigenvalues to gain more insights about theUA(1)symmetry breaking in QCD.