High Energy Physics Lattice

All approaches currently used to study finite baryon density lattice QCD suffer from uncontrolled systematic uncertainties in addition to the well-known sign problem. We formulate and test an algorithm, sign reweighting, that works directly at finiteμ=μB/3and is yet free from any such uncontrolled systematics. With this algorithm the {\em only} problem is the sign problem itself. This approach involves the generation of configurations with the positive fermionic weight|RedetD(μ)|whereD(μ)is the Dirac matrix and the signssign(RedetD(μ))=±1are handled by a discrete reweighting. Hence there are only two sectors,+1and−1and as long as the average⟨±1⟩≠0(with respect to the positive weight) this discrete reweighting by the signs carries no overlap problem and the results are reliable. The approach is tested onNt=4lattices with2+1flavors and physical quark masses using the unimproved staggered discretization. By measuring the Fisher (sometimes also called Lee-Yang) zeros in the bare coupling on spatial latticesL/a=8,10,12we conclude that the cross-over present atμ=0becomes stronger atμ>0and is consistent with a true phase transition at aroundμB/T∼2.4.

I review recent new lattice QCD results on a few selected topics which are relevant to the heavy ion physics community. Special emphasis is put on the QCD phase diagram towards the chiral limit and at nonzero baryon density as well as the fate of quarkonia and heavy quark drag coefficients.

In this work, we present the first-ever calculation of the isovector flavor combination of the twist-3 parton distribution functiongT(x)for the proton from lattice QCD. We use an ensemble of gauge configurations with two degenerate light, a strange and a charm quark (Nf=2+1+1) of maximally twisted mass fermions with a clover improvement. The lattice has a spatial extent of 3~fm, lattice spacing of 0.093~fm, and reproduces a pion mass of260MeV. We use the quasi-distribution approach and employ three values of the proton momentum boost, 0.83 GeV, 1.25 GeV, and 1.67 GeV. We use a source-sink separation of 1.12~fm to suppress excited-states contamination. The lattice data are renormalized non-perturbatively. We calculate the matching equation within Large Momentum Effective Theory, which is applied to the lattice data in order to obtaingT. The final distribution is presented in theMS¯¯¯¯¯¯¯scheme at a scale of 2 GeV. We also calculate the helicity distributiong1to test the Wandzura-Wilczek approximation forgT. We find that the approximation works well for a broad range ofx. This work demonstrates the feasibility of accessing twist-3 parton distribution functions from novel methods within lattice QCD and can provide essential insights into the structure of hadrons.

We construct several classes of hadronic matrix elements and relate them to the low-energy constants in Chiral Perturbation Theory that describe the electromagnetic effects in the semileptonic beta decay of the pion and the kaon. We propose to calculate them using lattice QCD, and argue that such a calculation will make an immediate impact to a number of interesting topics at the precision frontier, including the outstanding anomalies in|Vus|and the top-row Cabibbo-Kobayashi-Maskawa matrix unitarity.

The type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. In the Lorentzian version, in particular, the emergence of (3+1)D expanding space-time was observed by Monte Carlo studies of this model. Here we provide new perspectives on the (3+1)D expanding space-time that have arised from recent studies. First it was found that the matrix configurations generated by the simulation are singular in that the submatrices representing the expanding 3D space have only two large eigenvalues associated with the Pauli matrices. This problem was conjectured to occur due to the approximation used to avoid the sign problem in simulating the model. In order to confirm this conjecture, the complex Langevin method was applied to overcome the sign problem instead of using the approximation. The results indeed showed a clear departure from the Pauli-matrix structure, while the (3+1)D expanding behavior remained unaltered. It was also found that classical solutions obtained within a certain ansatz show quite generically a (3+1)D expanding behavior with smooth space-time structure.

A random matrix model for lattice QCD which takes into account the positive definite nature of the Wilson term is introduced. The corresponding effective theory for fixed index of the Wilson Dirac operator is derived to next to leading order. It reveals a new term proportional to the topological index of the Wilson Dirac operator and the lattice spacing. The new term appears naturally in a fixed index spurion analysis. The spurion approach reveals that the term is the first in a new family of such terms and that equivalent terms are relevant for the effective theory of continuum QCD.

We study scalar fields propagating on Euclidean dynamical triangulations (EDT). In this work we study the interaction of two scalar particles, and we show that in the appropriate limit we recover an interaction compatible with Newton's gravitational potential in four dimensions. Working in the quenched approximation, we calculate the binding energy of a two-particle bound state, and we study its dependence on the constituent particle mass in the non-relativistic limit. We find a binding energy compatible with what one expects for the ground state energy by solving the Schrödinger equation for Newton's potential. Agreement with this expectation is obtained in the infinite-volume, continuum limit of the lattice calculation, providing non-trivial evidence that EDT is in fact a theory of gravity in four dimensions. Furthermore, this result allows us to determine the lattice spacing within an EDT calculation for the first time, and we find that the various lattice spacings are smaller than the Planck length, suggesting that we can achieve a separation of scales and that there is no obstacle to taking a continuum limit. This lends further support to the asymptotic safety scenario for gravity.

We study thermodynamic properties of Nf=2+1 QCD on the lattice adopting O(a)-improved Wilson quark action and Iwasaki gauge action. To cope with the problems due to explicit violation of the Poincare and chiral symmetries, we apply the Small Flow-time eXpansion (SFtX) method based on the gradient flow, which is a general method to correctly calculate any renormalized observables on the lattice. In this method, the matching coefficients in front of operators in the small flow-time expansion are calculated by perturbation theory. In a previous study using one-loop matching coefficients, we found that the SFtX method works well for the equation of state, chiral condensates and susceptibilities. In this paper, we study the effect of two-loop matching coefficients by Harlander et al. We also test the influence of the renormalization scale in the SFtX method. We find that, by adopting the mu_0 renormalization scale of Harlander et al. instead of the conventional mu_d=1/sqrt{8t} scale, the linear behavior at large t is improved so that we can perform the t -> 0 extrapolation of the SFtX method more confidently. In the calculation of the two-loop matching coefficients by Harlander et al., the equation of motion for quark fields was used. For the entropy density in which the equation of motion has no effects, we find that the results using the two-loop coefficients agree well with those using one-loop coefficients. On the other hand, for the trace anomaly which is affected by the equation of motion, we find discrepancies between the one- and two-loop results at high temperatures. By comparing the results of one-loop coefficients with and without using the equation of motion, the main origin of the discrepancies is suggested to be attributed to O((aT)^2)=O(1/N_t^2) discretization errors in the equation of motion at N_t =< 10.

We present a strategy to define non-perturbatively the energy-momentum tensor in Quantum Chromodynamics (QCD) which satisfies the appropriate Ward identities and has the right trace anomaly. The tensor is defined by regularizing the theory on a lattice, and by fixing its renormalization constants non-perturbatively by suitable Ward identities associated to the Poincare' invariance of the continuum theory. The latter are derived in thermal QCD with a non-zero imaginary chemical potential formulated in a moving reference frame. A renormalization group analysis leads to simple renormalization-group-invariant definitions of the gluonic and fermionic contributions to either the singlet or the non-singlet components of the tensor, and therefore of their form factors among physical states. The lattice discussion focuses on the Wilson discretization of quark fields but the strategy is general. Specific to that case, we also carry out the analysis for the on-shell O(a)-improvement of the energy-momentum tensor. The renormalization and improvement programs profit from the fact that, as shown here, the thermal theory enjoys de-facto automatic O(a)-improvement at finite temperature. The validity of the proposal is scrutinized analytically by a study to 1-loop order in lattice perturbation theory with shifted and twisted (for quarks only) boundary conditions. The latter provides also additional useful insight for a precise non-perturbative calculation of the renormalization constants. The strategy proposed here is accessible to Monte Carlo computations, and in this sense it provides a practical way to define non-perturbatively the energy-momentum tensor in QCD.

We present the nonperturbative computation of renormalization factors in the RI'-(S)MOM schemes for the QCD gauge field ensembles generated by the CLS (coordinated lattice simulations) effort with three flavors of nonperturbatively improved Wilson (clover) quarks. We use ensembles with the standard (anti-)periodic boundary conditions in the time direction as well as gauge field configurations with open boundary conditions. Besides flavor-nonsinglet quark-antiquark operators with up to two derivatives we also consider three-quark operators with up to one derivative. For the RI'-SMOM scheme results we make use of the recently calculated three-loop conversion factors to the modified minimal subtraction scheme.