High Energy Physics Lattice

We present a lattice QCD calculation of theΔI=1/2,K→ππdecay amplitudeA0andε′, the measure of direct CP-violation inK→ππdecay, improving our 2015 calculation of these quantities. Both calculations were performed with physical kinematics on a323×64lattice with an inverse lattice spacing ofa−1=1.3784(68)GeV. However, the current calculation includes nearly four times the statistics and numerous technical improvements allowing us to more reliably isolate theππground-state and more accurately relate the lattice operators to those defined in the Standard Model. We findRe(A0)=2.99(0.32)(0.59)×10−7GeV andIm(A0)=−6.98(0.62)(1.44)×10−11GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental resultRe(A0)=3.3201(18)×10−7GeV. These results forA0can be combined with our earlier lattice calculation ofA2to obtainRe(ε′/ε)=21.7(2.6)(6.2)(5.0)×10−4, where the third error represents omitted isospin breaking effects, and Re(A0)/Re(A2)=19.9(2.3)(4.4). The first agrees well with the experimental result ofRe(ε′/ε)=16.6(2.3)×10−4. A comparison of the second with the observed ratio Re(A0)/Re(A2)=22.45(6), demonstrates the Standard Model origin of this "ΔI=1/2rule" enhancement.

We show that standard identities and theorems for lattice models withU(1)symmetry get re-expressed discretely in the tensorial formulation of these models. We explain the geometrical analogy between the continuous lattice equations of motion and the discrete selection rules of the tensors. We construct a gauge-invariant transfer matrix in arbitrary dimensions. We show the equivalence with its gauge-fixed version in a maximal temporal gauge and explain how a discrete Gauss's law is always enforced. We propose a noise-robust way to implement Gauss's law in arbitrary dimensions. We reformulate Noether's theorem for global, local, continuous or discrete Abelian symmetries: for each given symmetry, there is one corresponding tensor redundancy. We discuss semi-classical approximations for classical solutions with periodic boundary conditions in two solvable cases. We show the correspondence of their weak coupling limit with the tensor formulation after Poisson summation. We briefly discuss connections with other approaches and implications for quantum computing.

Non-zero topological charge is prohibited in the chiral limit of gauge-fermion systems because any instanton would create a zero mode of the Dirac operator. On the lattice, however, the geometricQgeom=⟨FF~⟩/32π2definition of the topological charge does not necessarily vanish even when the gauge fields are smoothed for example with gradient flow. Small vacuum fluctuations (dislocations) not seen by the fermions may be promoted to instanton-like objects by the gradient flow. We demonstrate that these artifacts of the flow cause the gradient flow renormalized gauge coupling to increase and run faster. In step-scaling studies such artifacts contribute a term which increases with volume. The usuala/L→0continuum limit extrapolations can hence lead to incorrect results. In this paper we investigate these topological lattice artifacts in the SU(3) 10-flavor system with domain wall fermions and the 8-flavor system with staggered fermions. Both systems exhibit nonzero topological charge at the strong coupling, especially when using Symanzik gradient flow. We demonstrate how this artifact impacts the determination of the renormalized gauge coupling and the step-scalingβfunction.

We investigate some properties of Karsten-Wilczek and Borici-Creutz fermions, which are the best known varieties in the class of minimally doubled lattice fermion actions. Our focus is on the dispersion relation and the distribution of eigenvalues in the free-field theory. We consider the situation in two and four space-time dimensions, and we discuss how properties vary as a function of the Wilson-like lifting parameterr.

For a given Markov chain Monte Carlo (MCMC) algorithm, we define the distance between configurations that quantifies the difficulty of transitions. This distance enables us to investigate MCMC algorithms in a geometrical way, and we investigate the geometry of the simulated tempering algorithm implemented for an extremely multimodal system with highly degenerate vacua. We show that the large scale geometry of the extended configuration space is given by an asymptotically anti-de Sitter metric, and argue in a simple, geometrical way that the tempering parameter should be best placed exponentially to acquire high acceptance rates for transitions in the extra dimension. We also discuss the geometrical optimization of the tempered Lefschetz thimble method, which is an algorithm towards solving the numerical sign problem.

Extraction of hadronic observables at finite-momenta from Lattice QCD (LQCD) is constrained by the well-known signal-to-noise problems afflicting all such LQCD calculations. Traditional quark smearing algorithms are commonly used tools to improve the statistical quality of hadronicn-point functions, provided operator momenta are small. The momentum smearing algorithm of Bali et al. extends the range of momenta that are cleanly accessible, and has facilitated countless novel lattice calculations. Momentum smearing has, however, not been explicitly demonstrated within the framework of distillation. In this work we extend the momentum-smearing idea, by exploring a few modifications to the distillation framework. Together with enhanced time slice sampling and expanded operator bases engendered by distillation, we find ground-state nucleon energies can be extracted reliably for∣∣p→∣∣≲3 GeVand matrix elements featuring a large momentum dependence can be resolved.

We present the first lattice QCD calculation of the distribution amplitudes of longitudinally and transversely polarized vector mesonsK∗andϕusing large momentum effective theory. We use the clover fermion action on three ensembles with 2+1+1 flavors of highly improved staggered quarks (HISQ) action, generated by MILC collaboration, at physical pion mass and \{0.06, 0.09, 0.12\} fm lattice spacings, and choose three different hadron momentaPz={1.29,1.72,2.15}GeV. The resulting lattice matrix elements are nonperturbatively renormalized in a hybrid scheme proposed recently. Also an extrapolation to the continuum and infinite momentum limit is carried out. We find that while the longitudinal distribution amplitudes tend to be close to the asymptotic form, the transverse ones deviate rather significantly from the asymptotic form. Our final results provide crucial {\it ab initio} theory inputs for analyzing pertinent exclusive processes.

Energy momentum tensor (EMT) characterizes the response of the vacuum as well as the thermal medium under the color electromagnetic fields. We define the EMT by means of the gradient flow formalism and study its spatial distribution around a static quark in the deconfined phase of SU(3) Yang-Mills theory on the lattice. Although no significant difference can be seen between the EMT distributions in the radial and transverse directions except for the sign, the temporal component is substantially different from the spatial ones near the critical temperatureTc. This is in contrast to the prediction of the leading-order thermal perturbation theory. The lattice data of the EMT distribution also indicate the thermal screening at long distance and the perturbative behavior at short distance.

We perform a lattice study of double parton distributions in the pion, using the relationship between their Mellin moments and pion matrix elements of two local currents. A good statistical signal is obtained for almost all relevant Wick contractions. We investigate correlations in the spatial distribution of two partons in the pion, as well as correlations involving the parton polarisation. The patterns we observe depend significantly on the quark mass. We investigate the assumption that double parton distributions approximately factorise into a convolution of single parton distributions.

We study double-winding Wilson loops inSU(N)lattice Yang-Mills gauge theory by using both strong coupling expansions and numerical simulations. First, we examine how the area law falloff of a ``coplanar'' double-winding Wilson loop average depends on the number of colorN. Indeed, we find that a coplanar double-winding Wilson loop average obeys a novel ``max-of-areas law'' forN=3and the sum-of-areas law forN≥4, although we reconfirm the difference-of-areas law forN=2. Second, we examine a ``shifted'' double-winding Wilson loop, where the two constituent loops are displaced from one another in a transverse direction. We evaluate its average by changing the distance of a transverse direction and we find that the long distance behavior does not depend on the number of colorN, while the short distance behavior depends strongly onN.