Operators In Lattice QCD Research Articles

Optimized two-baryon operators in lattice QCD

A set of optimized interpolating operators which are dominantly coupled to each eigenstate of two baryons on the lattice is constructed by the HAL QCD method. To test its validity, we consider heavy dibaryons ${\mathrm{\ensuremath{\Omega}}}_{3Q}{\mathrm{\ensuremath{\Omega}}}_{3Q}$ ($Q=s$, $c$) calculated by ($2+1$)-flavor lattice QCD simulations with nearly physical pion mass. The optimized two-baryon operators are shown to provide effective energies of the ground and excited states, separately stable as a function of the Euclidean time. Also they agree with the eigenenergies in a finite lattice box obtained from the leading-order HAL QCD potential $V(\mathbit{r})$ within statistical errors. The overlapping factors between the optimized sink operators and the state created by the wall-type source operator indicate that $V(\mathbit{r})$ can be reliably extracted, no matter whether the spacetime correlation of two baryons is dominated by the ground state or the excited state. It is suggested that the optimized set of operators is useful for variational studies of hadron-hadron interactions.

Determination of the quark condensate from heavy-light current-current correlators in full lattice QCD

We derive the Operator Product Expansion whose vacuum expectation value gives the time-moments of the pseudoscalar heavy-light current-current correlator up to and including terms in $\alpha_s^2$ multiplying $\langle\overline{\psi}\psi\rangle/M^3$ and terms in $\alpha_s$ multiplying $\langle \alpha_s G^2 \rangle/M^4$, where $M$ is the heavy-quark mass. Using lattice QCD results for heavy-strange correlators obtained for a variety of heavy quark masses on gluon field configurations including $u$, $d$ and $s$ quarks in the sea at three values of the lattice spacing, we are able to show that the contribution of the strange-quark condensate to the time-moments is very substantial. We use our lattice QCD time-moments and the OPE to determine a value for the condensate, fitting the 4th, 6th, 8th and 10th time-moments simultaneously. Our result, $\langle \overline{s}s \rangle^{\overline{\text{MS}}}(2 \text{GeV}) = -(296(11) \,\mathrm{MeV})^3$, agrees well with HPQCD's earlier, more direct, lattice QCD determination~\cite{McNeile:2012xh}. As well as confirming that the $s$ quark condensate is close in value to the light quark condensate, this demonstrates clearly the consistency of the Operator Product Expansion for fully nonperturbative calculations of matrix elements of short-distance operators in lattice QCD.

Tetraquark operators in lattice QCD and exotic flavour states in the charm sector

We present a general class of operators resembling compact tetraquarks which have a range of colour-flavour-spin structures, transform irreducibly under the symmetries of the lattice and respect other relevant symmetries. These constructions are demonstrated in lattice QCD calculations with light quarks corresponding to mπ = 391 MeV. Using the distillation framework, correlation functions involving large bases of meson-meson and tetraquark operators are computed in the isospin-1 hidden-charm and doubly-charmed sectors, and finite-volume spectra are extracted with the variational method. We find the spectra are insensitive to the addition of tetraquark operators to the bases of meson-meson operators. For the first time, through using diverse bases of meson-meson operators, the multiple energy levels associated with meson-meson levels which would be degenerate in the non-interacting limit are extracted reliably. The number of energy levels in each spectrum is found to be equal to the number of expected non-interacting meson-meson levels in the energy region considered and the majority of energies lie close to the non-interacting levels. Therefore, there is no strong indication for any bound state or narrow resonance in the channels we study.

Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD

A new method of stochastically estimating the low-lying effects of quark propagation is proposed which allows accurate determinations of temporal correlations of single-hadron and multihadron operators in lattice QCD. The method is well suited for calculations in large volumes. Contributions involving quark propagation connecting hadron sink operators at the same final time can be handled in a straightforward manner, even for a large number of final time slices. The method exploits Laplacian Heaviside (LapH) smearing. ${Z}_{N}$ noise is introduced in a novel way, and variance reduction is achieved using judiciously-chosen noise-dilution projectors. The method is tested using isoscalar mesons in the scalar, pseudoscalar, and vector channels, and using the two-pion system of total isospin $I=0$, 1, 2 on large anisotropic ${24}^{3}\ifmmode\times\else\texttimes\fi{}128$ lattices with spatial spacing ${a}_{s}\ensuremath{\sim}0.12\text{ }\text{ }\mathrm{fm}$ and temporal spacing ${a}_{t}\ensuremath{\sim}0.034\text{ }\text{ }\mathrm{fm}$ for pion masses ${m}_{\ensuremath{\pi}}\ensuremath{\approx}390$ and 240 MeV.

Group-theoretical construction of extended baryon operators in lattice QCD

The design and implementation of large sets of spatially-extended, gauge-invariant operators for use in determining the spectrum of baryons in lattice QCD computations are described. Group-theoretical projections onto the irreducible representations of the symmetry group of a cubic spatial lattice are used in all isospin channels. The operators are constructed to maximize overlaps with the low-lying states of interest, while minimizing the number of sources needed in computing the required quark propagators. Issues related to the identification of the spin quantum numbers of the states in the continuum limit are addressed.

Non-perturbative renormalisation of composite operators in lattice QCD

We investigate the non-perturbative renormalisation of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields. These include operators which are relevant to the calculation of moments of hadronic structure functions. The computations are based on Monte Carlo simulations using quenched Wilson fermions.

Composite operators in lattice QCD: nonperturbative renormalization

We investigate the nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields. These include operators which are relevant to the calculation of moments of hadronic structure functions. The computations are based on Monte Carlo simulations using quenched Wilson fermions.

Perturbative calculation of improvement coefficients toO(g2a)for bilinear quark operators in lattice QCD

We calculate the ${O(g}^{2}a)$ mixing coefficients of bilinear quark operators in lattice QCD using a standard perturbative evaluation of on-shell Green's functions. Our results for the plaquette gluon action are in agreement with those previously obtained with the Schr\"odinger functional method. The coefficients are also calculated for a class of improved gluon actions having six-link terms.

Evaluating sea quark contributions to flavour-singlet operators in lattice QCD

Evaluating sea quark contributions to flavour-singlet operators in lattice QCD

Evaluating sea quark contributions to flavour-singlet operators in lattice QCD

In a full QCD lattice study with N f = 2 Wilson fermions, we seek to optimize the signals for the disconnected contributions to the matrix element of flavour-singlet operators between nucleon states, which are indicative for sea quark effects. We demonstrate, in form of a fluctuation analysis to the noisy estimator technique, that — in order to achieve a tolerable signal to noise-ratio in full QCD — it is advantageous to work with a Z 2- noise source rather than to rely only on gauge invariance to cancel non-gauge-invariant background. In the case of the πN σ- term, we find that 10 Z 2- noise sources suffice on our sample (about 150 independent QCD configurations at β = 5.6 on 16 3 × 32 with κ sea = 0.157, equivalent to M π / M ϱ = 0.76 (1), to achieve decent signals and adequate fluctuations, rather than 300 such sources as recently used in quenched simulations.

Improved lattice QCD

I discuss the strategy to improve to O ( a ) matrix elements of fermion operators in lattice QCD.

Mixing of DIS operators in lattice QCD

We extend to the “unquenched” case the results of the perturbative calculation in lattice QCD with Wilson fermions of the mixing and renormalization coefficients of the operators entering into the expression of the lowest moment of the F 2 structure function. We argue that the rank two finite operator with vanishing anomalous dimension that we construct for unlike indices, is to be identified with the lattice energy-momentum tensor.

Improved actions, redundant operators and scaling in lattice SU(3)

Schwinger-Dyson equations are used to systematically calculate redundant operators in lattice QCD and their role in perturbatively improved actions is analyzed. The criteria for improved actions in Monte Carlo simulations are discussed and their usefulness also. In particular the renormalized trajectory is estimated for the b = 3 renormalization group transformation in a four-parameter space and its scaling behavior is studied for future use in spectrum calculations.