Symanzik Improvement Research Articles

Improvement, generalization, and scheme conversion of Wilson-line operators on the lattice in the auxiliary field approach

Nonlocal quark bilinear operators connected by link paths are used for studying parton distribution functions (PDFs) and transverse momentum-dependent PDFs of hadrons using lattice QCD. The nonlocality makes it difficult to understand the renormalization and improvement of these operators using standard methods. In previous work, we showed that by introducing an auxiliary field on the lattice, one can understand an on-axis Wilson-line operator as the product of two local operators in an extended theory. In this paper, we provide details about the calculation in perturbation theory of the factor for conversion from our lattice-suitable renormalization scheme to the MS-bar scheme. Extending our work, we study Symanzik improvement of the extended theory to understand the pattern of discretization effects linear in the lattice spacing, $a$, which are present even if the lattice fermion action exactly preserves chiral symmetry. This provides a prospect for an eventual $O(a)$ improvement of lattice calculations of PDFs. We also generalize our approach to apply to Wilson lines along lattice diagonals and to piecewise-straight link paths.

Symanzik improvement with dynamical charm: a 3+1 scheme for Wilson quarks

We discuss the problem of lattice artefacts in QCD simulations enhanced by the introduction of dynamical charmed quarks. In particular, we advocate the use of a massive renormalization scheme with a close to realistic charm mass. To maintain O(a) improvement for Wilson type fermions in this case we define a finite size scheme and carry out a nonperturbative estimation of the clover coefficient csw. It is summarized in a fit formula csw(g02) that defines an improved action suitable for future dynamical charm simulations.

Symanzik improvement of the gradient flow in lattice gauge theories.

We apply the Symanzik improvement programme to the 4+1-dimensional local re-formulation of the gradient flow in pure SU(N) lattice gauge theories. We show that the classical nature of the flow equation allows one to eliminate all cutoff effects at mathcal O(a^2), which originate either from the discretised gradient flow equation or from the gradient flow observable. All the remaining mathcal O(a^2) effects can be understood in terms of local counterterms at the zero flow-time boundary. We classify these counterterms and provide a complete set as required for on-shell improvement. Compared to the 4-dimensional pure gauge theory only a single additional counterterm is required, which corresponds to a modified initial condition for the flow equation. A consistency test in perturbation theory is passed and allows one to determine all counterterm coefficients to lowest non-trivial order in the coupling.

Taste-split staggered actions: Eigenvalues, chiralities, and Symanzik improvement

The eigenvalue spectra of staggered fermions with an Adams and/or Hoelbling mass term are studied. The chiralities of the eigenmodes reflect whether the chirality linked to the unflavored approximate (\gamma_5 \times 1) or the flavored exact (\gamma_5 \times \xi_5) staggered symmetry is considered, and which one of the RR, LR, RL, LL eigenmode definitions is used. In either case a sensitivity to the topological charge of the gauge background is found. We discuss how to remove the leading cut-off effects of these actions by means of a properly tuned improvement term and/or the overlap procedure. The combination of Symanzik improvement and link smearing radically improves the properties of the physical branch.

Symanzik improvement of lattice QCD with four flavors of Wilson quarks

We have determined the non-perturbative O ( a ) -improvement coefficient c sw for four flavors of Wilson quarks with the plaquette gauge action in a range of β ⩾ 5.0 . The data are fitted with several Padé approximation formulae to get an impression of the stability. A small extrapolation below β = 5.0 seems acceptable.

Highly improved staggered quarks on the lattice with applications to charm physics

We use perturbative Symanzik improvement to create a new staggered-quark action (HISQ) that has greatly reduced one-loop taste-exchange errors, no tree-level order ${a}^{2}$ errors, and no tree-level order $(am{)}^{4}$ errors to leading order in the quark's velocity $v/c$. We demonstrate with simulations that the resulting action has taste-exchange interactions that are 3--4 times smaller than the widely used ASQTAD action. We show how to bound errors due to taste exchange by comparing ASQTAD and HISQ simulations, and demonstrate with simulations that such errors are likely no more than 1% when HISQ is used for light quarks at lattice spacings of $1/10\text{ }\text{ }\mathrm{fm}$ or less. The suppression of $(am{)}^{4}$ errors also makes HISQ the most accurate discretization currently available for simulating $c$ quarks. We demonstrate this in a new analysis of the $\ensuremath{\psi}\ensuremath{-}{\ensuremath{\eta}}_{c}$ mass splitting using the HISQ action on lattices where $a{m}_{c}=0.43$ and 0.66, with full-QCD gluon configurations (from MILC). We obtain a result of 111(5) MeV which compares well with the experiment. We discuss applications of this formalism to $D$ physics and present our first high-precision results for ${D}_{s}$ mesons.

Bs and Ds decay constants in three-flavor lattice QCD.

Capitalizing on recent advances in lattice QCD, we present a calculation of the leptonic decay constants f(B(s)) and f(D(s)) that includes effects of one strange sea quark and two light sea quarks via an improved staggered action. By shedding the quenched approximation and the associated lattice scale uncertainty, lattice QCD greatly increases its predictive power. Nonrelativistic QCD is used to simulate heavy quarks with masses between 1.5m(c) and m(b). We arrive at the following results: f(B(s))=260+/-7+/-26+/-8+/-5 and f(D(s))=290+/-20+/-29+/-29+/-6 MeV. The first quoted error is the statistical uncertainty, and the rest estimate the sizes of higher order terms neglected in this calculation. All of these uncertainties are systematically improvable by including another order in the weak coupling expansion, the nonrelativistic expansion, or the Symanzik improvement program.

O(a)-improved quark action on anisotropic lattices and perturbative renormalization of heavy-light currents

We investigate the Symanzik improvement of the Wilson quark action on anisotropic lattices. Taking first a general action with nearest-neighbor and clover interactions, we study the mass dependence of the ratio of the hopping parameters, the clover coefficients, and an improvement coefficient for heavy-light vector and axial vector currents. We show how tree-level improvement can be achieved. For a particular choice of the spatial Wilson coupling, the results simplify, and $O(m_0a_\tau)$ improvement is possible. (Here $m_0$ is the bare quark mass and $a_\tau$ the temporal lattice spacing.) With this choice we calculate the renormalization factors of heavy-light bilinear operators at one-loop order of perturbation theory employing the standard plaquette gauge action.

O(a) improved twisted mass lattice QCD

Lattice QCD with Wilson quarks and a chirally twisted mass term (tmQCD) has been introduced in refs. [1, 2]. We here apply Symanzik's improvement programme to this theory and list the counterterms which arise at first order in the lattice spacinga. Based on the generalised transfer matrix, we define the tmQCD Schrödinger functional and use it to derive renormalized on-shell correlation functions. By studying their continuum approach in perturbation theory we then determine the new O(a) counterterms of the action and of a few quark bilinear operators to one-loop order.

Non-perturbative renormalization in lattice field theory

A review the strategies which have been developped in recent years to solve the non-perturbative renormalization problem in lattice field theories. Although the techniques are general, the focus will be on applications to lattice QCD. I discuss the momentum subtraction and finite volume schemes, and their application to scale dependent renormalizations. The problem of finite renormalizations is illustrated with the example of explicit chiral symmetry breaking, and I give a short status report concerning Symanzik's improvement programme to O( a).

Further evidence for an unstable H-dibaryon?

We present preliminary results for the mass of the 6q flavor-singlet state ( J P = 0 +, S = −2) called H-dibaryon, calculated in quenched QCD on 16 3×30 and 24 3×30 lattices with improved gauge and fermion actions (Symanzik improvement, Clover action). For both lattice sizes we applied the fuzzing technique to enhance the overlap with the ground state. We observe a H-mass above the ΛΛ-threshold for strong decay. The difference in mass, m H − 2 m Λ , increases with increasing lattice size.

The glueball spectrum from novel improved actions

Results for the inter-quark potential and low-lying SU(3) glueball spectrum from simulations using a new improved action are presented. The action, suitable for highly anisotropic lattices, contains a two-plaquette term coupling with a negative coefficient as well as incorporating Symanzik improvement.

Nucleon form factors and O( a) improvement

Nucleon form factors have been extensively studied both experimentally and theoretically for many years. We report here on new results of a high statistics quenched lattice QCD calculation of vector and axial-vector nucleon form factors at low momentum transfer within the Symanzik improvement programme. The simulations are performed at three κ and three β values allowing first an extrapolation to the chiral limit and then an extrapolation in the lattice spacing to the continuum limit. The computations are all fully non-perturbative. A comparison with experimental results is made.

Finite temperature phase diagram of QCD with improved Wilson fermions

We present results of an ongoing study of two flavour QCD with Wilson fermions at finite temperature. We have used tree level Symanzik improvement in both the gauge and fermion part of the action. The phase diagram was previously determined on an 8 3 × 4 lattice and the existence of Aoki's phase demonstrated. On our current lattice of 12 2 × 24 × 4 we have extended the set of observables and studied chiral and thermal properties at light quark masses.

Flavor-symmetry restoration and Symanzik improvement for staggered quarks

We resolve contradictions in the literature concerning the origins and size of unphysical flavor-changing strong interactions generated by the staggered-quark discretization of QCD. We show that the leading contributions are tree-level in $\order(a^2)$ and that they can be removed by adding three correction terms to the link operator in the standard action. These corrections are part of the systematic Symanzik improvement of the staggered-quark action. We present a new improved action for staggered quarks that is accurate up to errors of $\order(a^4,a^2\alpha_s)$ --- more accurate than most, if not all, other discretizations of light-quark dynamics.

Fixed point actions and on-shell tree-level Symanzik improvement

In this paper it is argued that the properties of the fixed point action of a renormalization group transformation can be used to implement the on-shell tree-level Symanzik improvement of lattice actions to any given order in the expansion in the lattice spacing, in a way which does not involve any perturbative calculations. In particular, a well-known technique for the lowest order improvement of SU(N) lattice gauge theories is revisited from the point of view of fixed point actions, which allows to shed light on some subtle points.

O(a) improvement of nucleon matrix elements

We report on preliminary results of a high statistics quenched lattice QCD calculation of nucleon matrix elements within the Symanzik improvement programme. Using the recently determined renormalisation constants from the Alpha Collaboration we present a fully non-perturbative calculation of the forward nucleon axial matrix element with O(a) lattice artifacts completely removed. Runs are made at β = 6.0 and β = 6.2, in an attempt to check scaling and O(a 2) effects. We shall also briefly describe results for ⇄χ↩, the matrix element of a higher derivative operator.

Finite temperature phase diagramm of QCD with improved Wilson fermions

We present first results of a study of two flavour QCD with Wilson fermions at finite temperature. We have used tree level Symanzik improvement in both the gauge and fermion part of the action. In a first step we explore the phase diagramm on an 8 3 × 4 lattice, with particular emphasis on checking Aoki's conjecture with an improved action.

On-shell-improved lattice QCD with staggered fermions

By using Symanzik's improvement program, we study on-shell improved lattice QCD with staggered fermions. We find that there are as many as 15 independent lattice operators of dimension of six~(including both gauge and fermion operators) which must be added to the unimproved action to form an $O(a^2)$ improved action. Among them, the total number of dimension-6 gauge operators and fermion bilinears is 5. The other 10 terms are four-fermion operators. At the tree-level and tadpole-improved tree-level, all the 10 four fermion operators are absent.

Perturbative improvement for lattice QCD: An update

Recent developments in the Symanzik improvement program for lattice QCD are reviewed.