Non-perturbative Improvement Research Articles

Pion in a uniform background magnetic field with clover fermions

Background field methods provide an important nonperturbative formalism for the determination of hadronic properties which are complementary to matrix-element calculations. However, new challenges are encountered when utilising a fermion action exposed to additive mass renormalisations. In this case, the background field can induce an undesired field-dependent additive mass renormalisation that acts to change the quark mass as the background field is changed. For example, in a calculation utilising Wilson fermions in a uniform background magnetic field, the Wilson term introduced a field-dependent renormalisation to the quark mass which manifests itself in an unphysical increase of the neutral-pion mass for large magnetic fields. Herein, the clover fermion action is studied to determine the extent to which the removal of $\mathcal{O}(a)$ discretisation errors suppresses the field-dependent changes to the quark mass. We illustrate how a careful treatment of nonperturbative improvement is necessary to resolve this artefact of the Wilson term. Using the $32^3 \times 64$ dynamical-fermion lattices provided by the PACS-CS Collaboration we demonstrate how our technique suppresses the unphysical mass renormalisation over a broad range of magnetic field strengths.

Erratum: Nonperturbative improvement of the vector current in Wilson lattice QCD [Phys. Rev. D 92 , 114503 (2015)

Received 16 November 2018DOI:https://doi.org/10.1103/PhysRevD.99.059905© 2019 American Physical Society

Nonperturbative improvement of the vector current in Wilson lattice QCD

Many observables of interest in lattice QCD are extracted from correlation functions involving the vector current. If Wilson fermions are used, it is therefore of practical importance that, besides the action, the current be O($a$) improved in order to remove the leading discretization errors from the observables. Here we introduce and apply a new method to determine the improvement coefficient for the two most widely used discretizations of the current.

Non-perturbative improvement of the axial current in [formula omitted] lattice QCD with Wilson fermions and tree-level improved gauge action

The coefficient cA required for O(a) improvement of the axial current in lattice QCD with Nf=3 flavors of Wilson fermions and the tree-level Symanzik-improved gauge action is determined non-perturbatively. The standard improvement condition using Schrödinger functional boundary conditions is employed at constant physics for a range of couplings relevant for simulations at lattice spacings of ≈0.09 fm and below. We define the improvement condition projected onto the zero topological charge sector of the theory, in order to avoid the problem of possibly insufficient tunneling between topological sectors in our simulations at the smallest bare coupling. An interpolation formula for cA(g02) is provided together with our final results.

Improving the continuum limit of gradient flow step scaling

We introduce a non-perturbative improvement for the renormalization group step scaling function based on the gradient flow running coupling, which may be applied to any lattice gauge theory of interest. Considering first SU(3) gauge theory with N f = 4 massless staggered fermions, we demonstrate that this improvement can remove $ \mathcal{O}\left( {{a^2}} \right) $ lattice artifacts, and thereby increases our control over the continuum extrapolation. Turning to the 12-flavor system, we observe an infrared fixed point in the infinite-volume continuum limit. Applying our proposed improvement reinforces this conclusion by removing all observable $ \mathcal{O}\left( {{a^2}} \right) $ effects. For the finite-volume gradient flow renormalization scheme defined by $ c={{{\sqrt{8t }}} \left/ {L=0.2 } \right.} $ , we find the continuum conformal fixed point to be located at $ g_{\star}^2=6.2(2) $ .

Nonperturbative improvement of SU(2) lattice gauge theory with adjoint or fundamental flavours

The gauge theory with SU(2) color group and two fermion species, each transforming under the adjoint representation, may appear conformal or almost conformal in the infrared, and is one of the candidate theories for building models for technicolor. Early lattice Monte Carlo studies of this model have used unimproved Wilson fermion formulation, which can be expected to have large lattice cutoff effects. In this paper we present the calculation of the O(a) improved lattice Wilson-clover action of the theory. The Sheikholeslami-Wohlert coefficient has been determined nonperturbatively, and various boundary improvement terms, needed for the Schrödinger functional formalism, have been calculated in perturbation theory. For comparison, we have also determined the improvement coefficients for SU(2) gauge theory with two fundamental representation fermions. The calculation paves way for more accurate lattice Monte Carlo analyses of the theory in the future.

Improvement via hypercubic smearing in triplet and sextet QCD

We study nonperturbative improvement in SU(3) lattice gauge theory coupled to fermions in the fundamental and two-index symmetric representations. Our lattice action is defined with hypercubic smeared links incorporated into the Wilson--clover fermion kernel. Using standard Schr\"odinger-functional techniques, we estimate the clover coefficient ${c}_{\mathrm{SW}}$ and find that discretization errors are much smaller than in thin-link theories.

Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation

Using a method mixing Mellin-Barnes representation and Borel resummation we show how to obtain hyperasymptotic expansions from the (divergent) formal power series which follow from the perturbative evaluation of arbitrary "$N$-point" functions for the simple case of zero-dimensional $\phi^4$ field theory. This hyperasymptotic improvement appears from an iterative procedure, based on inverse factorial expansions, and gives birth to interwoven non-perturbative partial sums whose coefficients are related to the perturbative ones by an interesting resurgence phenomenon. It is a non-perturbative improvement in the sense that, for some optimal truncations of the partial sums, the remainder at a given hyperasymptotic level is exponentially suppressed compared to the remainder at the preceding hyperasymptotic level. The Mellin-Barnes representation allows our results to be automatically valid for a wide range of the phase of the complex coupling constant, including Stokes lines. A numerical analysis is performed to emphasize the improved accuracy that this method allows to reach compared to the usual perturbative approach, and the importance of hyperasymptotic optimal truncation schemes.

Lattice Wess-Zumino model with Ginsparg-Wilson fermions: One-loop results and GPU benchmarks

We numerically evaluate the one-loop counterterms for the four-dimensional Wess-Zumino model formulated on the lattice using Ginsparg-Wilson fermions of the overlap (Neuberger) variety, together with an auxiliary fermion (plus superpartners), such that a lattice version of $U(1)_R$ symmetry is exactly preserved in the limit of vanishing bare mass. We confirm previous findings by other authors that at one loop there is no renormalization of the superpotential in the lattice theory, but that there is a mismatch in the wavefunction renormalization of the auxiliary field. We study the range of the Dirac operator that results when the auxiliary fermion is integrated out, and show that localization does occur, but that it is less pronounced than the exponential localization of the overlap operator. We also present preliminary simulation results for this model, and outline a strategy for nonperturbative improvement of the lattice supercurrent through measurements of supersymmetry Ward identities. Related to this, some benchmarks for our graphics processing unit code are provided. Our simulation results find a nearly vanishing vacuum expectation value for the auxiliary field, consistent with approximate supersymmetry at weak coupling.

Non-perturbative improvement of quark mass renormalization in two-flavour lattice QCD

We non-perturbatively determine the renormalization constant and the improvement coefficients relating the renormalized current and subtracted quark mass of (quenched) valence quarks propagating in a sea of O(a) improved two massless quarks. We employ the Schrödinger functional scheme and fix the physical extent of the box by working at a constant value of the renormalized coupling. Our calculation yields results which cover two regions of bare parameter space. One is the weak-coupling region suitable for volumes of about half a fermi. By making simulations in this region, quarks as heavy as the bottom can be propagated with the full relativistic QCD action and renormalization problems in HQET can be solved non-perturbatively by a matching to QCD infinite volume. The other region refers to the common parameter range in large-volume simulations of two-flavour lattice QCD, where our results have particular relevance for charm physics applications.

Nonperturbative improvement of stout-smeared three-flavor clover fermions

We discuss a three-flavor lattice QCD action with clover improvement in which the fermion matrix has single level stout smearing for the hopping terms together with unsmeared links for the clover term. With the (tree-level) Symanzik improved gluon action this constitutes the stout link nonperturbative clover or SLiNC action. To cancel $O(a)$ terms the clover term coefficient has to be tuned. We present here results of a nonperturbative determination of this coefficient using the Schr\odinger functional and as a by-product a determination of the critical hopping parameter. Comparisons of the results are made with lowest order perturbation theory.

Non-perturbative improvement of the axial current with three dynamical flavors and the Iwasaki gauge action

We perform a non-perturbative determination of the improvement coefficient c_A to remove O(a) discretization errors in the axial vector current in three-flavor lattice QCD with the Iwasaki gauge action and the standard O$(a)$-improved Wilson quark action. An improvement condition with a good sensitivity to c_A is imposed at constant physics. Combining our results with the perturbative expansion, c_A is now known rather precisely for 1/a \gtrsim 1.6 GeV.

Non-perturbative improvement of the axial current for dynamical Wilson fermions

A non-perturbative determination of the axial current improvement coefficient cA is performed with two flavors of dynamical improved Wilson fermions and plaquette gauge action. The improvement condition is formulated with Schroedinger functional boundary conditions and enforced at constant physical volume. Large sensitivity is obtained by using two different pseudo-scalar states in the PCAC relation. We estimate the resulting correction to F_PS at beta=5.2 to be around 10%.

Three flavor dynamical QCD project by CP-PACS/JLQCD

The CP-PACS and JLQCD Collaborations have been made systematic studies of lattice QCD carrying out both chiral and continuum extrapolations. Importance of dynamical quark effects has been clarified by a comparison of quenched QCD and two flavor full QCD simulations. In two flavor simulations, the dynamical effects of u and d quarks are taken into account, but the third quark s is still treated in a quenched approximation. As the final step towards a fully realistic lattice simulation of QCD, two collaborations started a joint project of three flavor QCD, concentrating all big computers available. Based on a series of preparative studies of exact simulation algorithm and non-perturbative improvement coefficient, a large scale simulation of three flavor QCD has been started. I present the results of light hadron spectrum and light quark masses from the first production runs.

QCD on 2 + 2 anisotropic lattices

We discuss the implementation of QCD on 2 + 2 anisotropic lattices. Technical details regarding the choice of the action as well as perturbative and non-perturbative improvement are analyzed. The physical applications of the program are presented.

Light quark simulations with FLIC fermions

Hadron masses are calculated in quenched lattice QCD in order to probe the scaling behavior of a novel fat-link clover fermion action in which only the irrelevant operators of the fermion action are constructed using APEsmeared links. Light quark masses providing am π/m p mass ratio of 0.35 are considered to assess the exceptional configuration problem of clover-fermion actions. This Fat-Link Irrelevant Clover (FLIC) fermion action provides scaling which is superior to mean-field improvement and offers advantages over non-perturbative improvement including a reduced exceptional configuration problem.

Nonperturbative improvement and tree-level correction of the quark propagator

We extend an earlier study of the Landau gauge quark propagator in quenched QCD where we used two forms of the $\mathcal{O}(a)$-improved propagator with the Sheikholeslami-Wohlert quark action. In the present study we use the nonperturbative value for the clover coefficient ${c}_{\mathrm{sw}}$ and mean-field improvement coefficients in our improved quark propagators. We compare this with our earlier results which used the mean-field ${c}_{\mathrm{sw}}$ and tree-level improvement coefficients for the propagator. We also compare three different implementations of tree-level correction: additive, multiplicative, and hybrid. We show that the hybrid approach is the most robust and reliable and can successfully deal even with strong ultraviolet behavior and zero crossing of the lattice tree-level expression. We find good agreement between our improved quark propagators when using the appropriate nonperturbative improvement coefficients and hybrid tree-level correction. We also present a simple extrapolation of the quark mass function to the chiral limit.

Non-perturbative improvement of lattice QCD at large momenta

We propose a method to improve lattice operators composed of Wilson fermions which allows the removal of all corrections of O( a), including those proportional to the quark mass. It requires off-shell improvement of quark fields and composite operators, which is achieved by studying the behaviour of quark and gluon correlation functions at large momenta.

Non-perturbative improvement of bilinears in unquenched QCD

We describe how the improvement of quark bilinears generalizes from quenched to unquenched QCD, and discuss which of the additional improvement constants can be determined using Ward Identities.

Non-perturbative improvement of bilinears in unquenched QCD

We describe how the improvement of quark bilinears generalizes from quenched to unquenched QCD, and discuss which of the additional improvement constants can be determined using Ward Identities.