Hadron masses are calculated in quenched lattice QCD on a variety of lattices in order to probe the scaling behavior of the Fat-Link Irrelevant Clover (FLIC) fermion action, a fat-link clover fermion action in which the purely irrelevant operators of the fermion action are constructed using APE-smeared links. The scaling analysis indicates FLIC fermions provide a new form of nonperturbative O(a) improvement where near-continuum results are obtained at finite lattice spacing.
The chiral properties of the fat-link irrelevant clover (FLIC) fermion action are examined. The improved chiral properties of fermion actions incorporating smoothed links are realized in the FLIC action where only the irrelevant operators of the fermion action are constructed with smoothed links. In particular, the histogram of the additive mass renormalization encountered in chiral-symmetry breaking Wilson-type fermion actions is seen to narrow upon introducing fat-links in the irrelevant operators. The exceptional configuration problem of quenched QCD is reduced, enabling access to the light…
The Fat-Link Irrelevant Clover (FLIC) fermion action provides a new form of nonperturbative O(a)-improvement in lattice fermion actions offering near continuum results at finite lattice spacing. It provides computationally inexpensive access to the light quark mass regime of QCD where chiral nonanalytic behaviour associated with Goldstone bosons is revealed. The motivation and formulation of FLIC fermions, its excellent scaling properties and its low-lying hadron mass phenomenology are presented.
APE smearing the links in the irrelevant operators of clover fermions (Fat-Link Irrelevant Clover (FLIC) fermions) provides significant improvement in the condition number of the Hermitian-Dirac operator and gives rise to a factor of two savings in computing the overlap operator. This report investigates the effects of using a highly-improved definition of the lattice field-strength tensor F_mu_nu in the fermion action, made possible through the use of APE-smeared fat links in the construction of the irrelevant operators. Spurious double-zero crossings in the spectral flow of the Hermitian-Wil…
The Fat Link Irrelevant Clover (FLIC) fermion action is a variant of the $O(a)$-improved Wilson action where the irrelevant operators are constructed using smeared links. While the use of such smearing allows for the use of highly improved definitions of the field strength tensor $F_{μν},$ we show that the standard 1-loop clover term with a mean field improved coefficient $c_{\rm sw}$ is sufficient to remove the $O(a)$ errors, avoiding the need for non-perturbative tuning. This result enables efficient dynamical simulations in QCD with the FLIC fermion action.
The use of APE smearing or other blocking techniques in fermion actions can provide many advantages. There are many variants of these fat link actions in lattice QCD currently, such as FLIC fermions. The FLIC fermion formalism makes use of the APE blocking technique in combination with a projection of the blocked links back into the special unitary group. This reunitarisation is often performed using an iterative maximisation of a gauge invariant measure. This technique is not differentiable with respect to the gauge field and thus prevents the use of standard Hybrid Monte Carlo simulation alg…
The action of the overlap-Dirac operator on a vector is typically implemented indirectly through a multi-shift conjugate gradient solver. The compute-time required depends upon the condition number, $κ$, of the matrix that is used as the overlap kernel. While the Wilson action is typically used as the overlap kernel, the FLIC (Fat Link Irrelevant Clover) action has an improved condition number and provides up to a factor of two speedup in evaluating the overlap action. We summarize recent progress on the use of FLIC overlap 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 APE-smeared links. Light quark masses corresponding to an m_pi / m_rho 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 nonperturbative improvement, including reduced exceptional configu…
The Fat-Link Irrelevant Clover (FLIC) fermion action provides a new form of nonperturbative O(a) improvement and allows efficient access to the light quark-mass regime. FLIC fermions enable the construction of the nonperturbatively O(a)-improved conserved vector current without the difficulties associated with the fine tuning of the improvement coefficients. The simulations are performed with an O(a^2) mean-field improved plaquette-plus-rectangle gluon action on a 20^3 x 40 lattice with a lattice spacing of 0.128 fm, enabling the first simulation of baryon form factors at light quark masses on…
We investigate the mass of the $1^{-+}$ exotic meson, created with hybrid interpolating fields. Access to light quark masses approaching 25 MeV is facilitated by the use of the Fat-Link Irrelevant Clover (FLIC) fermion action, and large ($20^3 \times 40$) lattices. Our results indicate that the $1^{-+}$ exotic exhibits significant curvature close to the chiral limit, and yield a $1^{-+}$ mass in agreement with the $π_1 (1600)$ candidate and exclusive of the $π_1 (1400)$.
The Fat-Link Irrelevant Clover (FLIC) fermion action provides a new form of nonperturbative O(a) improvement and allows efficient access to the light quark-mass regime. FLIC fermions enable the construction of the nonperturbatively O(a)-improved conserved vector current without the difficulties associated with the fine tuning of the improvement coefficients. The simulations are performed with an O(a^2) mean-field improved plaquette-plus-rectangle gluon action on a 20^3 x 40 lattice with a lattice spacing of 0.128 fm, enabling the first simulation of baryon form factors at light quark masses on…
The spectral properties of hybrid meson interpolating fields are investigated. The quantum numbers of the meson are carried by smeared-source fermion operators and highly-improved chromo-electric and -magnetic field operators composed with APE-smeared links. The effective masses of standard and hybrid operators indicate that the ground state meson is effectively isolated using both standard and hybrid interpolating fields. Focus is placed on interpolating fields in which the large spinor components of the quark and antiquark fields are merged. In particular, the effective mass of the exotic $1…
Masses of positive and negative parity excited nucleons and hyperons are calculated in quenched lattice QCD using an O(a^2) improved gluon action and a fat-link clover fermion action in which only the irrelevant operators are constructed with fat links. The results are in agreement with earlier N* simulations with improved actions, and exhibit a clear mass splitting between the nucleon and its parity partner, as well as a small mass splitting between the two low-lying J^P={1/2}^- N* states. Study of different Lambda interpolating fields suggests a similar splitting between the lowest two {1/2}…
By imposing the constraints of charge symmetry we show that the strangeness magnetic moment of the nucleon can be expressed in terms of empirical magnetic moments and ratios of valence quark magnetic moments. The latter are determined using modern chiral extrapolation techniques and recent low mass lattice QCD simulations of the individual quark contributions to the magnetic moments of the nucleon octet. The result is a precise determination of G_M^s, namely -0.043 +/- 0.026 mu_N, which is consistent with the latest experimental measurements.
FLIC overlap fermions are a variant of the standard (Wilson) overlap action, with the FLIC (Fat Link Irrelevant Clover) action as the overlap kernel rather than the Wilson action. The structure of the FLIC overlap fermion propagator in momentum space is studied, and a comparison against previous studies of the Wilson overlap propagator in quenched QCD is performed. To explore the scaling properties of the propagator for the two actions, numerical calculations are performed in Landau Gauge across three lattices with different lattice spacing $a$ and similar physical volumes. We find that at lig…
A pedagogical overview of the formulation of the Fat Link Irrelevant Clover (FLIC) fermion action and its associated phenomenology is described. The scaling analysis indicates FLIC fermions provide a new form of nonperturbative O(a) improvement where near-continuum results are obtained at finite lattice spacing. Spin-1/2 and spin-3/2, even and odd parity baryon resonances are investigated in quenched QCD, where the nature of the Roper resonance and Lambda(1405) are of particular interest. FLIC fermions allow efficient access to the light quark-mass regime, where evidence of chiral nonanalytic …
The use of APE smearing or other blocking techniques in lattice fermion actions can provide many advantages. There are many variants of these fat link actions in lattice QCD currently, such as FLIC fermions. The FLIC fermion formalism makes use of the APE blocking technique in combination with a projection of the blocked links back into the special unitary group. This reunitarisation is often performed using an iterative maximisation of a gauge invariant measure. This technique is not differentiable with respect to the gauge field and thus prevents the use of standard Hybrid Monte Carlo simula…
First results from lattice QCD revealing the chiral nonanalytic behavior of nucleon and Delta baryon magnetic moments are presented. Numerical simulations in the light quark mass regime employing the nonperturbatively O(a)-improved conserved vector current are enabled via FLIC fermions. Quenched chiral perturbation theory for the nucleon and Delta magnetic moments is derived to next to next to leading nonanalytic order. Numerical simulation results for the proton and Delta baryon magnetic moments in quenched QCD reveal dramatic signatures of the quenched meson cloud, which are in accord with t…
The electromagnetic properties of the baryon octet are calculated in quenched QCD on a 20^3 x 40 lattice with a lattice spacing of 0.128 fm using the fat-link irrelevant clover (FLIC) fermion action. FLIC fermions enable simulations to be performed efficiently at quark masses as low as 300 MeV. By combining FLIC fermions with an improved-conserved vector current, we ensure that discretisation errors occur only at O(a^2) while maintaining current conservation. Magnetic moments and electric and magnetic radii are extracted from the electric and magnetic form factors for each individual quark sec…
The spectral properties of hybrid meson interpolating fields are investigated. The quantum numbers of the meson are carried by smeared-source fermion operators and highly-improved chromo-electric and -magnetic field operators composed with APE-smeared links. The effective masses of standard and hybrid operators indicate that the ground state meson is effectively isolated using both standard and hybrid interpolating fields. Focus is placed on interpolating fields in which the large spinor components of the quark and antiquark fields are merged. In particular, the effective mass of the exotic $1…
In this work we examine the Fat-Link Irrelevant Clover (FLIC) overlap quark propagator and the gluon propagator on both dynamical and quenched lattices. The tadpole-improved Luscher-Weisz gauge action is used in both cases. The dynamical gauge fields use the FLIC fermion action for the sea quark contribution. We observe that the presence of sea quarks causes a suppression of the mass function, quark renormalization function and gluon dressing function in the infrared. The ultraviolet physics is unaffected.
The use of APE smearing or other blocking techniques in fermion actions can provide many advantages. There are many variants of these fat link actions in lattice QCD currently, such as FLIC fermions. Frequently, fat link actions make use of the APE blocking technique in combination with a projection of the blocked links back into the special unitary group. This reunitarisation is often performed using an iterative maximisation of a gauge invariant measure. This technique is not differentiable with respect to the gauge field and thus prevents the use of standard Hybrid Monte Carlo simulation al…
The hadron mass spectrum is calculated in lattice QCD using a novel fat-link clover fermion action in which only the irrelevant operators of the fermion action are constructed using smeared links. The simulations are performed on a 16^3 X 32 lattice with a lattice spacing of a=0.125 fm. We compare actions with n=4 and 12 smearing sweeps with a smearing fraction of 0.7. The n=4 Fat Link Irrelevant Clover (FLIC) action provides scaling which is superior to mean-field improvement, and offers advantages over nonperturbative O(a) improvement.
The hadron mass spectrum is calculated in lattice QCD using a novel fat-link clover fermion action in which only the irrelevant operators in the fermion action are constructed using smeared links. The simulations are performed on a 16^3 x 32 lattice with a lattice spacing of a=0.125 fm. We compare actions with n=4 and 12 smearing sweeps with a smearing fraction of 0.7. The n=4 Fat-Link Irrelevant Clover (FLIC) action provides scaling which is superior to mean-field improvement, and offers advantages over nonperturbative 0(a) improvement, including a reduced exceptional configuration problem.
We present first results for masses of positive and negative parity excited baryons in lattice QCD using an O(a^2) improved gluon action and a Fat Link Irrelevant Clover (FLIC) fermion action in which only the irrelevant operators are constructed with fat links. The results are in agreement with earlier calculations of N^* resonances using improved actions and exhibit a clear mass splitting between the nucleon and its chiral partner, even for the Wilson fermion action. The results also indicate a splitting between the lowest J^P = 1/2^- states for the two standard nucleon interpolating fields.
The majority of compute time doing lattice QCD is spent inverting the fermion matrix. The time that this takes increases with the condition number of the matrix. The FLIC(Fat Link Irrelevant Clover) action displays, among other properties, an improved condition number compared to standard actions and hence is of interest due to potential compute time savings. However, due to its two different link sets there is a factor of two cost in floating point multiplications compared to the Wilson action. An additional factor of two has been attributed due to the loss of the so-called spin projection tr…
We discuss the scaling behaviour of different fermion actions in dynamical simulations of the 2-dimensional massive Schwinger model. We have chosen Wilson, hypercube, twisted mass and overlap fermion actions. As physical observables, the pion mass and the scalar condensate are computed for the above mentioned actions at a number of coupling values and fermion masses. We also discuss possibilities to simulate overlap fermions dynamically avoiding problems with low-lying eigenvalues of the overlap kernel.
I describe studies of quenched spectroscopy, using crude approximations to fixed point actions for fermions interacting with SU(3) gauge fields. These actions have a hypercubic kinetic term and a complicated lattice anomalous magnetic moment term. They show improved scaling compared to the conventional Wilson action.
I carry out a finite-size scaling study of the correlation length in SU(3) lattice gauge theory coupled to 12 fundamental flavor fermions, using recent data published by Fodor, Holland, Kuti, Nogradi and Schroeder. I make the assumption that the system is conformal in the zero-mass, infinite volume limit, that scaling is violated by both nonzero fermion mass and by finite volume, and that the scaling function in each channel is determined self-consistently by the data. From several different observables I extract a common exponent for the scaling of the correlation length xi with the fermion m…
Extended simulation results and their analysis are reported in a strongly coupled gauge theory with twelve fermion flavors in the fundamental SU(3) color representation. The conformality of the model is probed using mass deformed conformal finite size scaling (FSS) theory driven by the fermion mass anomalous dimension. Two independent conformal FSS fitting procedures are used in the analysis. The first one deploys physics motivated scaling functions, complemented by a second fitting procedure with spline based general B-forms for the scaling functions. The results at fixed gauge coupling show …
We present scaling studies for heavy-quark observables calculated with an $O(a^2)$-improved fermion action on tree-level Symanzik improved gauge configurations. Lattices of $1/a = $ 2.0-3.8 GeV with an equal physical volume 1.6 fm are used. The results are compared with the standard domain-wall and naive Wilson fermions.
We compute non-perturbatively the renormalization constants of composite operators for overlap fermions by using the regularization independent scheme. The scaling behavior of the renormalization constants is investigated using the data from three lattices with similar physical volumes and different lattice spacings. The approach of the renormalization constants to the continuum limit is explored.
We present the results of a mixed action approach, employing dynamical twisted mass fermions in the sea sector and overlap valence fermions, with the aim of testing the continuum limit scaling behaviour of physical quantities, taking the pion decay constant as an example. To render the computations practical, we impose for this purpose a fixed finite volume with lattice size $L\approx1.3$ fm. We also briefly review the techniques we have used to deal with overlap fermions.
We compute non--perturbatively the renormalization coefficients of scalar and pseudoscalar operators, local vector and axial currents, conserved vector and axial currents, and $O_{LL}^{ΔS=2}$ over a wide range of energy scales using a scaling technique that connects the results of simulations at different values of coupling $β$. We use the domain wall fermion formulation in the quenched approximation at a series of three values of $β, 6.0, 6.45, 7.05$ corresponding to lattice spacing scaling by factors of two.
We investigate a strongly coupled U(1) gauge theory with fermions and scalars on the lattice and analyze whether the continuum limit might be a renormalizable theory with dynamical mass generation. Most attention is paid to the phase with broken chiral symmetry in the vicinity of the tricritical point found in the model. There we investigate the scaling of the masses of the composite fermion and of some bosonic bound states. As a by-product we confirm the mean-field exponents at the endpoint in the U(1)-Higgs model, by analyzing the scaling of the Fisher zeros.
We compute non-perturbatively the renormalization coefficients of scalar and pseudoscalar operators, local vector and axial currents, conserved vector and axial currents, and $O^{ΔS=2}_{LL}$ over a wide range of energy scales using a scaling technique that connects the results of simulations at different values of coupling $β$. We use the domain wall fermion formulation in the quenched approximation at a series of three values of $β= 6.0, 6.45, 7.05$ corresponding to lattice spacing scaling by factors of two.
The MFA approach for simulations with dynamical fermions in lattice gauge theories allows in principle to explore the parameters space of the theory (e.g. the $β, m$ plane for the study of chiral condensate in QED) without the need of computing the fermionic determinant at each point. We exploit this possibility for extracting both the renormalization group trajectories ("constant physics lines") and the scaling function, and we test it in the Schwinger Model. We discuss the applicability of this method to realistic theories.
We calculate the 3-loop perturbative expansion of the average plaquette in lattice QCD with N_f massive Wilson fermions and gauge group SU(N). The corrections to asymptotic scaling in the corresponding energy scheme are also evaluated. We have also improved the accuracy of the already known pure gluonic results at 2 and 3 loops.
I observe a rough volume-dependent scaling of the low eigenvalues of a chiral Dirac operator in lattice studies of SU(3) lattice gauge theory with two flavors of color sextet fermions, in its weak-coupling phase. The mean value of the ith eigenvalue scales with the simulation volume V=L^4 as <lambda_i>L^p ~zeta_i, where zeta_i is a volume-independent constant. The exponent p is about 1.4. A possible explanation for this phenomenon is that p is the leading relevant exponent associated with the fermion mass dependence of correlation functions in a theory whose zero-mass limit is conformal.
If we construct a lattice fermion formulation, there are a number of goals to be considered: doubling should be avoided; even at finite lattice spacing, we want to represent chiral symmetry in a sound way; and we are seeking a good scaling behavior. Conceptually we have to require locality, and for practical purposes we even desire a high level of locality. A further issue is a good approximation to rotation invariance. Last but not least the formulation should be simple enough to allow for efficient simulations. Here we report on a construction, which is designed to do justice to all of these…
We present a framework for phenomenological lattice QCD calculations which makes use of a tree level Symanzink improved action for gluons and stout-link Wilson fermions. We give details of our efficient HMC/RHMC algorithm and present a scaling study of the low-lying N_f=3 baryon spectrum. We find a scaling region that extends to a~<0.16fm and conclude that our action and algorithm are suitable for large scale phenomenological investigations of N_f=2+1 QCD. We expect this conclusion to hold for other comparable actions.
We test the scaling behaviour of Wilson, hypercube, maximally twisted mass and overlap fermion actions in dynamical simulations of the 2-dimensional massive Schwinger model. We also present possibilities to simulate overlap fermions dynamically by replacing the exact overlap operator by an approximate version. This approximation is used either as only the guidance Hamiltonian, keeping the exact overlap operator as the accept/reject Hamiltonian or for both, the guidance and accept/reject Hamiltonian in the Hybrid Monte Carlo algorithm. In the latter case we test whether the approximation error …
We construct a number of lattice fermions, which fulfill the Ginsparg-Wilson relation either exactly or approximately, and test them in the framework of the 2-flavor Schwinger model. We start from explicit approximations within a short range, and study this formulation, as well as its correction to an exact Ginsparg-Wilson fermion by the ``overlap formula''. Then we suggest a new method to realize this correction perturbatively, without using the tedious square root operator. In this way we combine many favorable properties: good chiral behavior, small mass renormalization, excellent scaling a…
The goal of this study is to investigate the scaling behaviour of our 2 HEX action. For this purpose, we compute the $N_f=3$ spectrum and compare the results to our 6 EXP action. We find a large scaling window up to $\sim 0.15\,\mathrm{fm}$ along with small scaling corrections at the 2%-level and full compatibility with our previous study. As a second important observable to be tested for scaling, we chose the non-perturbatively renormalized quenched strange quark mass. Here we find a fairly flat scaling with a broad scaling range up to $\simeq 0.15\,\mathrm{fm}$ and perfect agreement with the…
In the possible scaling region for an SU(2) lattice chiral fermion advocated in {\it Nucl. Phys.} B486 (1997) 282, no hard spontaneous symmetry breaking occurs and doublers are gauge-invariantly decoupled via mixing with composite three-fermion-states that are formed by local multifermion interactions. However the strong coupling expansion breaks down due to no ``static limit'' for the low-energy limit ($pa\sim 0$). In both neutral and charged channels, we further analyze relevant truncated Green functions of three-fermion-operators by the strong coupling expansion and analytical continuation …
We present a scaling study of the QCD spectrum using a smeared P4 staggered fermion formulation, in which three, five, and seven-link staples are added to reduce the effects of flavor symmetry breaking. These studies are performed on quenched lattices generated using the one-loop improved Symanzik gauge action, with Beta=10/g^2=7.40,7.75,8.00. The corresponding lattice spacings are a = .31 fm, .21 fm, and .14 fm. Particularly, we study the O(a^2) flavor symmetry violations in the pion spectrum as well as the scaling dependence of m_rho, measured in physical units, on lattice spacing. These res…
We investigate the continuum limit scaling of the scalar condensate in the $N_f=2$ Schwinger model on the lattice. We employ maximally twisted mass Wilson fermions and overlap fermions. We compute the scalar condensate by taking the trace of the propagator (direct method) and by utilizing the integrated Ward-Takahashi identity. While the scalar condensate comes out consistent using these two methods for a given kind of lattice fermions, we find --quite surprisingly-- large discrepancies for the scalar condensate between twisted mass and overlap fermions. These discrepancies are only resolved w…
We present a scaling analysis in the 1-flavor Schwinger model with the full overlap and the rooted staggered determinant. In the latter case the chiral and continuum limit of the scalar condensate do not commute, while for overlap fermions they do. For the topological susceptibility a universal continuum limit is suggested, as is for the partition function and the Leutwyler-Smilga sum rule. In the heavy-quark force no difference is visible even at finite coupling. Finally, a direct comparison between the complete overlap and the rooted staggered determinant yields evidence that their ratio is …
The strongly coupled lattice gauge models show an interesting mechanism of dynamical mass generation. If a suitable continuum limit can be found, one may think of it as an alternative to the Higgs mechanism. We present data on the spectrum, obtained in the model with U(1) gauge symmetry with dynamical fermions. They indicate that the fermion mass scales in the vicinity of the whole chiral phase transition line. In contrast to this, the composite scalar boson mass seems to get small only in the region near the endpoint E of the Higgs phase transition. Thus this point is the most interesting can…
The overlap fermion offers the tremendous advantage of exact chiral symmetry on the lattice, but is numerically intensive. This can be made affordable while still providing large lattice volumes, by using coarse lattice spacing, given that good scaling and localization properties are established. Here, using overlap fermions on quenched Iwasaki gauge configurations, we demonstrate directly that the overlap Dirac operator's range is comfortably small in lattice units for each of the lattice spacings 0.20 fm, 0.17 fm, and 0.13 fm (and scales to zero in physical units in the continuum limit). In …
We investigate the scaling behaviour of quenched Wilson twisted mass fermions at maximal twist applying two definitions of the critical mass. The first definition uses the vanishing of the pseudoscalar meson mass m_PS while the second employs the vanishing of the PCAC quark mass m_PCAC. We confirm in both cases the expected O(a) improvement. In addition, we show that the PCAC quark mass definition leads to substantially reduced O(a^2) cut-off effects even when the pseudoscalar meson mass m_PS is as small as 270 MeV. At a fixed value of m_PS we perform continuum limits for the vector meson mass…
We study scaling behavior of a chiral order parameter in the low density region, performing a simulation of two-flavor QCD with improved Wilson quarks. The scaling behavior of the chiral order parameter defined by a Ward-Takahashi identity agrees with the scaling function of the three-dimensional O(4) spin model at zero chemical potential. We extend the scaling study to finite density QCD. Applying the reweighting method and calculating derivatives of the chiral order parameter with respect to the chemical potential, the scaling properties of the chiral phase transition are discussed in the lo…
The overlap fermion offers the considerable advantage of exact chiral symmetry on the lattice, but is numerically intensive. This can be made affordable while still providing large lattice volumes, by using coarse lattice spacing, given that good scaling and localization properties are established. Here, using overlap fermions on quenched Iwasaki gauge configurations, we demonstrate directly that, with appropriate choice of negative Wilson's mass, the overlap Dirac operator's range is comfortably small in lattice units for each of the lattice spacings 0.20 fm, 0.17 fm, and 0.13 fm (and scales …
We study the pion spectrum (and in particular taste-symmetry breaking within it) using HYP-smeared valence staggered fermions on the coarse and fine MILC lattices (which have asqtad staggered sea quarks). We focus on the dependence on lattice spacing and sea-quark mass. We also update our results on source dependence. Our main conclusion is that on the MILC fine lattices the appropriate power-counting for SU(3) staggered chiral perturbation theory may have discretization errors entering at next-to-leading order rather than at leading-order.
The chiral symmetry relation and scaling of the overlap fermions are studied numerically on the quenched lattices at 3 couplings with about the same physical volume. We find that the generalized Gell-Mann-Oakes-Renner relation is satisfied to better than 1% down to the smallest quark mass at $m_0a = 0.006$. We also obtain the quark mass from the PCAC relation and the pseudoscalar masses. The renormalization group invariant quark mass is shown to be fairly independent of scale. The $π$ and $ρ$ masses at a fixed $m_π/m_ρ$ ratio indicate small $O(a^2)$ corrections. It is found that the critical s…
In this work we present the results of a numerical investigation of SU(2) gauge theory with N_f = 3/2 flavours of fermions, corresponding to 3 Majorana fermions, which transform in the adjoint representation of the gauge group. At two values of the gauge coupling, the masses of bound states are considered as a function of the fundamental fermion mass, represented by the PCAC quark mass. The scaling of bound states masses indicates an infrared conformal behaviour of the theory. We obtain estimates for the fixed-point value of the mass anomalous dimension $γ^{\ast}$ from the scaling of masses an…
We report on the progress of our calculation of form factors for the exclusive semileptonic decay of $B$ mesons to pions on $2+1$ flavour lattices with spacings from $0.080~\mathrm{fm}$ down to $0.044~\mathrm{fm}$. Using the Möbius domain wall fermion action for all quarks, we simulate pions with masses down to $230~\mathrm{MeV}$ and extrapolate to the physical bottom quark mass by utilizing a range of heavy quark masses up to $2.44$ times the mass of the charm quark. We discuss the dependence on the pion mass, heavy quark mass and lattice spacing in our form factors results.
We have simulated lattice QCD with 2 flavours of massless staggered quarks. An irrelevant chiral 4-fermion interaction was added to the standard quark action to allow us to simulate at zero quark mass. Thermodynamics was studied on lattices of temporal extent 6. Clear evidence for a second order chiral transition was observed and the critical exponents $β_{mag}$, $δ$, $ν$ and $γ_{mag}$ were measured. These exponents did not agree with those expected by standard universality arguments. They were, however, consistent with tricritical behaviour. The $π$ and $σ$ screening masses were measured and …
We test exact and approximate Ginsparg-Wilson fermions with respect to their chiral and scaling behavior in the 2-flavor Schwinger model. We first consider explicit approximate GW fermions in a short range, then we proceed to their chiral correction by means of the ``overlap formula'', and finally we discuss a numerically efficient perturbative chiral correction. In this way we combine very good chiral and scaling properties with a relatively modest computational effort.
In the large-volume limit $V\to\infty$ with $V << 1/m_π^4$ the mass-dependent chiral condensate is predicted to satisfy exact finite-volume scaling laws that fall into three major universality classes. We test these analytical predictions with staggered fermions and overlap fermions in gauge field sectors of fixed topological charge $ν$.
{We present the results of a numerical investigation of SU(2) gauge theory with $N_f=3/2$ flavours of fermions, corresponding to 3 Majorana fermions, which transform in the adjoint representation of the gauge group. At two values of the gauge coupling, the masses of bound states are considered as a function of the PCAC quark mass. The scaling of bound states masses indicates an infrared conformal behaviour of the theory. We obtain estimates for the fixed-point value of the mass anomalous dimension $γ^*$ from the scaling of masses and from the scaling of the mode number of the Wilson-Dirac oper…
