We compute the ratio Lambda_L/Lambda_MS, where the scale parameter Lambda_L is associated with a lattice formulation of QCD. We consider a 3-parameter family of gluon actions, which are most frequently used for O(a) improvement a` la Symanzik. The gluon action is put togeter with standard discretizations for fermions (Wilson/clover, overlap), to provide Lambda_L for several possible combinations of fermion and gluon actions. We employ the background field technique in order to calculate the 1PI 2-point function of the background field; this leads to the coupling constant renormalization function, Z_g, at 1-loop level.
Our results are obtained for an extensive range of values for the Symanzik coefficients.
We calculate the 1-loop renormalization of the fermion self-energy, all local fermion bilinears, as well as a set of extended bilinears which form a basis corresponding to moments of the parton distribution functions. We use the overlap action for fermions and Symanzik improved action for gluons. Our results are presented as a function of the overlap parameter rho and the parameters entering the Symanzik action.
We calculate perturbative renormalization properties of the topological charge, using the standard lattice discretization given by a product of twisted plaquettes. We use the overlap and clover action for fermions, and the Symanzik improved gluon action for 4- and 6-link loops. We compute the multiplicative renormalization of the topological charge density to one loop; this involves only the gluon part of the action. The power divergent additive renormalization of the topological susceptibility is calculated to 3 loops.
We calculate the critical value of the hopping parameter, $κ_c$, in Lattice QCD, up to two loops in perturbation theory. We employ the Sheikholeslami-Wohlert (clover) improved action for fermions and the Symanzik improved gluon action with 4- and 6-link loops. The quantity which we study is a typical case of a vacuum expectation value resulting in an additive renormalization; as such, it is characterized by a power (linear) divergence in the lattice spacing, and its calculation lies at the limits of applicability of perturbation theory. Our results are polynomial in $c_{SW}$ (clover parameter)…
We calculate the critical value of the hopping parameter, kappa_c, in Lattice QCD, up to two loops in perturbation theory. We employ the Sheikholeslami-Wohlert (clover) improved action for Wilson fermions and the Symanzik improved gluon action for 4- and 6-link loops. The quantity which we study is a typical case of a vacuum expectation value resulting in an additive renormalization; as such, it is characterized by a power (linear) divergence in the lattice spacing, and its calculation lies at the limits of applicability of perturbation theory. Our results are polynomial in c_{SW} (clover para…
We calculate corrections to the fermion propagator and to the Green's functions of all fermion bilinear operators of the form $\barΨΓΨ$, to one-loop in perturbation theory. We employ the Wilson/clover action for fermions and a family of Symanzik improved actions for gluons. The novel aspect of our calculations is that they are carried out to second order in the lattice spacing, $O(a^2)$. Consequently, they have addressed a number of new issues, most notably the appearance of loop integrands with strong IR divergences (convergent only beyond 6 dimensions). Such integrands are not present in $O(…
Using plaquette and Symanzik improved gauge action and stout link clover fermions we determine the improvement coefficient $c_{SW}$ in one-loop lattice perturbation theory from the off-shell quark-quark-gluon three-point function. In addition, we compute the coefficients needed for the most general form of quark field improvement and present the one-loop result for the critical hopping parameter $κ_c$. We discuss mean field improvement for $c_{SW}$ and $κ_c$ and the choice of the mean field coupling for the actions we have considered.
We determine the improvement factor $c_{SW}$ in one-loop lattice perturbation theory for the plaquette and Symanzik improved gauge actions. The fermionic action is ${\mathcal{O}(a)}$ clover improved with one-time stout smearing. $c_{SW}$ is derived from the one-loop correction to the quark-quark-gluon vertex in the off-shell regime. We give a first numerical value for the one-loop contribution to the non gauge-invariant improvement coefficient $c_{NGI}$ for the quark field using the plaquette action. A discussion of mean field improvement is included.
We present a 1-loop perturbative calculation of the fermion propagator, up to O(a^2) (a: lattice spacing). The fermions are described by Wilson, clover and twisted-mass actions; for gluons we use Symanzik improved actions (Plaquette, Tree-level Symanzik, Iwasaki, TILW, DBW2). Our results are given in a general covariant gauge, and their dependence on the coupling constant, the external momentum, the masses and the clover parameter is shown explicitly. We also study the O(a^2) corrections to matrix elements of unpolarized/polarized fermion bilinear operators, which include up to one derivative.…
We present the results of our perturbative calculations of the static quark potential, small Wilson loops, the static quark self energy, and the mean link in Landau gauge. These calculations are done for the one loop Symanzik improved gluon action, and the improved staggered quark action.
We calculate one-loop renormalization factors of bilinear quark operators for gluon action including six-link loops and $O(a)$-improved quark action in the limit of massless quark. We find that finite parts of one-loop coefficients of renormalization factors diminish monotonically as either of the coefficients $c_1$ or $c_2+c_3$ of the six-link terms are decreased below zero. Detailed numerical results are given, for general values of the clover coefficient, for the tree-level improved gluon action in the Symanzik approach $(c_1=-1/12, c_2=c_3=0)$ and for the choices suggested by Wilson $(c_1=…
We discuss critical slowing-down of several gauge-fixing algorithms for the so-called lambda-gauges in the SU(2) case at zero temperature. For these gauges we also evaluate the gluon propagator using different definitions of the lattice gluon field, corresponding to discretization errors of different orders.
We calculate the corrections to the amputated Green's functions of 4-fermion operators, in 1-loop Lattice Perturbation theory. The novel aspect of our calculations is that they are carried out to second order in the lattice spacing, O(a^2). We employ the Wilson/clover action for massless fermions (also applicable for the twisted mass action in the chiral limit) and the Symanzik improved action for gluons. Our calculations have been carried out in a general covariant gauge. Results have been obtained for several popular choices of values for the Symanzik coefficients (Plaquette, Tree-level Syma…
We utilise a recently developed minimal MOM scheme to determine the QCD Lambda parameter from the gluon and ghost propagators in lattice Landau gauge. We discuss uncertainties in the analysis and report our preliminary zero and two flavour results, which are r_0*LambdaMS^{(0)}=0.62(1) and r_0*LambdaMS^{(2)}=0.60(3)(2), with the second error due to an extrapolation uncertainty.
Lattice gluon propagators are studied using tadpole and Symanzik improved gauge action in Landau gauge. The study is performed using anisotropic lattices with asymmetric volumes. The Landau gauge dressing function for the gluon propagator measured on the lattice is fitted according to a leading power behavior: $Z(q^2)\simeq (q^2)^{2κ}$ with an exponent $κ$ at small momenta. The gluon propagators are also fitted using other models and the results are compared. Our result is compatible with a finite gluon propagator at zero momentum in Landau gauge.
We present results for one-loop matching factors of four-fermion operators composed of HYP-smeared staggered fermions. We generalize previous calculations by using the tree-level improved Symanzik gauge action. These results are needed for our companion numerical calculation of $B_K$ and related matrix elements. We find that the impact on one-loop matching factors of using the improved gluon action is much smaller than that from the use of either HYP smearing or mean-field improvement. The one-loop coefficients for mean-field improved, HYP-smeared operators with the Symanzik gauge action have …
In this work we calculate the corrections to the amputated Green's functions of 4-fermion operators, in 1-loop Lattice Perturbation theory. One of the novel aspects of our calculations is that they are carried out to O(a^2) (a: lattice spacing). We employ the Wilson/clover action for massless fermions (also applicable for the twisted mass action in the chiral limit) and a family of Symanzik improved actions for gluons. Our calculations have been carried out in a general covariant gauge. Results have been obtained for several popular choices of values for the Symanzik coefficients. While our Gr…
We introduce a new Symanzik improved action by adding a 2x2 plaquette in such a way that the Feynman rules in the covariant gauge simplify. We call this the square Symanzik action. Some comparisons with the continuum and the standard Wilson action are made in intermediate volumes, where mass ratios are accurately known and the precise amount of improvement can be determined. Ratios of the Lambda parameters will be presented, as well as partial results for the one-loop improvement coefficients. We discuss some of the intricacies that arise because of violations of unitarity at the scale of the …
We calculate perturbative renormalization properties of the topological charge, using the standard lattice discretization given by a product of twisted plaquettes. We use the overlap and clover action for fermions, and the Symanzik improved gluon action for 4- and 6-link loops. We compute the multiplicative renormalization of the topological charge density to one loop; this involves only the gluon part of the action. The power divergent additive renormalization of the topological susceptibility is calculated to 3 loops. Our work serves also as a test case of the techniques and limitations of l…
Using the infrared dispersion relation of the on shell gluon, we calculate the renormalisation of the the anisotropy to one loop in perturbation theory for lattice Yang-Mills theories, including the Wilson action and actions with Symanzik and/or tadpole improvement. Using twisted boundary conditions as a gauge invariant infrared regulator, we show for an SU(3) gauge group in D=3+1 dimensions that the one loop anisotropy is accurate to O(3%) for a range of g^2 and chi covering current simulations. In doing so we also present Feynman rules for SU(N) gauge groups with generic anisotropy structure…
In this paper we present the perturbative computation of the renormalization functions for the quark field and for a complete set of ultra-local fermion bilinears. The computation of the relevant Green's functions was carried out at 1-loop level for the staggered action using massive fermions. The gluon links which appear both in the fermion action and in the definition of the bilinears have been improved by applying a stout smearing procedure up to 2 times, iteratively. In the gluon sector we employed the Symanzik improved gauge action for different sets of values of the Symanzik coefficients…
We present the corrections to the fermion propagator, to second order in the lattice spacing, O(a^2), in 1-loop perturbation theory. The fermions are described by the clover action and for the gluons we use a 3-parameter family of Symanzik improved actions. Our calculation has been carried out in a general covariant gauge. The results are provided as a polynomial of the clover parameter, and are tabulated for 10 popular sets of the Symanzik coefficients (Plaquette, Tree-level Symanzik, Iwasaki, TILW and DBW2 action). We also study the O(a^2) corrections to matrix elements of fermion bilinear o…
We study the gluon propagator and the singlet potential in Landau gauge in the deconfined phase of SU(2) lattice gauge theory, using both the standard Wilson action and a tree-level Symanzik improved action. From the long-distance behavior of correlation functions of temporal and spatial components of the gauge fields we extract electric (m_e) and magnetic (m_m) screening masses. For the magnetic mass we find m_m(T) = 0.456(6) g^2(T) T. The electric mass can be described by a next-to leading order ansatz, obtained from one loop resummed perturbation theory. However, the best description is giv…
We give an update on our lattice determination of r_0 LambdaMS for different Nf. Our calculations employ the strong coupling constant in the minimal MOM scheme for QCD in Landau gauge, and we report here on our progress towards a quantitative understanding of the intrinsic lattice discretization artifacts at large momenta. This is important for a high-precision analysis, in particular for the unquenched calculations for which the access to small lattice spacings is restricted by the available gauge configurations.
The pressure and energy density of the quark-gluon plasma at finite baryon chemical potential are calculated using the Complex Langevin equation. The stout smearing procedure is generalized for the SL(3,$\mathcal{C}$) manifold allowing the usage of an improved action in the Complex Langevin setup. Four degenerate flavors of staggered quarks with $m_π=500-700$ MeV are used with a tree-level Symanzik improved gauge action on $16^3 \times 8 $ lattices. Results are compared to the Taylor expansion and good agreement is found for small chemical potentials.
The infrared behavior of the gluon propagator is directly related to confinement in QCD. Indeed, the Gribov-Zwanziger scenario of confinement predicts an infrared vanishing (transverse) gluon propagator in Landau-like gauges, implying violation of reflection positivity and gluon confinement. Finite-volume effects make it very difficult to observe (in the minimal Landau gauge) an infrared suppressed gluon propagator in lattice simulations of the four-dimensional case. Here we report results for the SU(2) gluon propagator in a gauge that interpolates between the minimal Landau gauge (for gauge p…
We present one-loop matching coefficients between continuum and lattice QCD for the heavy-light four-fermion operators relevant for neutral B meson mixing both within and beyond the Standard Model. For the lattice theory we use nonrelativistic QCD (NRQCD) to describe b quarks and improved staggered fermions (AsqTad) for light quarks. The gauge action is the tree-level Symanzik improved gauge action. Matching to full QCD is carried out through order alpha_s, Lambda_{QCD}/M_b, and alpha_s/(aM_b).
We investigate the occurrence of power terms $(Lambda^2/p^2$ in the running QCD coupling by analysing non-perturbative measurements of $α_s(p)$ at quite low momenta obtained from the lattice three-gluon vertex. Our study provides some evidence for such a contribution. The phenomenological implications of such a presence are reviewed.
We discuss testing improved actions in the context of finite volume gauge theories, where both results for the continuum and the Wilson lattice action are known analytically for volumes up to 0.7 fermi across. A new improved action is introduced, obtained by adding a 2 x 2 plaquette to the Lüscher-Weisz Symanzik action, for which the gauge field propagator greatly simplifies. We call this the square Symanzik action. We present the tree-level parameters of this improved action and the value of its Lambda parameter. We also give some Monte Carlo results and discuss some of the issues related to …
We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD generated using a Symanzik-improved gluon action. We find a clear separation of the spectrum of eigenvalues into would-be zero modes and others. The number of would-be zero modes depends on the topological charge as expected from the Index Theorem, and their chirality expectation value is large. The remaining modes have low chirality and show clear signs of clustering into quartets and approaching the random matrix theory predictions for all topological charge sectors. We conclude that improv…
The dependence of thermodynamic properties of QCD on the number of quark flavours is investigated. Lattice results for the equation of state are presented for 2, 2+1 and 3 quark flavours. The simulations have been performed with the improved p4-staggered fermion and a Symanzik improved gluon action on lattices of size 16^3 x 4
We compute the difference in the renormalization of flavor singlet and nonsinglet fermion bilinear operators, to two loops in perturbation theory. Our results are applicable to a rather wide class of lattice actions with Symanzik improved gluons, stout links and clover fermions, including the Twisted Mass and SLiNC actions. A more detailed presentation of our results, along with relevant references, will appear in a forthcoming publication.
We report on some efforts recently made in order to gain a better understanding of some IR properties of the 3-point gluon Green's function by exploiting results from large-volume quenched lattice simulations. These lattice results have been obtained by using both tree-level Symanzik and the standard Wilson action, in the aim of assessing the possible impact of effects presumably resulting from a particular choice for the discretization of the action. The main resulting feature is the existence of a negative logaritmic divergence at zero-momentum, which pulls the 3-gluon form factors down at l…
We present results for the renormalization of gauge invariant nonlocal fermion operators which contain a Wilson line, to one loop level in lattice perturbation theory. Our calculations have been performed for Wilson/clover fermions and a wide class of Symanzik improved gluon actions. The extended nature of such `long-link' operators results in a nontrivial renormalization, including contributions which diverge linearly as well as logarithmically with the lattice spacing, along with additional finite factors. We present nonperturbative prescriptions to extract the linearly divergent contributio…
In this preprint we present our results on the study of the electromagnetic conductivity in dense quark-gluon plasma obtained within lattice simulations with $N_f = 2 + 1$ dynamical quarks. We employ stout improved rooted staggered quarks at the physical point and the tree-level Symanzik improved gauge action. The simulations are performed at imaginary baryon chemical potential, and the Tikhonov regularisation method is used to extract the conductivity from current-current correlators. Our results indicate an increase of QGP electromagnetic conductivity with real baryon density, and this depen…
We present results for matching factors for bilinear operators composed of HYP-smeared staggered fermions and constructed using HYP-smeared fat links. The matching factors are calculated perturbatively at one-loop order. The new feature of our calculation compared to previous work on HYP-smeared staggered fermions is the use of the Symanzik-improved gluon propagator, which allows our results to be applied to our ongoing simulations based on configurations generated by the MILC collaboration. We address the issue of the relative efficiency of various improvement schemes in reducing one-loop cor…
We investigate the deconfinement transition in SU(Nc) gauge theories, and properties of the deconfined phase. A detailed lattice study of SU(4) and SU(6) gauge theories are conducted, and finite volume and cutoff effects on thermodynamic observables are studied. The scaling of the deconfinement transition point with lattice spacing is used to calculate the scale, Lambda_MSbar. The continuum estimates of the thermodynamic quantities are used to study properties of the gluon plasma. In particular, the approach to conformal limit is studied. We do not find any evidence of a strongly coupled, conf…
We report on advances in the non-perturbative determination of the ratio $Z_S/Z_P$ of the pseudoscalar to the scalar renormalization constants in three-flavour lattice QCD with Wilson-clover quarks and tree-level Symanzik improved gluons. The computations are based on the Ward identity approach, using Schrödinger functional boundary conditions. Our results for $Z_S/Z_P$ cover a range of couplings along a line of constant physics with lattice spacings of about 0.09 fm and below, relevant for phenomenological applications such as the calculation of renormalized quark masses.
We present results for one-loop perturbative matching factors using bilinear operators composed of improved staggered fermions, using unimproved (Wilson) and improved (Symanzik, Iwasaki, and DBW2) gluon actions. We consider two fermions actions---HYP/$\bar{\text{Fat7}}$-smeared and "asqtad". The former is being used in calculations of electroweak matrix elements, while the latter have been used extensively by the MILC collaboration. We observe that using the improved gluon action leads to small reductions in the perturbative corrections, but that these reductions are smaller than those obtaine…
In this paper we present the perturbative evaluation of the difference between the renormalization functions of flavor singlet and nonsinglet bilinear quark operators on the lattice. The computation is performed to two loops and to lowest order in the lattice spacing, for a class of improved lattice actions, including Wilson, tree-level (TL) Symanzik and Iwasaki gluons, twisted mass and SLiNC Wilson fermions, as well as staggered fermions with twice stout-smeared links. In the staggered formalism, the stout smearing procedure is also applied to the definition of bilinear operators.
We calculate the Polyakov loop susceptibilities in the SU(3) lattice gauge theory using the Symanzik improved gauge action on different-sized lattices. The longitudinal and transverse fluctu- ations of the Polyakov loop, as well as, that of its absolute value are considered. We analyze their properties in relation to the confinement-deconfinement phase transition. We also present results based on simulations of (2+1)-flavor QCD on 32^3 x 8 lattice using Highly Improved Staggered Quark (HISQ) action by the HotQCD collaboration. The influences of fermions on the Polyakov loop fluctuations are di…
The quark-gluon vertex in Landau gauge is studied in the quenched approximation using the Sheikholeslami-Wohlert (SW) fermion action with mean-field improvement coefficients in the action and for the quark fields. We see that the form factor that includes the running coupling is substantially enhanced in the infrared, over and above the enhancement arising from the infrared suppression of the quark propagator alone. We define two different momentum subtraction renormalisation schemes -- \MOMT (asymmetric) and \MOMB\ (symmetric) -- and determine the running coupling in both schemes. We find Lam…
A possible explanation of the apparent disrepency between the theoretical prediction and experimental measurement of the ratio of lifetimes $τ(Λ_b)/τ(B_d)$ is that ``spectator effects'', which appear at $O(1/m_b^3)$ in the heavy quark expansion, contribute significantly. We investigate this possibility by computing the corresponding operator matrix elements in a lattice simulation. We find that spectator effects are indeed significant, but do not appear to be sufficiently large to account for the full discrepency. We stress, however, that this is an exploratory study, and it is important to ch…
Perturbative and non-perturbative results are presented on the renormalization constants of the quark field and the vector, axial-vector, pseudoscalar, scalar and tensor currents. The perturbative computation, carried out at one-loop level and up to second order in the lattice spacing, is performed for a fermion action, which includes the clover term and the twisted mass parameter yielding results that are applicable for unimproved Wilson fermions, as well as for improved clover and twisted mass fermions. We consider ten variants of the Symanzik improved gauge action corresponding to ten diffe…
We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD generated using a Symanzik-improved gluon action. We find a clear separation of the spectrum into would-be zero modes and others. The number of would-be zero modes depends on the topological charge as expected from the Index Theorem, and their chirality expectation value is large (approximately 0.7). The remaining modes have low chirality and show clear signs of clustering into quartets and approaching the random matrix theory predictions for all topological charge sectors. We conclude that i…
The Chromomagnetic operator (CMO) mixes with a large number of operators under renormalization. We identify which operators can mix with the CMO, at the quantum level. Even in dimensional regularization (DR), which has the simplest mixing pattern, the CMO mixes with a total of 9 other operators, forming a basis of dimension-five, Lorentz scalar operators with the same flavor content as the CMO. Among them, there are also gauge noninvariant operators; these are BRST invariant and vanish by the equations of motion, as required by renormalization theory. On the other hand using a lattice regulari…
We compute the quark-gluon vertex in quenched QCD, in the Landau gauge using an off-shell mean-field O(a)-improved fermion action. The running coupling is calculated in an `asymmetric' momentum subtraction scheme (MOM~). We obtain a crude estimate for Lambda_MSbar=170+/-65 MeV, which is considerably lower than other determinations of this quantity. However, substantial systematic errors remain.
We investigated the finite temperature (T) phase transition for SU(Nc) gauge theory with Nc=4, 6, 8 and 10 at lattice spacing, a, of 1/(6T) or less. We found that these theories have first order transitions at such small a. In many cases we were able to find the critical couplings with precision as good as a few parts in 10^4. We also investigated the use of two-loop renormalization group equations in extrapolating the lattice results to the continuum, thus fixing the temperature scale in units of the phase transition temperature, Tc. We found that when a \le 1/(8Tc) the two-loop extrapolation…
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}…
This work presents the calculation of the relation between the bare coupling constant g_0 and the MSbar-renormalized coupling g_MS, g_0 = Z_g(g_0,aμ) g_MS, to 2 loops in perturbation theory, with fermions in an arbitrary representation of the gauge group SU(N). Our calculation is performed using overlap fermions and Wilson gluons, and the background field technique has been chosen for convenience. The corresponding results in the fundamental representation appear in our longer publication [arXiv:0709.4368]. The 3-loop coefficient of the bare beta-function, b_2^L, is extracted using the 2-loop …
We discuss a 3-flavour 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 Non-perturbative Clover or SLiNC action. To cancel O(a) terms the clover term coefficient has to be tuned. We present here results of a non-perturbative determination of this coefficient using the Schroedinger functional and as a by-product a determination of the critical hopping parameter. Comparisons of the resul…
We study a systematic improvement of perturbation theory for gauge fields on the lattice; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed for the Wilson gluon action, is extended here to encompass all possible gluon actions made of closed Wilson loops; any fermion action can be employed as well. The effect of resummation is to replace various parameters in the action (coupling constant, Symanzik coefficients, clover coefficient) by ``dressed'' values; the latter are solutions to certain coupled…
We present first results for the masses of positive and negative parity excited baryons calculated 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 APE-smeared 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. An correlation matrix analysis reveals two low-lying J^P=(1/2)^- states with a small mass splitting. The study of different Lambda interpol…
We investigate and clarify the role of topology and the issues surrounding the epsilon regime for staggered quarks. We study unimproved and improved staggered quark Dirac operators on quenched lattice QCD gluon backgrounds generated using a Symanzik-improved gluon action. For the improved Dirac operators we find a clear separation of the spectrum into would-be zero modes and others. The number of would-be zero modes depends on the topological charge as predicted by the continuum Index Theorem, and the expectation values of their chirality are large for the most improved actions (approx 0.7). T…
We study the Landau-gauge quark-gluon vertex with 2 flavours of O(a)improved Wilson fermions, for several lattice spacings and quark masses. In the limit of vanishing gluon momentum, we find that all nonzero form factors have a significant infrared strength, and that the leading form factor lambda_1, multiplying the tree-level vertex structure, is significantly enhanced in the infrared compared to the quenched case. We find that all form factors are further enhanced in the infrared as the chiral and continuum limits are approached.
We present some evidence that in Lattice Gauge Theory the condensate contains a non-perturbative contribution proportional to $Λ^2$, the square of the physical scale. This result is based on an analysis of the Wilson loop plaquette expectation from Monte Carlo simulations and its perturbative expansion computed to eight loops. The analysis is not fully conclusive since the calculations are done on a finite lattice and one needs an extrapolation to infinite lattice. It has been recently suggested that in the gluon condensate a $Λ^2$-contribution could be present coming from the large momentum b…
We discuss an action 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 Non-perturbative Clover or SLiNC action. To cancel O(a) terms the clover coefficient, csw, has to be tuned. We present here preliminary results of a non-perturbative determination of csw using the Schrodinger functional and as a by-product also a determination of the critical hopping parameter. A determination of the renormalisation constant for the local vec…
New lattice data for the Pi_u and Sigma_u^- potentials at short distances are presented. We compare perturbation theory to the lower static hybrid potentials and find good agreement at short distances, once the renormalon ambiguities are accounted for. We use the non-perturbatively determined continuum-limit static hybrid and ground state potentials at short distances to determine the gluelump energies. The result is consistent with an estimate obtained from the gluelump data at finite lattice spacings. For the lightest gluelump, we obtain Lambda_B^{RS}(nu_f=2.5/r_0)=[2.25\pm 0.10(latt.)\pm 0.…
