arXiv subjects
Publications and source records attributed to P. E. L. Rakow.
By considering the local vector current between nucleon states and imposing charge conservation we determine, for $O(a)$ improved Wilson fermions, its renormalisation constant and quark mass improvement coefficient. The computation is performed for both quenched and two flavour unquenched fermions.
In this contribution we present results from quenched QCD simulations with the parameterized fixed-point (FP) and the chirally improved (CI) Dirac operator. Both these operators are approximate solutions of the Ginsparg-Wilson equation and have good chiral properties. We focus our discussion on observables sensitive to chirality. In particular we explore pion masses down to 210 MeV in light hadron spectroscopy, quenched chiral logs, the pion decay constant and the pion scattering length. We discuss finite volume effects, scaling properties of the FP and CI operators and performance issues in their numerical implementation.
The internal spin structure of the Lambda is of special importance for the understanding of the spin structure of hadrons in general. The comparison between the nucleon and Lambda allows for a test of the relevant flavour-symmetry breaking effects. Using nonperturbatively O(a) improved Wilson fermions in the quenched approximation we have calculated the first moments of the unpolarised, longitudinally polarised and transversity quark distribution functions in the Lambda. The results indicate that flavour symmetry breaking has little effect on the internal spin structure, in accordance with model based expectations.
As an example of an application of lattice QCD we describe a computation of four-quark operators in the nucleon. The results are interpreted in a diquark language.
We present a calculation of the lowest-lying baryon masses in the quenched approximation to QCD. The calculations are performed using a non-perturbatively improved clover fermion action, and a splitting is found between the masses of the nucleon and its parity partner. An analysis of the mass of the first radial excitation of the nucleon finds a value considerably larger than that of the parity partner of the nucleon, and thus little evidence for the Roper resonance as a simple three-quark state
We discuss the extraction of negative-parity baryon masses from lattice QCD calculations. The mass of the lowest-lying negative-parity $J = 1/2^{-}$ state is computed in quenched lattice QCD using an ${\cal O}(a)$-improved clover fermion action, and a splitting found with the nucleon mass. The calculation is performed on two lattice volumes, and three lattice spacings enabling a study of both finite-volume and finite-lattice-spacing uncertainties. A measurement of the first excited radial excitation of the nucleon finds a mass considerably larger than that of the negative-parity ground state, in accord with other lattice determinations but in disagreement with experiment. Results are also presented for the lightest negative-parity $I=3/2$ state.
We present a calculation of the mass of the lowest-lying negative-parity J=1/2- state in quenched QCD. Results are obtained using a non-perturbatively O(a)-improved clover fermion action, and a splitting is found between the mass of the nucleon and its parity partner. The calculation is performed on two lattice volumes and at three lattice spacings, enabling a study of both finite-volume and finite lattice-spacing uncertainties. A comparison is made with results obtained using the unimproved Wilson fermion action.
Quenched SU(3) lattice gauge theory shows three phase transitions, namely the chiral, the deconfinement and the Z3 phase transition. Knowing whether or not the chiral and the deconfinement phase transition occur at the same temperature for all Z3 sectors could be crucial to understand the underlying microscopic dynamics. We use the existence of a gap in the Dirac spectrum as an order parameter for the restoration of chiral symmetry. We find that the spectral gap opens up at the same critical temperature in all Z3 sectors in contrast to earlier claims in the literature.
We compute $Λ_{\bar{MS}}$ for two flavors of light dynamical quarks using non-perturbatively $O(a)$ improved Wilson fermions. We improve on a recent calculation by employing Padé-improved two-loop and three-loop perturbation theory to convert the lattice numbers to the $\bar{MS}$ scheme.
We study spectra, localization properties and local chirality of eigenvectors of the lattice Dirac operator. We analyze ensembles of quenched SU(3) configurations on both sides of the QCD phase transition. Our Dirac operator is a systematic expansion in path length of a solution of the Ginsparg-Wilson equation. Analyzing the finite volume behavior of our observables and their scaling with the gauge coupling we come up with a consistent picture of topological excitations on both sides of the QCD phase transition. Our results support the interpretation of the dominant gauge field excitations seen by the Dirac operator as a fluid of instanton-like objects.
We compare the behavior of different lattice Dirac operators in gauge backgrounds which are lattice discretizations of a classical instanton. In particular we analyze the standard Wilson operator, a chirally improved Dirac operator and the overlap operators constructed from these two operators. We discuss the flow of real eigenvalues as a function of the instanton size. An analysis of the eigenvectors shows that overlap fermions with the Wilson operator as input operator have difficulties with reproducing the continuum zero mode already for moderately small instantons. This problem is greatly reduced when using the chirally improved operator for the overlap projection.
We study localization and chirality properties of eigenvectors of the lattice Dirac operator. In particular we focus on the dependence of our observables on the size of the corresponding eigenvalue, which allows us to study the transition of a near-zero mode into a bulk mode. We analyze ensembles of quenched SU(3) configurations using a Dirac operator which is a systematic expansion in path length of a solution of the Ginsparg-Wilson equation. Our results support the interpretation of the excitations relevant for chiral symmetry breaking as interacting instantons and anti-instantons.
We try to separate the perturbative and non-perturbative contributions to the plaquette of pure SU(3) gauge theory. To do this we look at the large-n asymptotic behaviour of the perturbation series in order to estimate the contribution of the as-yet uncalculated terms in the series. We find no evidence for the previously reported Lambda^2 contribution to the gluon condensate. Attempting to determine the conventional Lambda^4 condensate gives a value of approximately 0.03(2) GeV^4, in reasonable agreement with sum rule estimates, though with very large uncertainties.
We analyze the eigenvalues and eigenvectors of the staggered Dirac operator in quenched lattice QCD in the vicinity of the deconfinement phase transition using the Lüscher-Weisz gauge action. The spectral and localization properties of the low-lying eigenmodes show characteristic differences between the Z_3 sectors above the critical temperature T_c. These findings can be interpreted in terms of calorons.
It has been suggested to use the production of Lambda hyperons for investigating the nucleon spin structure. The viability of this idea depends crucially on the spin structure of the Lambda. Using nonperturbatively O(a) improved Wilson fermions in the quenched approximation we have studied matrix elements of two-quark operators in the Lambda. We present results for the axial vector current, which give us the contributions of the u, d, and s quarks to the Lambda spin.
We discuss the construction and properties of an approximate solution of the Ginsparg-Wilson equation, the so-called chirally improved lattice Dirac operator. In particular we study the behavior of its eigenmodes in smooth instanton backgrounds as well as for thermalized gauge configurations on both sides of the QCD phase transition. We compare with results from other Dirac operators including the overlap operator. The results support the picture of chiral symmetry breaking being closely related to instantons.
The scale parameter $Λ_{\overline{MS}}$ is computed on the lattice in the quenched approximation and for $N_f = 2$ flavors of light dynamical quarks. The dynamical calculation is done with non-perturbatively $O(a)$ improved Wilson fermions. In the continuum limit we obtain $Λ_{\overline{MS}}^{N_f=0} = 243(1)(10)$ MeV and $Λ_{\overline{MS}}^{N_f=2} = 217(16)(11)$ MeV, respectively.
In this talk we highlight recent lattice calculations of the nucleon form factors and structure functions.