Georg P. Engel

Meson and baryon spectrum for QCD with two light dynamical quarks

We present results of meson and baryon spectroscopy using the Chirally Improved Dirac operator on lattices of size 16{sup 3}x32 with two mass-degenerate light sea quarks. Three ensembles with pion masses of 322(5), 470(4), and 525(7) MeV and lattice spacings close to 0.15 fm are investigated. Results for ground and excited states for several channels are given, including spin two mesons and hadrons with strange valence quarks. The analysis of the states is done with the variational method, including two kinds of Gaussian sources and derivative sources. We obtain several ground states fairly precisely and find radial excitations in various channels. Excited baryon results seem to suffer from finite size effects, in particular, at small pion masses. We discuss the possible appearance of scattering states, considering masses and eigenvectors. Partially quenched results in the scalar channel suggest the presence of a 2-particle state, however, in most channels we cannot identify them. Where available, we compare our results to results of quenched simulations using the same action.

QCD with two light dynamical chirally improved quarks: Mesons

We present results for the spectrum of light and strange mesons on configurations with two flavors of mass-degenerate Chirally Improved sea quarks. The calculations are performed on seven ensembles of lattice size 16^3x32 at three different gauge couplings and with pion masses ranging from 250 to 600 MeV. To reliably extract excited states, we use the variational method with an interpolator basis containing both gaussian and derivative quark sources. Both conventional and exotic channels up to spin 2 are considered. Strange quarks are treated within the partially quenched approximation. For kaons we investigate the mixing of interpolating fields corresponding to definite C-parity in the SU(3) limit. This enlarged basis allows for an improved determination of the low-lying kaon spectrum. In addition to masses we also extract the ratio of the pseudoscalar decay constants of the kaon and pion and obtain F_K/F_\pi=1.215(41). The results presented here include some ensembles from previous publications and the corresponding results supersede the previously published values.

Non-Gaussianities in the topological charge distribution of the SU(3) Yang--Mills theory

We study the topological charge distribution of the SU(3) Yang--Mills theory with high precision in order to be able to detect deviations from Gaussianity. The computation is carried out on the lattice with high statistics Monte Carlo simulations by implementing a naive discretization of the topological charge evolved with the Yang--Mills gradient flow. This definition is far less demanding than the one suggested from Neubergers fermions and, as shown in this paper, in the continuum limit its cumulants coincide with those of the universal definition appearing in the chiral Ward identities. Thanks to the range of lattice volumes and spacings considered, we can extrapolate the results for the second and fourth cumulant of the topological charge distribution to the continuum limit with confidence by keeping finite volume effects negligible with respect to the statistical errors. Our best results for the topological susceptibility is t_0^2*chi=6.67(7)*10^-4, where t_0 is a standard reference scale, while for the ratio of the forth cumulant over the second we obtain R=0.233(45). The latter is compatible with the expectations from the large Nc expansion, while it rules out the theta-behavior of the vacuum energy predicted by the dilute instanton model. Its large distance from 1 implies that, in the ensemble of gauge configurations that dominate the path integral, the fluctuations of the topological charge are of quantum non-perturbative nature.

Low-lying

In a lattice QCD calculation with two light dynamical Chirally Improved (CI) quarks we determine ground state and some excited state masses in all four Lambda baryon channels 1/2^\pm and 3/2^\pm. We perform an infinite volume extrapolation and confirm the widely discussed Lambda(1405). We also analyze the amount of octet-singlet mixing, which is helpful in comparing states with the quark model.

\Lambda

A distinctive feature of the presence of spontaneous chiral symmetry breaking in QCD is the condensation of low modes of the Dirac operator near the origin. The rate of condensation must be equal to the slope of M πF 2 π/2 with respect to the quark mass m in the chiral limit, where Mπ and Fπ are the mass and the decay constant of the Nambu-Goldstone bosons. We compute the spectral density of the (Hermitian) Dirac operator, the quark mass, the pseudoscalar meson mass and decay constant by numerical simulations of lattice QCD with two light degenerate Wilson quarks. We use CLS lattices at three values of the lattice spacing in the range 0.05–0.08 fm, and for several quark masses corresponding to pseudoscalar mesons masses down to 190 MeV. Thanks to this coverage of parameters space, we can extrapolate all quantities to the chiral and continuum limits with confidence. The results show that the low quark modes do condense in the continuum as expected by the Banks–Casher mechanism, and the rate of condensation agrees with the Gell–Mann-Oakes-Renner (GMOR) relation. For the renormalisation-group-invariant ratios we obtain [Σ]/F = 2.77(2)(4) and Λ/F = 3.6(2), which correspond to [Σ(2GeV)] = 263(3)(4) MeV and F = 85.8(7)(20) MeV if FK is used to set the scale by supplementing the theory with a quenched strange quark.

baryons from the lattice

We compute the spectral density of the (Hermitean) Dirac operator in Quantum Chromodynamics with two light degenerate quarks near the origin. We use CLS/ALPHA lattices generated with two flavours of O(a)-improved Wilson fermions corresponding to pseudoscalar meson masses down to 190 MeV, and with spacings in the range 0.05-0.08 fm. Thanks to the coverage of parameter space, we can extrapolate our data to the chiral and continuum limits with confidence. The results show that the spectral density at the origin is non-zero because the low modes of the Dirac operator do condense as expected in the Banks-Casher mechanism. Within errors, the spectral density turns out to be a constant function up to eigenvalues of approximately 80 MeV. Its value agrees with the one extracted from the Gell-Mann-Oakes-Renner relation.

Chiral symmetry breaking in QCD with two light flavors.

We report on our ongoing project of determining the chiral condensate of two-flavor QCD from the Banks-Casher relation. We compute the mode number of the O(a)-improved Wilson-Dirac operator for several values of Λ, and we discuss different fitting strategies to extract the chiral condensate from its mass and Λ dependence. Our preliminary results haven been obtained at two different lattice spacings by using CLS-configurations.

Spectral density of the Dirac operator in two-flavor QCD

We test a recent proposal to use approximate trivializing maps in a field theory to speed up Hybrid Monte Carlo simulations. Simulating the CPN−1 model, we find a small improvement with the leading order transformation, which is however compensated by the additional computational overhead. The scaling of the algorithm towards the continuum is not changed. In particular, the effect of the topological modes on the autocorrelation times is studied.

Chiral condensate from the Banks-Casher relation

Inst. f. Theoret. Physik, Univ. Regensburg, Regensburg, GernmayE-mail:georg.engel@uni-graz.at, christof.gattringer@uni-graz.at,christian.lang@uni-graz.at, markus.limmer@uni-graz.at,daniel.mohler@uni-graz.at, andreas.schaefer@physik.uni-regensburg.deThe chirally improved (CI) fermion action allows us to obtain results for pion masses down to320 MeV on (in lattice units) comparatively small lattices with physical extent of 2.4 fm. We usedifferently smeared quarks sources to build sets of several interpolators. The variational methodthenleads to excellentgroundstate masses formost mesons andbaryons. Theexcitedstate signalsweaken in quality towards smaller quark masses. In particular the excited baryons come out toohigh.The XXVII International Symposium on Lattice Field Theory -LAT2009July 26-31 2009Peking University, Beijing, China

Testing trivializing maps in the Hybrid Monte Carlo algorithm.

Results for excited light and strange hadrons from the lattice with two flavors of Chirally Improved sea quarks are presented. We perform simulations at several values of the pion mass ranging from 250 to 600 MeV and extrapolate to the physical pion mass. The variational method is applied to extract excited energy levels but also to discuss the content of the states. Among others, we explore the flavor singlet/octet content of Lambda states. In general, our results agree well with experiment, in particular we confirm the Lambda(1405) and its dominant flavor singlet structure.