arXiv subjects
Publications and source records attributed to E. Laermann.
Results on the phase transition in QCD with two flavours of light staggered fermions from an ongoing simulation are presented. We find the restoration of the chiral SU(2) x SU(2) symmetry, but not of the axial U_A(1) symmetry.
The pressure and the energy density of the $SU(3)$ gauge theory are calculated on lattices with temporal extent $N_τ= 4$, 6 and 8 and spatial extent $N_σ=16$ and 32. The results are then extrapolated to the continuum limit. In the investigated temperature range up to five times $T_c$ we observe a $15\%$ deviation from the ideal gas limit. We also present new results for the critical temperature on lattices with temporal extent $N_τ= 8$ and 12. At the corresponding critical couplings the string tension is calculated on $32^4$ lattices to fix the temperature scale. An extrapolation to the continuum limit yields $T_c/\sqrtσ = 0.629(3)$. We furthermore present results on the electric and magnetic condensates as well as the temperature dependence of the spatial string tension. These observables suggest that the temperature dependent running coupling remains large even at $T\simeq 5T_c$. For the spatial string tension we find $\sqrt{σ_s}/T = 0.566(13) g^2(T)$ with $g^2(5T_c) \simeq 1.5$.
Finite cut-off effects strongly influence the thermodynamics of lattice regularized QCD at high temperature in the standard Wilson formulation. We analyze the reduction of finite cut-off effects in formulations of the thermodynamics of $SU(N)$ gauge theories with three different $O(a^2)$ and $O(a^4)$ improved actions. We calculate the energy density and pressure on finite lattices in leading order weak coupling perturbation theory ($T\rightarrow \infty$) and perform Monte Carlo simulations with improved $SU(3)$ actions at non-zero $g^2$. Already on lattices with temporal extent $N_τ=4$ we find a strong reduction of finite cut-off effects in the high temperature limit, which persists also down to temperatures a few times the deconfinement transition temperature.
Through a detailed investigation of the $SU(3)$ gauge theory at finite temperature on lattices of various size we can control finite lattice cut-off effects in bulk thermodynamic quantities. We calculate the pressure and energy density of the $SU(3)$ gauge theory on lattices with temporal extent $N_τ= 4$, 6 and 8 and spatial extent $N_σ=16$ and 32. The results are extrapolated to the continuum limit. We find a deviation from ideal gas behaviour of (15-20)\%, depending on the quantity, even at temperatures as high as $T\sim 3T_c$. A calculation of the critical temperature on lattices with temporal extent $N_τ= 8$ and 12 and the string tension on $32^4$ lattices at the corresponding critical couplings is performed to fix the temperature scale. An extrapolation to the continuum limit yields $T_c/\sqrtσ = 0.629(3)$.
We calculate the hadronic coupling constants $g_{NNπ}$ and $g_{ρππ}$ in QCD, including dynamical quarks in the framework of staggered fermions in the lattice approach. For the nucleon--pion coupling we obtain $g_{NNπ} = 13.8 \pm 5.8$, to be compared with the experimental value $13.13 \pm 0.07$. The $ρππ$ coupling has been analysed for two different sets of operators with the averaged result $g_{ρππ} = 4.2 \pm 1.9$ which is to be compared with the experimental value $6.06 \pm 0.01$.
We have investigated hadron screening masses, the chiral condensate, and the pion decay constant close to the deconfinement phase transition in the confined phase of QCD. The simulations were done in the quenched approximation, on a lattice of size \mbox{$32^{3}\times 8$}. We examined temperatures ranging from $0.75\tc$ up to $0.92\tc$. We see no sign of a temperature dependence in the chiral condensate or the meson properties, but some temperature dependence for the nucleon screening mass is not excluded.
We compute heavy quark potentials in pure gauge $SU(3)$ at high temperatures in $2+1$ dimensions and confront them with expectations emerging from perturbative calculations.
We establish a close relation between the spatial string tension of the (3+1)-dimensional $SU(3)$ gauge theory at finite temperature ($σ_s$) and the string tension of the 3-dimensional $SU(3)$ gauge theory ($σ_3$) which is similar to what has been found previously for $SU(2)$. We obtain $\sqrt{σ_3} = (0.554 \pm 0.004) g_3^2$ and $\sqrt{σ_s} = (0.586 \pm 0.045)g^2(T) T$, respectively. For temperatures larger than twice the critical temperature results are consistent with a temperature dependent coupling running according to the two-loop $β$-function with $Λ_T = 0.118(36)T_c$.
Hadronic correlation functions at finite temperature in QCD, with four flavours of dynamical quarks, have been analyzed both above and below the chiral symmetry restoration temperature. We have used both point and extended sources for spatial as well as temporal correlators. The effect of periodic temporal boundary conditions for the valence quarks on the spatial meson correlators has also been investigated. All our results are consistent with the existence of individual quarks at high temperatures. A measurement of the residual interaction between the quarks is presented.
We report on calculations of the hadronic coupling constants $g_{ρππ}$ and $g_{nnπ}$ based on lattice QCD with four flavors of dynamical staggered fermions. By computing 2--point and 3--point Green's functions we have been able to determine these coupling constants ab initio from QCD; the results are compatible with the experimental values.
A lattice calculation of the pi-N sigma term is described using dynamical staggered fermions. Preliminary results give a sea term comparable in magnitude to the valence term.
We will discuss here an indirect lattice evaluation of the baryon axial singlet current matrix element. This quantity may be related to the fraction of nucleon spin carried by the quarks. The appropriate structure function has recently been measured (EMC experiment). As in this experiment, we find that the quarks do not appear to carry a large component of the nucleon spin.
A lattice calculation of the pi-N sigma term is described using dynamical staggered fermions. Preliminary results give a sea term comparable in magnitude to the valence term.
Numerical simulations have become an important tool to understand and predict non-perturbative phenomena in particle physics. In this article we attempt to present a general overview over the field. First, the basic concepts of lattice gauge theories are described, including a discussion of currently used algorithms and the reconstruction of continuum physics from lattice results. We then proceed to present some results for QCD, both at low energies and at high temperatures, as well as for the electro-weak sector of the standard model.
The fraction of the nucleon spin that is carried by the quarks, $ΔΣ$, is computed in lattice QCD with dynamical staggered fermions. We obtain the value $ΔΣ= 0.18 \pm 0.02$.
A numerical calculation of the lattice staggered renormalisation constants at $β= 5.35$, $m = 0.01$ is presented. It is seen that there are considerable non-perturbative effects present. As an application the vector decay constant $f_ρ$ is estimated. (LAT92 contribution, one LATEX file with 3 postscript figures appended.)