Der thermische Übergang der Quantenchromodynamik mit Twisted-Mass-Fermionen

Subject of this thesis is the non-perturbative investigation of the thermal transition in Quantum Chromodynamics by means of lattice gauge theory and a particular type of lattice fermions, the so-called twisted mass fermions. These fermions offer the possibility of improvement as compared to the standard Wilson-type formulation. We investigate the properties of these fermions at finite temperature, i.e. the structure of the bare parameter space as well as leading order cutoff effects in the weak coupling limit. Then we focus on two-flavour simulations at finite pion mass. We identify the (pseudo-)critical temperatures for our set of pion masses (300 to 500 MeV) and discuss the extrapolation to the chiral limit for which the nature of the transition is still an open question. Besides pseudo-critical temperatures we consider the magnetic equation of state and screening observables. We find that the assumption of a second order transition (in the 3d O(4) universality class) agrees with our data without being able to exclude alternatives. Finally, we discuss the future inclusion of strange and charm quarks in dynamical twisted mass simulations and look at the corresponding cutoff effects in the free limit.Gegenstand dieser Dissertation ist die nicht-perturbative Untersuchung des thermischen Übergangs der Quantenchromodynamik in Gittereichtheorie mithilfe einer speziellen Fermiondiskretisierung, den sogenannten Wilson-Fermionen mit chiral verdrehtem Massenterm (twisted mass Fermionen). Diese Gitterfermionen weisen verbesserte Eigenschaften gegenüber den gewöhnlichen Wilson-Fermionen auf. Dabei untersuchen wir zum einen die grundsätzlichen Eigenschaften der twisted mass Fermionen bei endlichen Temperaturen. Dies umfasst die Phasenraumstruktur für die Parameter der Wirkung und die Betrachtung von Diskretisierungsartefakten führender Ordnung im Schwachkopplungslimes. Darüber hinaus liegt der Schwerpunkt der Arbeit auf Simulationen bei endlicher Pionmasse für zwei massenentartete Quark-Arten. Für diesen Fall identifizieren wir die (pseudo-)kritische Temperatur für die simulierten Pionmassen (300 bis 500 MeV) und diskutieren die Extrapolation zum chiralen Limes, für den die Natur des Phasenübergangs noch nicht abschließend geklärt ist. Neben der pseudo-kritischen Temperatur betrachten wir die magnetische Zustandsgleichung sowie Screening-Eigenschaften. Insgesamt finden wir ein selbstkonsistentes Bild, wenn wir Verhalten zweiter Ordnung (in der 3d O(4) Universalitätsklasse) im chiralen Limes annehmen, ohne aber alternative Szenarien ausschließen zu können. Die zusätzliche Verwendung von strange und charm Quarks wird für zukünftige Simulationen bei endlichen Temperaturen diskutiert. Insbesondere betrachten wir die Gitterartefakte für den wechselwirkungsfreien Fall

Towards the Nf = 2 deconfinement transition temperature with O(a) improved Wilson fermions

A lot of effort in lattice simulations over the last years has been devoted to studies of the QCD deconfinement transition. Most state-of-the-art simulations use rooted staggered fermions, while Wilson fermions are affected by large systematic uncertainties, such as coarse lattices or heavy sea quarks. Here we report on an ongoing study of the transition, using two degenerate flavours of nonperturbatively O(a) improved Wilson fermions. We start with Nt = 12 and 16 lattices and pion masses of 600 to 450 MeV, aiming at chiral and continuum limits with light quarks

Towards the N_f=2 deconfinement transition temperature with O(a) improved Wilson fermions: An update

We give an update on our current project to determine the transition temperature and the order of the deconfinement transition in the chiral limit of two flavour QCD. We use nonperturbatively O(a) improved Wilson fermions of the Sheikholeslami-Wohlert type, employing the efficient deflation accelerated DDHMC algorithm. We start at lattices with N_t>=12 and pion masses below 600 MeV, aiming at chiral and continuum limits with light quarks.Comment: 3 pages, 4 figures, talk given at "Quark Confinement and the Hadron Spectrum IX", Madrid, Spain, Aug. 30-Sep. 3, 2010, submitted to AIP Conference Proceeding

Cutoff effects of Wilson fermions on the QCD equation of state to O(g^2)

We compute the O(g^2) contribution to the thermodynamic pressure for Wilson fermions in the standard, the twisted mass, and clover improved formulation in lattice perturbation theory, including finite mass effects. We compare the continuum approaches of these discretizations for the massive ideal and interacting gas. In all cases, for N_t \geq 8 cutoff effects of Wilson type fermions are comparable to those of staggered fermions, but asymptotic scaling requires $N_\tau>10$.Comment: 9 pages, 4 figures. Version shortened to a brief report accepted by PR

Cutoff effects of Wilson fermions on the QCD equation of state to O(g^2)

We compute the O(g^2) contribution to the thermodynamic pressure for Wilson fermions in the standard, the twisted mass, and clover improved formulation in lattice perturbation theory, including finite mass effects. We compare the continuum approaches of these discretizations for the massive ideal and interacting gas. In all cases, for N_t \geq 8 cutoff effects of Wilson type fermions are comparable to those of staggered fermions, but asymptotic scaling requires $N_\tau>10$.Comment: 9 pages, 4 figures. Version shortened to a brief report accepted by PR

The finite-temperature phase structure of lattice QCD with twisted-mass Wilson fermions

We report progress in our exploration of the finite-temperature phase structure of two-flavour lattice QCD with twisted-mass Wilson fermions and a tree-level Symanzik-improved gauge action for a temporal lattice size Nt = 8. Extending our investigations to a wider region of parameter space we gain a global view of the rich phase structure. We identify the finite temperature transition/ crossover for a non-vanishing twisted-mass parameter in the neighbourhood of the zerotemperature critical line at sufficiently high b . Our findings are consistent with Creutz’s conjecture of a conical shape of the finite temperature transition surface. Comparing with NLO lattice cPT we achieve an improved understanding of this shape

LatticeQCD using OpenCL

We report on our implementation of LatticeQCD applications using OpenCL. We focus on the general concept and on distributing different parts on hybrid systems, consisting of both CPUs (Central Processing Units) and GPUs (Graphic Processing Units).Comment: 7 pages, 13 figures, proceedings of the XXIX International Symposium on Lattice Field Theory - Lattice 2011, July 10-16, 2011, Squaw Valley, Lake Tahoe, Californi

Pseudo-Critical Temperature and Thermal Equation of State from Nf = 2 Twisted Mass Lattice QCD

We report about the current status of our ongoing study of the chiral limit of two-flavor QCD at finite temperature with twisted mass quarks. We estimate the pseudo-critical temperature Tc for three values of the pion mass in the range of mPS ~ 300 and 500 MeV and discuss different chiral scenarios. Furthermore, we present first preliminary results for the trace anomaly, pressure and energy density. We have studied several discretizations of Euclidean time up to Nt = 12 in order to assess the continuum limit of the trace anomaly. From its interpolation we evaluate the pressure and energy density employing the integral method. Here, we have focussed on two pion masses with mPS ~ 400 and 700 MeV

Twisted mass QCD at finite temperature

We discuss the use of Wilson fermions with twisted mass for simulations of QCD thermodynamics. As a prerequisite for a future analysis of the finite-temperature transition making use of automatic O(a) improvement, we investigate the phase structure in the space spanned by the hopping parameter k , the coupling b , and the twisted mass parameter m. We present results for Nf = 2 degenerate quarks on a 163×8 lattice, for which we investigate the possibility of an Aoki phase existing at strong coupling and vanishing m, as well as of a thermal phase transition at moderate gauge couplings and non-vanishing m