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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.
Lattice simulations employing reweighting and Taylor expansion techniques have predicted a (m;T)-phase diagram according to general expectations, with an analytic quark-hadron crossover at m =0 turning into a first order transition at some critical chemical potential mE. By contrast, recent simulations using imgainary m followed by analytic continuation obtained a critical structure in the fmu;d;ms;T;mg parameter space favouring the absence of a critical point and first order line. I review the evidence for the latter scenario, arguing that the various raw data are not inconsistent with each other. Rather, the discrepancy appears when attempting to extract continuum results from the coarse (Nt =4) lattices simulated so far, and can be explained by cut-off effects. New (as yet unpublished) data are presented, which for Nf = 3 and on Nt = 4 confirm the scenario without a critical point. Moreover, simulations on finer Nt = 6 lattices show that even if there is a critical point, continuum extrapolation moves it to significantly larger values of mE than anticipated on coarse lattices.
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.
The QCD equation of state is not often discussed in cosmology. However, the relic density of
weakly interacting massive particles (WIMPs) depends on the entropy and the expansion rate of
the Universe when they freeze out, at a temperature in the range 400 MeV – 40GeV, where QCD
corrections are still important. We use recent analytic and lattice calculations of the QCD pressure
to produce a new equation of state suitable for use in relic density calculations. As an example,
we show that relic densities calculated by the dark matter package DarkSUSY receive corrections
of several per cent, within the observational accuracy of the Planck CMB mission, due for launch
in 2007.
I review recent developments in determining the QCD phase diagram by means of lattice simulations.
Since the invention of methods to side-step the sign problem a few years ago, a number
of additional variants have been proposed, and progress has been made towards understanding
some of the systematics involved. All available techniques agree on the transition temperature
as a function of density in the regime mq/T <~1. There are by now four calculations with signals
for a critical point, two of them at similar parameter values and with consistent results. However,
it also emerges that the location of the critical point is exceedingly quark mass sensitive. At the
same time sizeable finite volume, cut-off and step size effects have been uncovered, demanding
additional investigations with exact algorithms on larger and finer lattices before quantitative conclusions
can be drawn. Depending on the sign of these corrections, there is ample room for the
eventual phase diagram to look as expected or also quite different, with no critical point at all.
We review our knowledge of the phase diagram of QCD as a function of temperature, chemical potential and quark masses. The presence of tricritical lines at imaginary chemical potential m = i p 3 T, with known scaling behaviour in their vicinity, puts constraints on this phase diagram, especially in the case of two light flavors. We show first results in our project to determine the finite-temperature behaviour in the Nf = 2 chiral limit.
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.
LatticeQCD using OpenCL
(2011)
We perform a detailed study of the adjoint static potential in the pseudoparticle approach, which is a model for SU(2) Yang-Mills theory. We find agreement with the Casimir scaling hypothesis and there is clear evidence for string breaking. At the same time the potential in the fundamental representation is linear for large separations. Our results are in qualitative agreement with results from lattice computations.
We present the status of runs performed in the twisted mass formalism with Nf =2+1+1 flavours of dynamical fermions: a degenerate light doublet and a mass split heavy doublet. The procedure for tuning to maximal twist will be described as well as the current status of the runs using both thin and stout links. Preliminary results for a few observables obtained on ensembles at maximal twist will be given. Finally, a reweighting procedure to tune to maximal twist will be described.
The pseudoparticle approach is a numericalmethod to compute path integrals without discretizing spacetime. The basic idea is to consider only those field configurations, which can be represented as a linear superposition of a small number of localized building blocks (pseudoparticles), and to replace the functional integration by an integration over the pseudoparticle degrees of freedom. In previous papers we have successfully applied the pseudoparticle approach to SU(2) Yang-Mills theory. In this work we discuss the inclusion of fermionic fields in the pseudoparticle approach. To test our method, we compute the phase diagram of the 1+1-dimensional Gross-Neveu model in the large-N limit as well as the chiral condensate in the crystal phase.
We present a numerical technique for calculating path integrals in non-compact U(1) and SU(2) gauge theories. The gauge fields are represented by a superposition of pseudoparticles of various types with their amplitudes and color orientations as degrees of freedom. Applied to Maxwell theory this technique results in a potential which is in excellent agreement with the Coulomb potential. For SU(2) Yang-Mills theory the same technique yields clear evidence of confinement. Varying the coupling constant exhibits the same scaling behavior for the string tension, the topological susceptibility and the critical temperature while their dimensionless ratios are similar to those obtained in lattice calculations.
We compute the static-light baryon spectrum with Nf = 2 flavors of sea quarks using Wilson twisted mass lattice QCD. As light valence quarks we consider quarks, which have the same mass as the sea quarks with corresponding pion masses in the range 340MeV<∼ mPS<∼ 525MeV, as well as partially quenched quarks, which have the mass of the physical s quark. We extract masses of states with isospin I = 0,1/2,1, with strangeness S = 0,−1,−2, with angular momentum of the light degrees of freedom j = 0,1 and with parity P = +,−. We present a preliminary extrapolation in the light u/d and an interpolation in the heavy b quark mass to the physical point and compare with available experimental results.
We present unambiguous evidence from lattice simulations of Nf = 3 QCD for two tricritical points in the (T;m) phase diagram at fixed imaginary m=T = ip=3 mod. 2p=3, one in the light and one in the heavy quark regime. Together with similar results in the literature for Nf = 2 this implies the existence of a chiral and of a deconfinement tricritical line at those values of imaginary chemical potentials. These tricritical lines represent the boundaries of the analytically continued chiral and deconfinement critical surfaces, respectively, which delimit the parameter space with first order phase transitions. It is demonstrated that the shape of the deconfinement critical surface is dictated by tricritical scaling and implies the weakening of the deconfinement transition with real chemical potential. A qualitatively similar effect holds for the chiral critical surface.
We perform a two-flavor dynamical lattice computation of the Isgur-Wise functions t1/2 and t3/2
at zero recoil in the static limit. We find t1/2(1) = 0.297(26) and t3/2(1) = 0.528(23) fulfilling
Uraltsev’s sum rule by around 80%. We also comment on a persistent conflict between theory and
experiment regarding semileptonic decays of B mesons into orbitally excited P wave D mesons,
the so-called “1/2 versus 3/2 puzzle”, and we discuss the relevance of lattice results in this
context.
We discuss the implementation and results of a recently developed microscopic method for calculating ion-ion interaction potentials and fusion cross-sections. The method uses the TDHF evolution to obtain the instantaneous many-body collective state using a density constraint. The ion-ion potential as well as the coordinate dependent mass are calculated from these states. The method fully accounts for the dynamical processes present in the TDHF time-evolution and provides a parameter-free way of calculating fusion cross-sections.
We study the implications on compact star properties of a soft nuclear equation of state determined from kaon production at subthreshold energies in heavy-ion collisions. On one hand, we apply these results to study radii and moments of inertia of light neutron stars. Heavy-ion data provides constraints on nuclear matter at densities relevant for those stars and, in particular, to the density dependence of the symmetry energy of nuclear matter. On the other hand, we derive a limit for the highest allowed neutron star mass of three solar masses. For that purpouse, we use the information on the nucleon potential obtained from the analysis of the heavy-ion data combined with causality on the nuclear equation of state.
We present and compare new types of algorithms for lattice QCD with staggered fermions in the limit of infinite gauge coupling. These algorithms are formulated on a discrete spatial lattice but with continuous Euclidean time. They make use of the exact Hamiltonian, with the inverse temperature beta as the only input parameter. This formulation turns out to be analogous to that of a quantum spin system. The sign problem is completely absent, at zero and non-zero baryon density. We compare the performance of a continuous-time worm algorithm and of a Stochastic Series Expansion algorithm (SSE), which operates on equivalence classes of time-ordered interactions. Finally, we apply the SSE algorithm to a first exploratory study of two-flavor strong coupling lattice QCD, which is manageable in the Hamiltonian formulation because the sign problem can be controlled.