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Approaching the continuum limit of the deconfinement critical point for Nf=2 staggered fermions
(2022)
Quenched QCD at zero baryonic chemical potential undergoes a first-order deconfinement phase transition at a critical temperature Tc, which is related to the spontaneous breaking of the global center symmetry. The center symmetry is broken explicitly by including dynamical quarks, which weaken the first-order phase transition for decreasing quark masses. At a certain critical quark mass, which corresponds to the Z(2)-critical point, the first-order phase transition turns into a smooth crossover. We investigate the Z(2)-critical quark mass for Nf=2 staggered fermions on Nτ=8,10 lattices, where larger Nτ correspond to finer lattices. Monte-Carlo simulations are performed for several quark mass values and aspect ratios in order to extrapolate to the thermodynamic limit. We present final results for Nτ=8 and preliminary results for Nτ=10 for the critical mass, which are obtained from fitting to a kurtosis finite size scaling formula of the absolute value of the Polyakov loop.
In the strong coupling and heavy quark mass regime, lattice QCD dimensionally reduces to effective theories of Polyakov loops depending on the parameters of the original Wilson action β,κ and Nτ. We apply coarse graining techniques to such theories in 1d and 2d, corresponding to lattice QCD at finite temperature and non-zero chemical potential in 1+1d and 2+1d, respectively. In 1d the method is applied to the effective theories up to O(κ4). Using the transfer matrix, the recursion relations are solved analytically. The thermodynamic limit is taken for some observables. Afterwards, continuum extrapolation is performed numerically and results are discussed. In 2d the coarse graining method is applied in the pure gauge and static quark limit. Running couplings are obtained and the fixed points of the transformations are discussed. Finally, the critical coupling of the deconfinement transition is determined in both limits. Agreement to about 12% with Monte Carlo results of 2+1d Yang-Mills theory from the literature is observed.
Thermal leptogenesis, in the framework of the standard model with three additional heavy Majorana neutrinos, provides an attractive scenario to explain the observed baryon asymmetry in the universe. It is based on the out-of-equilibrium decay of Majorana neutrinos in a thermal bath of standard model particles, which in a fully quantum field theoretical formalism is obtained by solving Kadanoff-Baym equations. So far, the leading two-loop contributions from leptons and Higgs particles are included, but not yet gauge corrections. These enter at three-loop level but, in certain kinematical regimes, require a resummation to infinite loop order for a result to leading order in the gauge coupling. In this work, we apply such a resummation to the calculation of the lepton number density. The full result for the simplest “vanilla leptogenesis” scenario is by O(1) increased compared to that of quantum Boltzmann equations, and for the first time permits an estimate of all theoretical uncertainties. This step completes the quantum theory of leptogenesis and forms the basis for quantitative evaluations, as well as extensions to other scenarios.
We study a random matrix model for QCD at finite density via complex Langevin dynamics. This model has a phase transition to a phase with nonzero baryon density. We study the convergence of the algorithm as a function of the quark mass and the chemical potential and focus on two main observables: the baryon density and the chiral condensate. For simulations close to the chiral limit, the algorithm has wrong convergence properties when the quark mass is in the spectral domain of the Dirac operator. A possible solution of this problem is discussed.
We compute hybrid static potentials in SU(3) lattice gauge theory. We present a method to automatically generate a large set of suitable creation operators with defined quantum numbers from elementary building blocks. We show preliminary results for several channels and discuss, which structures of the gluonic flux tube seem to be realized by the ground states in these channels.
Lattice QCD and functional methods are making significant progress in constraining the QCD phase diagram. As an important milestone, the chiral phase transition with massless u, d-quarks at zero density is now understood to be of second order for all strange quark masses, and a smooth crossover as soon as mu,d, ≠ 0. Together with information on fluctuations and refined reweighted simulations, this bounds a possible critical point to be at µB/T ≲3. On the other hand, an approximately chiral-spin symmetric temperature window has been discovered above the chiral crossover, Tch<T ≳3Tch, with distinct correlator multiplet patterns and a pion spectral function suggesting resonance-like degrees of freedom, which dissolve graduallly with temperature.
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 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.
Effective three-dimensional Polyakov loop theories derived from QCD by strong coupling and hopping expansions are valid for heavy quarks and can also be applied to finite chemical potential μ, due to their considerably milder sign problem. We apply the Monte-Carlo method to the Nf=1,2 effective theories up to O(κ4) in the hopping parameter at μ=0 to determine the critical quark mass, at which the first-order deconfinement phase transition terminates. The critical end point obtained from the effective theory to order O(κ2) agrees well with 4-dimensional QCD simulations with a hopping expanded determinant by the WHOT-QCD collaboration. We also compare with full QCD simulations and thus obtain a measure for the validity of both the strong coupling and the hopping expansion in this regime.
The SU(3) pure gauge theory exhibits a first-order thermal deconfinement transition due to spontaneous breaking of its global Z3 center symmetry. When heavy dynamical quarks are added, this symmetry is broken explicitly and the transition weakens with decreasing quark mass until it disappears at a critical point. We compute the critical hopping parameter and the associated pion mass for lattice QCD with Nf=2 degenerate standard Wilson fermions on Nτ∈{6,8,10} lattices, corresponding to lattice spacings a=0.12 fm, a=0.09 fm, a=0.07 fm, respectively. Significant cutoff effects are observed, with the first-order region growing as the lattice gets finer. While current lattices are still too coarse for a continuum extrapolation, we estimate mcπ≈4 GeV with a remaining systematic error of ∼20%. Our results allow us to assess the accuracy of the leading-order and next-to-leading-order hopping expanded fermion determinant used in the literature for various purposes. We also provide a detailed investigation of the statistics required for this type of calculation, which is useful for similar investigations of the chiral transition.