Stefan Krieg

The QCD equation of state with dynamical quarks

The present paper concludes our investigation on the QCD equation of state with 2 + 1 staggered flavors and one-link stout improvement. We extend our previous study [JHEP01 (2006) 089] by choosing even finer lattices. Lattices with Nt=6, 8 and 10 are used, and the continuum limit is approached by checking the results at Nt= 12. A Symanzik improved gauge and a stout-link improved staggered fermion action is utilized. We use physical quark masses, that is, for the lightest staggered pions and kaons we fix the mπ/fK and mK/fK ratios to their experimental values. The pressure, the interaction measure, the energy and entropy density and the speed of sound are presented as functions of the temperature in the range 100 ... 1000MeV. We give estimates for the pion mass dependence and for the contribution of the charm quark. We compare our data to the equation of state obtained by the “hotQCD” collaboration.

Is there still any T c mystery in lattice QCD? Results with physical masses in the continuum limit III

The present paper concludes our investigations on the QCD cross-over transition temperatures with 2+1 staggered flavours and one-link stout improvement. We extend our previous two studies [Phys. Lett. B643 (2006) 46, JHEP 0906:088 (2009)] by choosing even finer lattices (Nt = 16) and we work again with physical quark masses. The new results on this broad cross-over are in complete agreement with our earlier ones. We compare our findings with the published results of the hotQCD collaboration. All these results are confronted with the predictions of the Hadron Resonance Gas model and Chiral Perturbation Theory for temperatures below the transition region. Our results can be reproduced by using the physical spectrum in these analytic calculations. The findings of the hotQCD collaboration can be recovered by using a distorted spectrum which takes into account lattice discretization artifacts and heavier than physical quark masses. This analysis provides a simple explanation for the observed discrepancy in the transition temperatures between our and the hotQCD collaborations.

Full result for the QCD equation of state with 2+1 flavors

We present a full result for the 2+1 flavor QCD equation of state. All the systematics are controlled, the quark masses are set to their physical values, and the continuum extrapolation is carried out. This extends our previous studies [JHEP 0601:089 (2006); 1011:077 (2010)] to even finer lattices and now includes ensembles with Nt = 6,8,10,12 up to Nt = 16. We use a Symanzik improved gauge and a stout-link improved staggered fermion action. Our findings confirm our earlier results. In order to facilitate the direct use of our equation of state we make our tabulated results available for download.

High-precision scale setting in lattice QCD

A bstractScale setting is of central importance in lattice QCD. It is required to predict dimensional quantities in physical units. Moreover, it determines the relative lattice spacings of computations performed at different values of the bare coupling, and this is needed for extrapolating results into the continuum. Thus, we calculate a new quantity, w0, for setting the scale in lattice QCD, which is based on the Wilson flow like the scale t0 (M. Luscher, JHEP 08 (2010) 071). It is cheap and straightforward to implement and compute. In particular, it does not involve the delicate fitting of correlation functions at asymptotic times. It typically can be determined on the few per-mil level. We compute its continuum extrapolated value in 2 + 1-flavor QCD for physical and non-physical pion and kaon masses, to allow for mass-independent scale setting even away from the physical mass point. We demonstrate its robustness by computing it with two very different actions (one of them with staggered, the other with Wilson fermions) and by showing that the results agree for physical quark masses in the continuum limit.

Ab initio calculation of the neutron-proton mass difference

Weighing the neutron against the proton Elementary science textbooks often state that protons have the same mass as neutrons. This is not far from the truth—the neutron is about 0.14% heavier (and less stable) than the proton. The precise value is important, because if the mass difference were bigger or smaller, the world as we know it would likely not exist. Borsanyi et al. calculated the mass difference to high precision using a sophisticated approach that took into account the various forces that exist within a nucleon. The calculations reveal how finely tuned our universe needs to be. Science, this issue p. 1452 Lattice quantum chromodynamics and quantum electrodynamics are used to calculate mass differences between pairs of hadrons. The existence and stability of atoms rely on the fact that neutrons are more massive than protons. The measured mass difference is only 0.14% of the average of the two masses. A slightly smaller or larger value would have led to a dramatically different universe. Here, we show that this difference results from the competition between electromagnetic and mass isospin breaking effects. We performed lattice quantum-chromodynamics and quantum-electrodynamics computations with four nondegenerate Wilson fermion flavors and computed the neutron-proton mass-splitting with an accuracy of 300 kilo–electron volts, which is greater than 0 by 5 standard deviations. We also determine the splittings in the Σ, Ξ, D, and Ξcc isospin multiplets, exceeding in some cases the precision of experimental measurements.

QCD equation of state at nonzero chemical potential: continuum results with physical quark masses at order μ 2

A bstractWe determine the equation of state of QCD for nonzero chemical potentials via a Taylor expansion of the pressure. The results are obtained for Nf = 2 + 1 flavors of quarks with physical masses, on various lattice spacings. We present results for the pressure, interaction measure, energy density, entropy density, and the speed of sound for small chemical potentials. At low temperatures we compare our results with the Hadron Resonance Gas model. We also express our observables along trajectories of constant entropy over particle number. A simple parameterization is given (the Matlab/Octave script parameterization.m, submitted to the arXiv along with the paper), which can be used to reconstruct the observables as functions of T and μ, or as functions of T and S/N.

Lattice QCD at the physical point: light quark masses

Abstract Ordinary matter is described by six fundamental parameters: three couplings (gravitational, electromagnetic and strong) and three masses: the electronʼs ( m e ) and those of the up ( m u ) and down ( m d ) quarks. An additional mass enters through quantum fluctuations: the strange quark mass ( m s ). The three couplings and m e are known with an accuracy of better than a few per mil. Despite their importance, m u , m d (their average m u d ) and m s are far less accurately known. Here we determine them with a precision below 2% by performing ab initio lattice quantum chromodynamics (QCD) calculations, in which all systematics are controlled. We use pion and quark masses down to (and even below) their physical values, lattice sizes of up to 6 fm, and five lattice spacings to extrapolate to continuum spacetime. All necessary renormalizations are performed nonperturbatively.

Sigma term and strangeness content of octet baryons

By using lattice QCD computations we determine the sigma terms and strangeness content of all octet baryons by means of an application of the Hellmann-Feynman theorem. In addition to polynomial and rational expressions for the quark-mass dependence of octet members, we use SU(3) covariant baryon chiral perturbation theory to perform the extrapolation to the physical up and down quark masses. Our Nf = 2 + 1 lattice ensembles include pion masses

Freeze-out parameters: lattice meets experiment

We present our results for ratios of higher order fluctuations of electric charge as functions of the temperature. These results are obtained in a system of 2+1 quark flavors at physical quark masses and continuum extrapolated. We compare them to preliminary data on higher order moments of the net electric charge distribution from the STAR collaboration. This allows us to determine the freeze-out temperature and chemical potential from first principles. We also show continuum-extrapolated results for ratios of higher order fluctuations of baryon number. These will allow us to test the consistency of the approach, by comparing them to the corresponding experimental data (once they become available) and thus, extracting the freeze-out parameters in an independent way.

Precision computation of the kaon bag parameter

Abstract Indirect CP violation in K → π π decays plays a central role in constraining the flavor structure of the Standard Model (SM) and in the search for new physics. For many years the leading uncertainty in the SM prediction of this phenomenon was the one associated with the nonperturbative strong interaction dynamics in this process. Here we present a fully controlled lattice QCD calculation of these effects, which are described by the neutral kaon mixing parameter B K . We use a two step HEX smeared clover-improved Wilson action, with four lattice spacings from a ≈ 0.054 fm to a ≈ 0.093 fm and pion masses at and even below the physical value. Nonperturbative renormalization is performed in the RI-MOM scheme, where we find that operator mixing induced by chiral symmetry breaking is very small. Using fully nonperturbative continuum running, we obtain our main result B K RI ( 3.5 GeV ) = 0.531 ( 6 ) stat ( 2 ) sys . A perturbative 2-loop conversion yields B K MS ¯ - NDR ( 2 GeV ) = 0.564 ( 6 ) stat ( 3 ) sys ( 6 ) PT and B ˆ K = 0.773 ( 8 ) stat ( 3 ) sys ( 8 ) PT , which is in good agreement with current results from fits to experimental data.