arXiv subjects

E. Laermann

Publications and source records attributed to E. Laermann.

At least 37 records · Page 2Linked to original sources

arXiv2010

The phase boundary for the chiral transition in (2+1)-flavor QCD at small values of the chemical potential

We determine the chiral phase transition line in (2+1)-flavor QCD for small values of the light quark chemical potential. We show that for small values of the chemical potential the curvature of the phase transition line can be deduced from an analysis of scaling properties of the chiral condensate and its susceptibilities. To do so we extend earlier studies of the magnetic equation of state in (2+1)-flavor QCD to finer lattice spacings, aT=1/8. We use these universal scaling properties of the chiral order parameter to extract the curvature of the transition line at two values of the cut-off, aT=1/4 and 1/8. We find that cut-off effects are small for the curvature parameter and determine the transition line in the chiral limit to leading order in the light quark chemical potential. We obtain Tc(μ_q)/Tc(0) = 1 - 0.059(2)(4) (μ_q/T)^2 +O(μ_q^4).

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arXiv2010

Equation of State for physical quark masses

We calculate the QCD equation of state for temperatures corresponding to the transition region with physical mass values for two degenerate light quark flavors and a strange quark using an improved staggered fermion action (p4-action) on lattices with temporal extent N_tau=8. We compare our results with previous calculations performed at twice larger values of the light quark masses as well as with results obtained from a resonance gas model calculation. We also discuss the deconfining and chiral aspects of the QCD transition in terms of renormalized Polyakov loop, strangeness fluctuations and subtracted chiral condensate. We show that compared to the calculations performed at twice larger value of the light quark mass the transition region shifts by about 5 MeV toward smaller temperatures

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arXiv2009

On the magnetic equation of state in (2+1)-flavor QCD

A first study of critical behavior in the vicinity of the chiral phase transition of (2+1)-flavor QCD is presented. We analyze the quark mass and volume dependence of the chiral condensate and chiral susceptibilities in QCD with two degenerate light quark masses and a strange quark. The strange quark mass (m_s) is chosen close to its physical value; the two degenerate light quark masses (m_l) are varied in a wide range 1/80 \le m_l/m_s \le 2/5, where the smallest light quark mass value corresponds to a pseudo-scalar Goldstone mass of about 75 MeV. All calculations are performed with staggered fermions on lattices with temporal extent Nt=4. We show that numerical results are consistent with O(N) scaling in the chiral limit. We find that in the region of physical light quark mass values, m_l/m_s \simeq 1/20, the temperature and quark mass dependence of the chiral condensate is already dominated by universal properties of QCD that are encoded in the scaling function for the chiral order parameter, the magnetic equation of state. We also provide evidence for the influence of thermal fluctuations of Goldstone modes on the chiral condensate at finite temperature. At temperatures below, but close to the chiral phase transition at vanishing quark mass, this leads to a characteristic dependence of the light quark chiral condensate on the square root of the light quark mass.

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arXiv2009

Baryon Number, Strangeness and Electric Charge Fluctuations in QCD at High Temperature

We analyze baryon number, strangeness and electric charge fluctuations as well as their correlations in QCD at high temperature. We present results obtained from lattice calculations performed with an improved staggered fermion action (p4-action) at two values of the lattice cut-off with almost physical up and down quark masses and a physical value for the strange quark mass. We compare these results, with an ideal quark gas at high temperature and a hadron resonance gas model at low temperature. We find that fluctuations and correlations are well described by the former already for temperatures about 1.5 times the transition temperature. At low temperature qualitative features of the lattice results are quite well described by a hadron resonance gas model. Higher order cumulants, which become increasingly sensitive to the light pions, however show deviations from a resonance gas in the vicinity of the transition temperature.

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arXiv2009

Equation of state and QCD transition at finite temperature

We calculate the equation of state in 2+1 flavor QCD at finite temperature with physical strange quark mass and almost physical light quark masses using lattices with temporal extent Nt=8. Calculations have been performed with two different improved staggered fermion actions, the asqtad and p4 actions. Overall, we find good agreement between results obtained with these two O(a^2) improved staggered fermion discretization schemes. A comparison with earlier calculations on coarser lattices is performed to quantify systematic errors in current studies of the equation of state. We also present results for observables that are sensitive to deconfining and chiral aspects of the QCD transition on Nt=6 and 8 lattices. We find that deconfinement and chiral symmetry restoration happen in the same narrow temperature interval. In an Appendix we present a simple parametrization of the equation of state that can easily be used in hydrodynamic model calculations. In this parametrization we also incorporated an estimate of current uncertainties in the lattice calculations which arise from cutoff and quark mass effects. We estimate these systematic effects to be about 10 MeV

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arXiv2008

The Spatial String Tension and Dimensional Reduction in QCD

We calculate the spatial string tension in (2+1) flavor QCD with physical strange quark mass and almost physical light quark masses using lattices with temporal extent N_tau=4,6 and 8. We compare our results on the spatial string tension with predictions of dimensionally reduced QCD. This suggests that also in the presence of light dynamical quarks dimensional reduction works well down to temperatures 1.5T_c.

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arXiv2008

Lattice cut-off effects and their reduction in studies of QCD thermodynamics at non-zero temperature and chemical potential

We clarify the relation between the improvement of dispersion relations in the fermion sector of lattice regularized QCD and the improvement of bulk thermodynamic observables. We show that in the infinite temperature limit the cut-off dependence in dispersion relations can be eliminated up to O(a^n) corrections, if the quark propagator is chosen to be rotationally invariant up to this order. In bulk thermodynamic observables this eliminates cut-off effects up to the same order at vanishing as well as non-vanishing chemical potential. We furthermore show, that in the infinite temperature, ideal gas limit the dependence of finite cut-off corrections on the chemical potential is given by Bernoulli polynomials which are universal as they do not depend on a particular discretization scheme. We explicitly calculate leading and next-to-leading order cut-off corrections for some staggered and Wilson fermion type actions and compare these with exact evaluations of the free fermion partition functions. This also includes the chirally invariant overlap and domain wall fermion formulations.

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arXiv2008

The QCD Equation of State with almost Physical Quark Masses

We present results on the equation of state in QCD with two light quark flavors and a heavier strange quark. Calculations with improved staggered fermions have been performed on lattices with temporal extent Nt =4 and 6 on a line of constant physics with almost physical quark mass values; the pion mass is about 220 MeV, and the strange quark mass is adjusted to its physical value. High statistics results on large lattices are obtained for bulk thermodynamic observables, i.e. pressure, energy and entropy density, at vanishing quark chemical potential for a wide range of temperatures, 140 MeV < T < 800 MeV. We present a detailed discussion of finite cut-off effects which become particularly significant for temperatures larger than about twice the transition temperature. At these high temperatures we also performed calculations of the trace anomaly on lattices with temporal extent Nt=8. Furthermore, we have performed an extensive analysis of zero temperature observables including the light and strange quark condensates and the static quark potential at zero temperature. These are used to set the temperature scale for thermodynamic observables and to calculate renormalized observables that are sensitive to deconfinement and chiral symmetry restoration and become order parameters in the infinite and zero quark mass limits, respectively.

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arXiv2006

Study of the finite temperature transition in 3-flavor QCD using the R and RHMC algorithms

We study the finite temperature transition in QCD with three flavors of equal masses using the R and RHMC algorithm on lattices with temporal extent N_τ=4 and 6. For the transition temperature in the continuum limit we find r_0 T_c=0.429(8) for the light pseudo-scalar mass corresponding to the end point of the 1st order transition region. When comparing the results obtained with the R and RHMC algorithms for p4fat3 action we see no significant step-size errors down to a lightest pseudo-scalar mass of m_{ps} r_0=0.4.

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arXiv2006

The transition temperature in QCD

We present a detailed calculation of the transition temperature in QCD with two light and one heavier (strange) quark mass on lattices with temporal extent N_t =4 and 6. Calculations with improved staggered fermions have been performed for various light to strange quark mass ratios in the range, 0.05 <= m_l/m_s <= 0.5, and with a strange quark mass fixed close to its physical value. From a combined extrapolation to the chiral (m_l -> 0) and continuum (aT = 1/N_t -> 0) limits we find for the transition temperature at the physical point T_c r_0 = 0.457(7) where the scale is set by the Sommer-scale parameter r_0 defined as the distance in the static quark potential at which the slope takes on the value, (dV_qq(r)/dr)_r=r_0 = 1.65/r_0^2. Using the currently best known value for r_0 this translates to a transition temperature T_c = 192(7)(4)MeV. The transition temperature in the chiral limit is about 3% smaller. We discuss current ambiguities in the determination of T_c in physical units and also comment on the universal scaling behavior of thermodynamic quantities in the chiral limit.

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arXiv2006

Meson correlation functions at high temperatures

We present preliminary results for the correlation- and spectral functions of different meson channels on the lattice. The main focus lies on gaining control over cut-off as well as on the finite-volume effects. Extrapolations of screening masses above the deconfining temperature are guided by the result of the free ($T=\infty$) case on the lattice and in the continuum. We study the quenched non-perturbatively improved Wilson-clover fermion as well as the hypercube fermion action which might show less cut-off effects.

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arXiv2005

The isentropic equation of state of 2-flavor QCD

Using Taylor expansions of the pressure obtained previously in studies of 2-flavor QCD at non-zero chemical potential we calculate expansion coefficients for the energy and entropy densities up to ${\cal O}(μ_q^6)$ in the quark chemical potential. We use these series in $μ_q/T$ to determine lines of constant entropy per baryon number ($S/N_B$) that characterize the expansion of dense matter created in heavy ion collisions. In the high temperature regime these lines are found to be well approximated by lines of constant $μ_q/T$. In the low temperature phase, however, the quark chemical potential is found to increase with decreasing temperature. This is in accordance with resonance gas model calculations. Along the lines of constant $S/N_B$ we calculate the energy density and pressure. Within the accuracy of our present analysis we find that the ratio $p/ε$ for $T>T_0$ as well as the softest point of the equation of state, $(p/ε)_{min}\simeq 0.075$, show no significant dependence on $S/N_B$.

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arXiv2005

Electromagnetic vertex function of the pion at T > 0

The matrix element of the electromagnetic current between pion states is calculated in quenched lattice QCD at a temperature of $T = 0.93 T_c$. The nonperturbatively improved Sheikholeslami-Wohlert action is used together with the corresponding ${\cal O}(a)$ improved vector current. The electromagnetic vertex function is extracted for pion masses down to $360 {\rm MeV}$ and momentum transfers $Q^2 \le 2.7 {\rm GeV}^2$.

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arXiv2005

The QCD equation of state for two flavours at non-zero chemical potential

We present results of a simulation of 2 flavour QCD on a $16^3\times4$ lattice using p4-improved staggered fermions with bare quark mass $m/T=0.4$. Derivatives of the thermodynamic grand canonical partition function $Z(V,T,μ_u,μ_d)$ with respect to chemical potentials $μ_{u,d}$ for different quark flavours are calculated up to sixth order, enabling estimates of the pressure and the quark number density as well as the chiral condensate and various susceptibilities as functions of $μ_{u,d}$ via Taylor series expansion. Results are compared to high temperature perturbation theory as well as a hadron resonance gas model. We also analyze baryon as well as isospin fluctuations and discuss the relation to the chiral critical point in the QCD phase diagram. We moreover discuss the dependence of the heavy quark free energy on the chemical potential.

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arXiv2005

Heavy quark free energies and screening at finite temperature and density

We study the free energies of heavy quarks calculated from Polyakov loop correlation functions in full 2-flavour QCD using the p4-improved staggered fermion action. A small but finite Baryon number density is included via Taylor expansion of the fermion determinant in the Baryo-chemical potential mu. For temperatures above Tc we extract Debye screening masses from the large distance behaviour of the free energies and compare their mu-dependence to perturbative results.

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arXiv2005

Screening of heavy quark free energies at finite temperature and non-zero baryon chemical potential

We analyze the dependence of heavy quark free energies on the baryon chemical potential (mu_b) in 2-flavour QCD using improved (p4) staggered fermions with a bare quark mass of m/T = 0.4. By performing a 6th order Taylor expansion in the chemical potential which circumvents the sign problem. The Taylor expansion coefficients of colour singlet and colour averaged free energies are calculated and from this the expansion coefficients for the corresponding screening masses are determined. We find that for small mu_b the free energies of a static quark anti-quark pair decrease in a medium with a net excess of quarks and that screening is well described by a screening mass which increases with increasing mu_b. The mu_b-dependent corrections to the screening masses are well described by perturbation theory for T > 2 T_c. In particular, we find for all temperatures above T_c that the expansion coefficients for singlet and colour averaged screening masses differ by a factor 2.

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arXiv2005

Heavy quark potential and quarkonia dissociation rates

Quenched lattice data for the quark-antiquark interaction (in terms of heavy quark free energies) in the color singlet channel at finite temperatures are fitted and used within the nonrelativistic Schroedinger equation formalism to obtain binding energies and scattering phase shifts for the lowest eigenstates in the charmonium and bottomonium systems in a hot gluon plasma. The partial dissociation rate due to the Bhanot-Peskin process is calculated using different assumptions for the gluon distribution function, including free massless gluons, massive gluons, and massive damped gluons. It is demonstrated that a temperature dependent gluon mass has an essential influence on the heavy quarkonia dissociation, but that this process alone is insufficient to describe the heavy quarkonia dissociation rates.

hep-ph↗

arXiv2005

QCD at non-zero temperature and density from the lattice

The study of systems as diverse as the cores of neutron stars and heavy-ion collision experiments requires the understanding of the phase structure of QCD at non-zero temperature, T, and chemical potential, mu_q. We review some of the difficulties of performing lattice simulations of QCD with non-zero mu_q, and outline the re-weighting method used to overcome this problem. This method is used to determine the critical endpoint of QCD in the (mu_q,T) plane. We study the pressure and quark number susceptibility at small mu_q.

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