Christian Schmidt | Universität Bielefeld (original) (raw)

Papers by Christian Schmidt

Research paper thumbnail of The strange degrees of freedom in QCD at high temperature

Proceedings of 31st International Symposium on Lattice Field Theory LATTICE 2013 — PoS(LATTICE 2013), 2014

We discuss recent results on fluctuations of conserved charges, and their approach to the hadron ... more We discuss recent results on fluctuations of conserved charges, and their approach to the hadron resonance gas at temperatures below the chiral crossover (T c) as well as to a gas of free quarks at very high temperatures. We will focus on the strange degrees of freedom and verify that they are consistent with those of an uncorrelated gas of hadrons for temperatures of T 160 MeV and that they can be described by a quasi particle model at best for T 2T c. To extract this information we use all cumulants of net baryon number and net strangeness fluctuations and their correlations up to the fourth order. In particular we propose observables that serve as indicator for the validity of the hadronic degrees of freedom and show that the partial pressures from different strangeness sectors agree separately with HRG model predicions.

Research paper thumbnail of Fluctuations and correlations of net baryon number, electric charge, and strangeness: A comparison of lattice QCD results with the hadron resonance gas model

Research paper thumbnail of Conserved charge fluctuations at vanishing net-baryon density from Lattice QCD

EPJ Web of Conferences, 2022

We present here continuum extrapolated results for all 2nd order cumulants using the most resent ... more We present here continuum extrapolated results for all 2nd order cumulants using the most resent results obtained by the HotQCD collaboration in (2+1)-flavor QCD. We constrain the applicability of various HRG models by presenting a detailed comparison of our results based on different sets of hadron spectra as well as with virial expansion based model calculations. A comparison with our lattice QCD results for 2nd order cumulants with models that parametrize repulsive interactions among baryons and anti-baryons in a hadron resonance gas through a single excluded volume parameter (EVHRG) is also shown.

Research paper thumbnail of Conjugate gradient solvers on Intel Xeon Phi and NVIDIA GPUs

ArXiv, 2014

Lattice Quantum Chromodynamics simulations typically spend most of the runtime in inversions of t... more Lattice Quantum Chromodynamics simulations typically spend most of the runtime in inversions of the Fermion Matrix. This part is therefore frequently optimized for various HPC architectures. Here we compare the performance of the Intel Xeon Phi to current Kepler-based NVIDIA Tesla GPUs running a conjugate gradient solver. By exposing more parallelism to the accelerator through inverting multiple vectors at the same time, we obtain a performance greater than 300 GFlop/s on both architectures. This more than doubles the performance of the inversions. We also give a short overview of the Knights Corner architecture, discuss some details of the implementation and the effort required to obtain the achieved performance.

Research paper thumbnail of Chiral and deconfinement aspects of the QCD transition

Physical Review D, 2012

We present results on the chiral and deconfinement properties of the QCD transition at finite tem... more We present results on the chiral and deconfinement properties of the QCD transition at finite temperature. Calculations are performed with 2 + 1 flavors of quarks using the p4, asqtad and HISQ/tree actions. Lattices with temporal extent Nτ = 6, 8 and 12 are used to understand and control discretization errors and to reliably extrapolate estimates obtained at finite lattice spacings to the continuum limit. The chiral transition temperature is defined in terms of the phase transition in a theory with two massless flavors and analyzed using O(N) scaling fits to the chiral condensate and susceptibility. We find consistent estimates from the HISQ/tree and asqtad actions and our main result is Tc = 154 ± 9 MeV.

Research paper thumbnail of Universal Scaling Properties of QCD Close to the Chiral Limit

Acta Physica Polonica B Proceedings Supplement, 2021

We present a lattice QCD based determination of the chiral phase transition temperature in QCD wi... more We present a lattice QCD based determination of the chiral phase transition temperature in QCD with two massless (up and down) and one strange quark having its physical mass. We propose and calculate two novel estimators for the chiral transition temperature for several values of the light quark masses, corresponding to Goldstone pion masses in the range of 58 MeV m π 163 MeV. The chiral phase transition temperature is determined by extrapolating to vanishing pion mass using universal scaling relations. After thermodynamic, continuum and chiral extrapolations we find the chiral phase transition temperature T 0 c = 132 +3 −6 MeV. We also show some preliminary calculations that use the conventional estimator for the pseudo-critical temperature and compare with the new estimators for T 0 c. Furthermore, we show results for the ratio of the chiral order parameter and its susceptibility and argue that this ratio can be used to differentiate between O(N) and Z 2 universality classes in a non-parametric manner.

Research paper thumbnail of 1 On the universal critical behavior in 3-flavor QCD

We analyze the universal critical behavior at the chiral critical point in QCD with three degener... more We analyze the universal critical behavior at the chiral critical point in QCD with three degenerate quark masses. We confirm that this critical point lies in the universality class of the three dimensional Ising model. The symmetry of the Ising model, which is Z(2), is not directly realized in the QCD Hamiltonian. After making an ansatz for the magnetization-and energy-like operators as linear admixtures of the chiral condensate and the gluonic action, we determine several non-universal mixing and normalization constants. These parameters determine an unambiguous mapping of the critical behavior in QCD to that of the 3d-Ising model. We verify its validity by showing that the thus obtained orderparameter scales in accordance with the magnetic equation of state of the 3d-Ising model.

Research paper thumbnail of oS(LATTICE 2007)175 Bulk thermodynamics and charge fluctuations at non-vanishing baryon density

We present results on bulk thermodynamic quantities as well as net baryon number, strangeness and... more We present results on bulk thermodynamic quantities as well as net baryon number, strangeness and electric charge fluctuations in QCD at non-zero density and temperature obtained from lattice calculations with almost physical quark masses for two values of the lattice cut-off aT = 1/4 and 1/6. We show that with our improved p4fa3-action the cut-off effects are under control when using lattices with a temporal extent of 6 or larger and that the contribution to the equation of state, which is due to a finite chemical potential is small for μq/T < 1. Moreover, at vanishing chemical potential, i.e. under conditions almost realized at RHIC and the LHC, quartic fluctuations of net baryon number and strangeness are large in a narrow temperature interval characterizing the transition region from the low to high temperature phase. At non-zero baryon number density, strangeness fluctuations are enhanced and correlated to fluctuations of the net baryon number. If strangeness is furthermore ...

Research paper thumbnail of Bulk Thermodynamics and charge fluctuations at non-vanishing baryon density

Proceedings of The XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007), 2008

We present results on bulk thermodynamic quantities as well as net baryon number, strangeness and... more We present results on bulk thermodynamic quantities as well as net baryon number, strangeness and electric charge fluctuations in QCD at non-zero density and temperature obtained from lattice calculations with almost physical quark masses for two values of the lattice cutoff aT = 1/4 and 1/6. We show that with our improved p4fa3-action the cutoff effects are under control when using lattices with a temporal extent of 6 or larger and that the contribution to the equation of state, which is due to a finite chemical potential is small for μ q /T < 1. Moreover, at vanishing chemical potential, i.e. under conditions almost realized at RHIC and the LHC, quartic fluctuations of net baryon number and strangeness are large in a narrow temperature interval characterizing the transition region from the low to high temperature phase. At non-zero baryon number density, strangeness fluctuations are enhanced and correlated to fluctuations of the net baryon number. If strangeness is furthermore forced to vanish, as it may be the case in systems created in heavy ion collisions, strangeness fluctuations are significantly smaller than baryon number fluctuations.

Research paper thumbnail of Universal critical behavior in three flavor QCD

Proceedings of XXIX International Symposium on Lattice Field Theory — PoS(Lattice 2011), 2012

We analyze the universal critical behavior at the chiral critical point in QCD with three degener... more We analyze the universal critical behavior at the chiral critical point in QCD with three degenerate quark masses. We confirm that this critical point lies in the universality class of the three dimensional Ising model. The symmetry of the Ising model, which is Z(2), is not directly realized in the QCD Hamiltonian. After making an ansatz for the magnetization-and energy-like operators as linear admixtures of the chiral condensate and the gluonic action, we determine several non-universal mixing and normalization constants. These parameters determine an unambiguous mapping of the critical behavior in QCD to that of the 3d-Ising model. We verify its validity by showing that the thus obtained orderparameter scales in accordance with the magnetic equation of state of the 3d-Ising model.

Research paper thumbnail of On the universal O(N) scaling behavior of (2+1)-flavor QCD

Proceedings of The XXVIII International Symposium on Lattice Field Theory — PoS(Lattice 2010), 2011

We show that for small values of the chemical potential the curvature of the phase transition lin... more 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. We make use of a recent analysis of the magnetic equation of state in (2+1)flavor QCD where a connection between the QCD parameters and the universal scaling fields could be established. The remaining dependence of the reduced temperature on the chemical potential can be fixed by an analysis of a mixed susceptibility, obtained from a derivative with respect to quark mass and chemical potential. We extract this dependence which describes the curvature of the phase transition line, at two values of the cutoff , aT = 1/4 and 1/8. We find that cutoff 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 T c (µ B)/T c (0) = 1 − 0.00656(66)(µ B /T) 2 + O(µ 4 B).

Research paper thumbnail of Quark Number Susceptibilities with Domain-Wall Fermions

Proceedings of The XXVI International Symposium on Lattice Field Theory — PoS(LATTICE 2008), 2009

We present results from calculations of different quark number and hadronic susceptibilities on 2... more We present results from calculations of different quark number and hadronic susceptibilities on 2+1-flavor dynamical domain wall ensembles. We find that the iso-spin and electric charge susceptibilities are especially well suited to determine the transition temperature, as these quantities show only small statistical errors. Moreover, the transition values of the coupling obtained from iso-spin and electrical charge susceptibilities are in good agreement with the one obtained from the chiral condensate.

Research paper thumbnail of QCD Thermodynamics with an almost realistic quark mass spectrum

AIP Conference Proceedings, 2006

We will report on the status of a new large scale calculation of thermodynamic quantities in QCD ... more We will report on the status of a new large scale calculation of thermodynamic quantities in QCD with light up and down quarks corresponding to an almost physical light quark mass value and a heavier strange quark mass. These calculations are currently being performed on the QCDOC Teraflops computers at BNL. We will present new lattice calculations of the transition temperature and various susceptibilities reflecting properties of the chiral transition. All these quantities are of immediate interest for heavy ion phenomenology.

Research paper thumbnail of Universal O(N) scaling and the chiral critical line in (2+1)-flavor QCD with small chemical potentials

We show that for small values of the chemical potential the curvature of the phase transition lin... more 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. We make use of a recent analysis of the magnetic equation of state in (2+1)flavor QCD where a connection between the QCD parameters and the universal scaling fields could be established. The remaining dependence of the reduced temperature on the chemical potential can be fixed by an analysis of a mixed susceptibility, obtained from a derivative with respect to quark mass and chemical potential. We extract this dependence which describes the curvature of the phase transition line, at two values of the cutoff , aT = 1/4 and 1/8. We find that cutoff 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 T c (µ B)/T c (0) = 1 − 0.00656(66)(µ B /T) 2 + O(µ 4 B).

Research paper thumbnail of The QCD equation of state from improved staggered fermions

We calculate the equation of state in 2+1 flavor QCD at finite temperature with physical strange ... more 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 Ntau=8N_{\tau}=8Ntau=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(a2)O(a^2)O(a2) 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 Ntau=6N_\tau=6Ntau=6 and 8 lattices. We find that deconfinement and chiral symmetry restoration happen in the same narrow temperature interval.

Research paper thumbnail of Study of QCD Thermodynamics at Finite Density by Taylor Expansion

Progress of Theoretical Physics Supplement, 2004

We discuss the phase structure and the equation of state for QCD at non-zero temperature and dens... more We discuss the phase structure and the equation of state for QCD at non-zero temperature and density. Derivatives of ln Z with respect to quark chemical potential µq up to fourth order are calculated for 2-flavor QCD, enabling estimates of the pressure, quark number density and associated susceptibilities as functions of µq via a Taylor series expansion. Also, the phase transition line for 2 and 3-flavor QCD and the critical endpoint in the (T, µq) plane are investigated in the low density regime.

Research paper thumbnail of Net-Baryon Number Fluctuations in (2+1)-Flavor QCD

Progress of Theoretical Physics Supplement, 2010

We present a lattice study of net-baryon number fluctuations in (2+1)-flavor QCD. The results are... more We present a lattice study of net-baryon number fluctuations in (2+1)-flavor QCD. The results are based on a Taylor expansion of the pressure with respect to the baryon chemical potential. We calculate higher moments of the net-baryon number fluctuations and compare with the corresponding resonance gas results. We find that for temperature below 0.9Tc the fluctuations seem to agree with the hadron resonance gas predictions. Close to Tc, higher moments are increasingly more sensitive to the critical behavior of the QCD phase transition. Furthermore, we estimate the radius of convergence of the Taylor series as well as the curvature of the transition line in the temperature chemical potential plane.

Research paper thumbnail of Lattice QCD at finite density

Nuclear Physics A, 1987

We discuss the behavior of the zero temperature limit of lattice field theories with finite chemi... more We discuss the behavior of the zero temperature limit of lattice field theories with finite chemical potential. The finite chemical potential lattice formalism is applied to the free fermion theory and the Gross-Neveu model where results can be compared with analytic solutions. Problems occuring in the application of this formalism in numerical simulations of lattice QCD are discussed.

Research paper thumbnail of The density of states method at non-zero chemical potential

Journal of High Energy Physics, 2007

We study the QCD phase diagram by first principle lattice calculations at so far unreached high d... more We study the QCD phase diagram by first principle lattice calculations at so far unreached high densities. For this purpose we employ the density of states method. Unimproved staggered fermions, which describe four quark flavors in the continuum are used in this analysis. Though the method is quite expensive, small lattices show an indication for a triple-point connecting three different phases on the phase diagram.

Research paper thumbnail of The QCD phase diagram at finite density

We study the density of states method to explore the phase diagram of the chiral transition on th... more We study the density of states method to explore the phase diagram of the chiral transition on the tempeature and quark chemical potential plane. Four quark flavours are used in the analysis. Though the method is quite expensive small lattices show an indication for a triple-point connecting three different phases on the phase diagram.

Research paper thumbnail of The strange degrees of freedom in QCD at high temperature

Proceedings of 31st International Symposium on Lattice Field Theory LATTICE 2013 — PoS(LATTICE 2013), 2014

We discuss recent results on fluctuations of conserved charges, and their approach to the hadron ... more We discuss recent results on fluctuations of conserved charges, and their approach to the hadron resonance gas at temperatures below the chiral crossover (T c) as well as to a gas of free quarks at very high temperatures. We will focus on the strange degrees of freedom and verify that they are consistent with those of an uncorrelated gas of hadrons for temperatures of T 160 MeV and that they can be described by a quasi particle model at best for T 2T c. To extract this information we use all cumulants of net baryon number and net strangeness fluctuations and their correlations up to the fourth order. In particular we propose observables that serve as indicator for the validity of the hadronic degrees of freedom and show that the partial pressures from different strangeness sectors agree separately with HRG model predicions.

Research paper thumbnail of Fluctuations and correlations of net baryon number, electric charge, and strangeness: A comparison of lattice QCD results with the hadron resonance gas model

Research paper thumbnail of Conserved charge fluctuations at vanishing net-baryon density from Lattice QCD

EPJ Web of Conferences, 2022

We present here continuum extrapolated results for all 2nd order cumulants using the most resent ... more We present here continuum extrapolated results for all 2nd order cumulants using the most resent results obtained by the HotQCD collaboration in (2+1)-flavor QCD. We constrain the applicability of various HRG models by presenting a detailed comparison of our results based on different sets of hadron spectra as well as with virial expansion based model calculations. A comparison with our lattice QCD results for 2nd order cumulants with models that parametrize repulsive interactions among baryons and anti-baryons in a hadron resonance gas through a single excluded volume parameter (EVHRG) is also shown.

Research paper thumbnail of Conjugate gradient solvers on Intel Xeon Phi and NVIDIA GPUs

ArXiv, 2014

Lattice Quantum Chromodynamics simulations typically spend most of the runtime in inversions of t... more Lattice Quantum Chromodynamics simulations typically spend most of the runtime in inversions of the Fermion Matrix. This part is therefore frequently optimized for various HPC architectures. Here we compare the performance of the Intel Xeon Phi to current Kepler-based NVIDIA Tesla GPUs running a conjugate gradient solver. By exposing more parallelism to the accelerator through inverting multiple vectors at the same time, we obtain a performance greater than 300 GFlop/s on both architectures. This more than doubles the performance of the inversions. We also give a short overview of the Knights Corner architecture, discuss some details of the implementation and the effort required to obtain the achieved performance.

Research paper thumbnail of Chiral and deconfinement aspects of the QCD transition

Physical Review D, 2012

We present results on the chiral and deconfinement properties of the QCD transition at finite tem... more We present results on the chiral and deconfinement properties of the QCD transition at finite temperature. Calculations are performed with 2 + 1 flavors of quarks using the p4, asqtad and HISQ/tree actions. Lattices with temporal extent Nτ = 6, 8 and 12 are used to understand and control discretization errors and to reliably extrapolate estimates obtained at finite lattice spacings to the continuum limit. The chiral transition temperature is defined in terms of the phase transition in a theory with two massless flavors and analyzed using O(N) scaling fits to the chiral condensate and susceptibility. We find consistent estimates from the HISQ/tree and asqtad actions and our main result is Tc = 154 ± 9 MeV.

Research paper thumbnail of Universal Scaling Properties of QCD Close to the Chiral Limit

Acta Physica Polonica B Proceedings Supplement, 2021

We present a lattice QCD based determination of the chiral phase transition temperature in QCD wi... more We present a lattice QCD based determination of the chiral phase transition temperature in QCD with two massless (up and down) and one strange quark having its physical mass. We propose and calculate two novel estimators for the chiral transition temperature for several values of the light quark masses, corresponding to Goldstone pion masses in the range of 58 MeV m π 163 MeV. The chiral phase transition temperature is determined by extrapolating to vanishing pion mass using universal scaling relations. After thermodynamic, continuum and chiral extrapolations we find the chiral phase transition temperature T 0 c = 132 +3 −6 MeV. We also show some preliminary calculations that use the conventional estimator for the pseudo-critical temperature and compare with the new estimators for T 0 c. Furthermore, we show results for the ratio of the chiral order parameter and its susceptibility and argue that this ratio can be used to differentiate between O(N) and Z 2 universality classes in a non-parametric manner.

Research paper thumbnail of 1 On the universal critical behavior in 3-flavor QCD

We analyze the universal critical behavior at the chiral critical point in QCD with three degener... more We analyze the universal critical behavior at the chiral critical point in QCD with three degenerate quark masses. We confirm that this critical point lies in the universality class of the three dimensional Ising model. The symmetry of the Ising model, which is Z(2), is not directly realized in the QCD Hamiltonian. After making an ansatz for the magnetization-and energy-like operators as linear admixtures of the chiral condensate and the gluonic action, we determine several non-universal mixing and normalization constants. These parameters determine an unambiguous mapping of the critical behavior in QCD to that of the 3d-Ising model. We verify its validity by showing that the thus obtained orderparameter scales in accordance with the magnetic equation of state of the 3d-Ising model.

Research paper thumbnail of oS(LATTICE 2007)175 Bulk thermodynamics and charge fluctuations at non-vanishing baryon density

We present results on bulk thermodynamic quantities as well as net baryon number, strangeness and... more We present results on bulk thermodynamic quantities as well as net baryon number, strangeness and electric charge fluctuations in QCD at non-zero density and temperature obtained from lattice calculations with almost physical quark masses for two values of the lattice cut-off aT = 1/4 and 1/6. We show that with our improved p4fa3-action the cut-off effects are under control when using lattices with a temporal extent of 6 or larger and that the contribution to the equation of state, which is due to a finite chemical potential is small for μq/T < 1. Moreover, at vanishing chemical potential, i.e. under conditions almost realized at RHIC and the LHC, quartic fluctuations of net baryon number and strangeness are large in a narrow temperature interval characterizing the transition region from the low to high temperature phase. At non-zero baryon number density, strangeness fluctuations are enhanced and correlated to fluctuations of the net baryon number. If strangeness is furthermore ...

Research paper thumbnail of Bulk Thermodynamics and charge fluctuations at non-vanishing baryon density

Proceedings of The XXV International Symposium on Lattice Field Theory — PoS(LATTICE 2007), 2008

We present results on bulk thermodynamic quantities as well as net baryon number, strangeness and... more We present results on bulk thermodynamic quantities as well as net baryon number, strangeness and electric charge fluctuations in QCD at non-zero density and temperature obtained from lattice calculations with almost physical quark masses for two values of the lattice cutoff aT = 1/4 and 1/6. We show that with our improved p4fa3-action the cutoff effects are under control when using lattices with a temporal extent of 6 or larger and that the contribution to the equation of state, which is due to a finite chemical potential is small for μ q /T < 1. Moreover, at vanishing chemical potential, i.e. under conditions almost realized at RHIC and the LHC, quartic fluctuations of net baryon number and strangeness are large in a narrow temperature interval characterizing the transition region from the low to high temperature phase. At non-zero baryon number density, strangeness fluctuations are enhanced and correlated to fluctuations of the net baryon number. If strangeness is furthermore forced to vanish, as it may be the case in systems created in heavy ion collisions, strangeness fluctuations are significantly smaller than baryon number fluctuations.

Research paper thumbnail of Universal critical behavior in three flavor QCD

Proceedings of XXIX International Symposium on Lattice Field Theory — PoS(Lattice 2011), 2012

We analyze the universal critical behavior at the chiral critical point in QCD with three degener... more We analyze the universal critical behavior at the chiral critical point in QCD with three degenerate quark masses. We confirm that this critical point lies in the universality class of the three dimensional Ising model. The symmetry of the Ising model, which is Z(2), is not directly realized in the QCD Hamiltonian. After making an ansatz for the magnetization-and energy-like operators as linear admixtures of the chiral condensate and the gluonic action, we determine several non-universal mixing and normalization constants. These parameters determine an unambiguous mapping of the critical behavior in QCD to that of the 3d-Ising model. We verify its validity by showing that the thus obtained orderparameter scales in accordance with the magnetic equation of state of the 3d-Ising model.

Research paper thumbnail of On the universal O(N) scaling behavior of (2+1)-flavor QCD

Proceedings of The XXVIII International Symposium on Lattice Field Theory — PoS(Lattice 2010), 2011

We show that for small values of the chemical potential the curvature of the phase transition lin... more 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. We make use of a recent analysis of the magnetic equation of state in (2+1)flavor QCD where a connection between the QCD parameters and the universal scaling fields could be established. The remaining dependence of the reduced temperature on the chemical potential can be fixed by an analysis of a mixed susceptibility, obtained from a derivative with respect to quark mass and chemical potential. We extract this dependence which describes the curvature of the phase transition line, at two values of the cutoff , aT = 1/4 and 1/8. We find that cutoff 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 T c (µ B)/T c (0) = 1 − 0.00656(66)(µ B /T) 2 + O(µ 4 B).

Research paper thumbnail of Quark Number Susceptibilities with Domain-Wall Fermions

Proceedings of The XXVI International Symposium on Lattice Field Theory — PoS(LATTICE 2008), 2009

We present results from calculations of different quark number and hadronic susceptibilities on 2... more We present results from calculations of different quark number and hadronic susceptibilities on 2+1-flavor dynamical domain wall ensembles. We find that the iso-spin and electric charge susceptibilities are especially well suited to determine the transition temperature, as these quantities show only small statistical errors. Moreover, the transition values of the coupling obtained from iso-spin and electrical charge susceptibilities are in good agreement with the one obtained from the chiral condensate.

Research paper thumbnail of QCD Thermodynamics with an almost realistic quark mass spectrum

AIP Conference Proceedings, 2006

We will report on the status of a new large scale calculation of thermodynamic quantities in QCD ... more We will report on the status of a new large scale calculation of thermodynamic quantities in QCD with light up and down quarks corresponding to an almost physical light quark mass value and a heavier strange quark mass. These calculations are currently being performed on the QCDOC Teraflops computers at BNL. We will present new lattice calculations of the transition temperature and various susceptibilities reflecting properties of the chiral transition. All these quantities are of immediate interest for heavy ion phenomenology.

Research paper thumbnail of Universal O(N) scaling and the chiral critical line in (2+1)-flavor QCD with small chemical potentials

We show that for small values of the chemical potential the curvature of the phase transition lin... more 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. We make use of a recent analysis of the magnetic equation of state in (2+1)flavor QCD where a connection between the QCD parameters and the universal scaling fields could be established. The remaining dependence of the reduced temperature on the chemical potential can be fixed by an analysis of a mixed susceptibility, obtained from a derivative with respect to quark mass and chemical potential. We extract this dependence which describes the curvature of the phase transition line, at two values of the cutoff , aT = 1/4 and 1/8. We find that cutoff 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 T c (µ B)/T c (0) = 1 − 0.00656(66)(µ B /T) 2 + O(µ 4 B).

Research paper thumbnail of The QCD equation of state from improved staggered fermions

We calculate the equation of state in 2+1 flavor QCD at finite temperature with physical strange ... more 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 Ntau=8N_{\tau}=8Ntau=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(a2)O(a^2)O(a2) 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 Ntau=6N_\tau=6Ntau=6 and 8 lattices. We find that deconfinement and chiral symmetry restoration happen in the same narrow temperature interval.

Research paper thumbnail of Study of QCD Thermodynamics at Finite Density by Taylor Expansion

Progress of Theoretical Physics Supplement, 2004

We discuss the phase structure and the equation of state for QCD at non-zero temperature and dens... more We discuss the phase structure and the equation of state for QCD at non-zero temperature and density. Derivatives of ln Z with respect to quark chemical potential µq up to fourth order are calculated for 2-flavor QCD, enabling estimates of the pressure, quark number density and associated susceptibilities as functions of µq via a Taylor series expansion. Also, the phase transition line for 2 and 3-flavor QCD and the critical endpoint in the (T, µq) plane are investigated in the low density regime.

Research paper thumbnail of Net-Baryon Number Fluctuations in (2+1)-Flavor QCD

Progress of Theoretical Physics Supplement, 2010

We present a lattice study of net-baryon number fluctuations in (2+1)-flavor QCD. The results are... more We present a lattice study of net-baryon number fluctuations in (2+1)-flavor QCD. The results are based on a Taylor expansion of the pressure with respect to the baryon chemical potential. We calculate higher moments of the net-baryon number fluctuations and compare with the corresponding resonance gas results. We find that for temperature below 0.9Tc the fluctuations seem to agree with the hadron resonance gas predictions. Close to Tc, higher moments are increasingly more sensitive to the critical behavior of the QCD phase transition. Furthermore, we estimate the radius of convergence of the Taylor series as well as the curvature of the transition line in the temperature chemical potential plane.

Research paper thumbnail of Lattice QCD at finite density

Nuclear Physics A, 1987

We discuss the behavior of the zero temperature limit of lattice field theories with finite chemi... more We discuss the behavior of the zero temperature limit of lattice field theories with finite chemical potential. The finite chemical potential lattice formalism is applied to the free fermion theory and the Gross-Neveu model where results can be compared with analytic solutions. Problems occuring in the application of this formalism in numerical simulations of lattice QCD are discussed.

Research paper thumbnail of The density of states method at non-zero chemical potential

Journal of High Energy Physics, 2007

We study the QCD phase diagram by first principle lattice calculations at so far unreached high d... more We study the QCD phase diagram by first principle lattice calculations at so far unreached high densities. For this purpose we employ the density of states method. Unimproved staggered fermions, which describe four quark flavors in the continuum are used in this analysis. Though the method is quite expensive, small lattices show an indication for a triple-point connecting three different phases on the phase diagram.

Research paper thumbnail of The QCD phase diagram at finite density

We study the density of states method to explore the phase diagram of the chiral transition on th... more We study the density of states method to explore the phase diagram of the chiral transition on the tempeature and quark chemical potential plane. Four quark flavours are used in the analysis. Though the method is quite expensive small lattices show an indication for a triple-point connecting three different phases on the phase diagram.