QCD equation of state at non-zero chemical potential (original) (raw)
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Journal of High Energy Physics, 2012
We determine the equation of state of QCD for nonzero chemical potentials via a Taylor expansion of the pressure. The results are obtained for = 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 and , or as functions of and / .
The QCD equation of state for two flavours at non-zero chemical potential
Nuclear Physics A, 2006
We present results of a simulation of 2 flavour QCD on a 163 x 4 lattice using p4improved staggered fermions with bare quark mass m/T = 0.4. Derivatives of the thermodynamic grand canonical partition function Z(V, T , ,uu, P d) with respect to chemical potentials p 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 c h i d condensate and various susceptibilities as functions of p!,,d via Taylor series expansion. Results are compared to high temperature perturbattion theory as well as a hadron resonance gas model. We also a*nalyze baryon as well a,s isospin fluctuations and discuss the relation to the chiral critica.1 point in the QCD phase diagram. We moreover discuss the dependence of the heavy quark free energy on the chemical potential.
QCD at small nonzero quark chemical potentials
Physical Review D, 2001
We study the effects of small chemical potentials associated with the three light quark flavors in QCD. We use a low-energy effective field theory that solely relies on the symmetries of the QCD partition function. We find three different phases: a normal phase, a pion superfluid phase and a kaon superfluid phase. The two superfluid phases are separated by a first order phase transition, whereas the normal phase and either of the superfluid phases are separated by a second order phase transition. We compute the quark-antiquark condensate, the pion condensate and the kaon condensate in each phase, as well as the isospin density, the strangeness density, and the mass spectrum.
QCD thermodynamics with nonzero chemical potential at N_{t}=6 and effects from heavy quarks
Physical Review D, 2010
We extend our work on QCD thermodynamics with 2+1 quark flavors at nonzero chemical potential to finer lattices with N t = 6. We study the equation of state and other thermodynamic quantities, such as quark number densities and susceptibilities, and compare them with our previous results at N t = 4. We also calculate the effects of the addition of the charm and bottom quarks on the equation of state at zero and nonzero chemical potential. These effects are important for cosmological studies of the early Universe.
Results for the equation of state in 2+1 flavor QCD at zero net baryon density using the Highly Improved Staggered Quark (HISQ) action by the HotQCD collaboration are presented. The strange quark mass was tuned to its physical value and the light (up/down) quark masses fixed to m l = 0.05m s corresponding to a pion mass of 160 MeV in the continuum limit. Lattices with temporal extent N t = 6, 8, 10 and 12 were used. Since the cutoff effects for N t > 6 were observed to be small, reliable continuum extrapolations of the lattice data for the phenomenologically interesting temperatures range 130MeV < T < 400MeV could be performed. We discuss statistical and systematic errors and compare our results with other published works.
QCD thermodynamics with nonzero chemical potential at N{sub t}=6 and effects from heavy quarks
Phys Rev D, 2010
We extend our work on QCD thermodynamics with 2+1 quark flavors at nonzero chemical potential to finer lattices with N t = 6. We study the equation of state and other thermodynamic quantities, such as quark number densities and susceptibilities, and compare them with our previous results at N t = 4. We also calculate the effects of the addition of the charm and bottom quarks on the equation of state at zero and nonzero chemical potential. These effects are important for cosmological studies of the early Universe.
QCD thermodynamics with 2+1 flavors at nonzero chemical potential
Physical Review D, 2008
We present results for the QCD equation of state, quark densities and susceptibilities at nonzero chemical potential, using 2+1 flavor asqtad ensembles with Nt=4N_t=4Nt=4. The ensembles lie on a trajectory of constant physics for which mudapprox0.1msm_{ud}\approx0.1m_smudapprox0.1ms. The calculation is performed using the Taylor expansion method with terms up to sixth order in mu/T\mu/Tmu/T.
Surprises for QCD at Nonzero Chemical Potential
Continuous Advances in QCD 2006, 2007
In this lecture we compare different QCD-like partition functions with bosonic quarks and fermionic quarks at nonzero chemical potential. Although it is not a surprise that the ground state properties of a fermionic quantum system and a bosonic quantum system are completely different, the behavior of partition functions with bosonic quarks does not follow our naive expectation. Among other surprises, we find that the partition function with one bosonic quark only exists at nonzero chemical potential if a conjugate bosonic quark and a conjugate fermionic quark are added to the partition function.
Thermodynamics of two flavor QCD to sixth order in quark chemical potential
2005
We present results of a simulation of two flavor QCD on a 16 3 ×4 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 flavors 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 q = (µ u + µ d)/2 via Taylor series expansion. Furthermore, we analyze baryon as well as isospin fluctuations and discuss the relation between the radius of convergence of the Taylor series and the chiral critical point in the QCD phase diagram. We argue that bulk thermodynamic observables do not, at present, provide direct evidence for the existence of a chiral critical point in the QCD phase diagram. Results are compared to high temperature perturbation theory as well as a hadron resonance gas model.
QCD equation of state with almost physical quark masses
Physical Review D, 2008
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 Nτ = 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 Nτ = 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.