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

The QCD equation of state for two flavor QCD at non-zero chemical potential. Shinji Ejiri (University of Tokyo) Collaborators: C. Allton, S. Hands (Swansea) , M. D öring, O.Kaczmarek, F.Karsch, E.Laermann ( Bielefeld), K.Redlich (Bielefeld & Wroclaw).

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

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  1. The QCD equation of state for two flavor QCD at non-zero chemical potential Shinji Ejiri (University of Tokyo) Collaborators: C. Allton, S. Hands (Swansea), M. Döring, O.Kaczmarek, F.Karsch, E.Laermann (Bielefeld), K.Redlich (Bielefeld & Wroclaw) (Phys. Rev. D71, 054508 (2005) +a) Quark Matter 2005, August 4-9, Budapest

  2. Numerical Simulations of QCD at finite Baryon Density • Boltzmann weight is complex for non-zero m. • Monte-Carlo simulations: Configurations are generated with the probability of the Boltzmann weight. • Monte-Carlo method is not applicable directly. • Reweighting method Sign problem 1, Perform simulations at m=0. for large m 2, Modify the weight for non-zero m.

  3. Studies at low density • Taylor expansion at m=0. • Calculations of Taylor expansion coefficients: free from the sign problem. • Interesting regime for heavy-ion collisions is low density. (mq/T~0.1 for RHIC, mq/T~0.5 for SPS) • Calculation of thermodynamic quantities. • The derivatives of lnZ: basic information in lattice simulations. Quark number density: Quark number susceptibility: Higher order terms: natural extension. Chiral condensate:

  4. QGP T hadron color super-conductor? m Equation of State via Taylor Expansion Equation of state at low density • ; quark-gluon gas is expected. Compare to perturbation theory • Near ; singularity at non-zero m (critical endpoint). Prediction from the sigma model • ; comparison to the models of free hadron resonance gas.

  5. Simulations Pressure: We perform simulations for =2 at ma=0.1 (mp/mr0.70 at Tc) and investigate T dependence of Taylor expansion coefficients. Moreover, Taylor expansion coefficients of chiral condensate and static quark-antiquark free energy are calculated. • Symanzik improved gauge action and p4-improved staggered fermion action • Lattice size: Quark number susceptibility: Isospin susceptibility:

  6. Derivatives of pressure and susceptibilities • Difference between and is small at m=0. • Perturbation theory: The difference is • Large spike for , the spike is milder for iso-vector. • at • Consistent with the perturbative prediction in .

  7. Difference of pressure for m>0 from m=0 Chemical potential effect is small. cf. pSB/T4~4 at m=0. RHIC :only ~1% for p. The effect from O(m6) term is small.

  8. Quark number susceptibility and Isospin susceptibility • Pronounced peak for around Critical endpoint in the (T,m)? • No peak for Consistent with the prediction from the sigma model.

  9. Chiral susceptibility • Peak height increases as increases. Consistent with the prediction from the sigma model. (disconnected part only)

  10. Comparison to hadron resonance gas model Hadron resonance gas prediction Hadron resonance gas • At , consistent with hadron resonance gas model. • At , approaches the value of a free quark-gluon gas. Free QG gas

  11. Hadron resonance gas model for Isospin susceptibility and chiral condensate • At ,consistent with hadron resonance gas model. Hadron resonance gas Hadron resonance gas Free QG gas

  12. Debye screening mass • QQ free energy from Polyakov loop correlation Singlet free energy (Coulomb gauge) Averaged free energy where : Polyakov loop • Assumption at T>Tc Color-electric screening mass: O.Kaczmarek and F.Zantow, Phys.Rev.D71 (2005) 114510 perturbative prediction (T. Toimela, Phys.Lett.B124(1983)407)

  13. Taylor expansion coefficients of screening mass perturbative prediction Consistent with perturbative prediction

  14. Summary • Derivatives of pressure with respect to mq up to 6th order are computed. • The hadron resonance gas model explains the behavior of pressure and susceptibilities very well at . • Approximation of free hadron gas is good in the wide range. • Quark number density fluctuations: A pronounced peak appears for . • Iso-spin fluctuations: No peak for . • Chiral susceptibility: peak height becomes larger as mq increases. This suggests the critical endpoint in plane? • Debye screening mass at non-zero mq is consistent with the perturbative result for . • To find the critical endpoint, further studies for higher order terms and small quark mass are required.

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