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Chiral and deconfinement transition in finite temperature QCD P é ter Petreczky

Chiral and deconfinement transition in finite temperature QCD P é ter Petreczky. Introduction : Deconfiniment in high T QCD Chiral and deconfinement transition at T>0 : lattice results and controversy Lattice results vs. HRG

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Chiral and deconfinement transition in finite temperature QCD P é ter Petreczky

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  1. Chiral and deconfinement transition in finite temperature QCD Péter Petreczky • Introduction : • Deconfiniment in high T QCD • Chiral and deconfinement transition at T>0: lattice results and controversy • Lattice results vs. HRG • Lattice calculations with HIGHLY IMPROVED STAGGERED QUARK (HISQ) • Chiral aspect of the QCD transition and universal scaling • Deconfinement transition in T>0 QCD, fluctuations of conserved charges and HRG • Summary DM 2010, Stellenbosch Institute for Advanced Studies, April 7, 2010

  2. Deconfinement at high T The quark number susceptibilities for T>300MeV agree with resummed petrurbative predictions A. Rebhan, arXiv:hep-ph/0301130 Blaizot et al, PLB 523 (01) 143 free gas of quarks and gluons = 18 quark+18 anti-quarks +16 gluons =52 light d.o.f P.P., NPA 830 (2009) 11 good agreement between lattice and resummed perturbative calculations of the entropy Rebhan, arXiv:hep-ph/0301130 Blaizot et al, PRL 83 (99) 2906 pion gas = 3 light d.o.f.

  3. Deconfinement and chiral transition stout : Budapest-Wuppertal Group, Aoki et al., PLB 643 (06) 46; arXiv:0903.4155: scale fK, Nτ=4,6,8,10,12, ms/27 p4, asqtad : HotQCD, Bazavov et al, arXiv:0903.4379: scale r0 , Nτ=8 ms/10 scale setting cutoff effects Renormalized chiral condensate Renormalized Polyakov loop stout action is optimized to reduce the effect of flavor symmetry breaking

  4. Deconfinement and chiral transition stout : Budapest-Wuppertal Group, Aoki et al., PLB 643 (06) 46; arXiv:0903.4155: scale fK, Nτ=4,6,8,10,12, ms/27 p4, asqtad : HotQCD, Bazavov et al, arXiv:0903.4379: scale r0 , Nτ=8 ms/10 Renormalized chiral condensate Strangeness fluctuations: agreement between HotQCD results and Budapest-Wuppertal results at high T

  5. Lattice results for “physical” quark masses Lattice calculations at the physical quark mass and Nτ=8, Cheng et al, arXiv:0911.2215 • Thermodynamics quantities are quark mass independent for T>200MeV • The quark mass effect is also small at low temperature and is similar to cutoff effects • Lattice results are significantly below the Hadron Resonance Gas

  6. Improved staggered calculations at finite temperature high-T region T>200MeV low-T region T<200 MeV cutoff effects are different in : a<0.125fm a>0.125fm hadronic degrees of freedom quark degrees of freedom improvement of the flavor symmetry is important quark dispersion relation → fat links for #flavors < 4 rooting trick p4, asqtad stout

  7. The Highly Improved Staggered Quark (HISQ) Action two levels of gauge field smearing with re-unitarization Follana et al, PRD75 (07) 054502 projection onto U(3) improves flavor symmetry Hasenfratz, arXiv:hep-lat/0211007 asqtad 3-link (Naik) term to improve the quark dispersion relation + asqtad smearing

  8. Calculations with HISQ action msphysical (at 1%), ml=0.05ms ,324, 323x8 and 243x6 lattices, Ls=(3.2-5.0)fm The lattice spacing is set through the calculation of static potential • The potential shows little cutoff dependence and similar to that calculated with asqtad and p4 • Significant improvement in hadron spectrum compared to asqtad calculations => • smaller cutoff effects at small T, independent consistency check on the scale setting

  9. Mass splitting of pseudo-scalar mesons Only one out of 16 PS mesons has zero mass in the chiral limit, the quadratic mass splitting is the measure of flavor symmetry breaking asqtad HISQ PS meson splittings in HISQ calculations are reduced by factor ~ 2.5 compared to asqtad at the same lattice spacing and are even smaller than for stout action => discretizations effects for Nτ=8HISQ calculations are similar to those in Nτ=12 asqtad calculations

  10. Deconfinement and chiral transition with HISQ action Renormalized Polyakov loop Renormalized chiral condensate • Good agreement between stout and HISQ calculation at low T and between lattice and HRG • At high T HISQ results agree well with p4 results • Transition region in the stout calculations is shifted to higher T when r0 is used instead of fK

  11. Chiral condensate susceptibility RG invariant, but vanishes in the chiral limit significant shift of the peak compared to Nτ=8 calculations Tc≈170MeV on Nτ=8both for stout and HISQ if r0 is used to set the scale (continuum extrapolation is needed)

  12. Chiral condensate susceptibility RG invariant, but vanishes in the chiral limit significant shift of the peak compared to Nτ=8 calculations the peak position shifts to smaller T if fK is used to set the scale

  13. Chiral transition and universal scaling For sufficiently heavy strange quark and small light quark masses the chiral transition is governed by universal O(4) ( O(2) )scaling : Nτ=4 Ejiri et al, PRD 80 (09) 094505

  14. QCD thermodynamics at non-zero chemical potential Taylor expansion : hadronic quark Taylor expansion coefficients give the fluctuations and correlations of conserved charges, e.g.

  15. Strangeness fluctuations and HRG • enhancement of strangeness fluctuations compared to the calculations performed on Nτ=8 • good agreement between HISQ and stout calculations All the lattice results are below the HRG. Hadron masses on the lattice are large than physical due to a2 discretization effects this needs to be taken into account, Huovinen, P.P, arXiv:0912.2541

  16. Strangeness fluctuations and HRG • enhancement of strangeness fluctuations compared to the calculations performed on Nτ=8 • good agreement between HISQ and stout calculations All the lattice results are below the HRG. Hadron masses on the lattice are large than physical due to a2 discretization effects this needs to be taken into account, Huovinen, P.P, arXiv:0912.2541 good agreement between lattice and modified HRG(Huovinen, P.P, arXiv:0912.2541)

  17. Deconfinement : correlations of conserved charges Cheng et al., arXiv:0811.1006, P.P, Hegde, Velytsky, PoS LAT2009 159 correlations of conserved charges at low temperatures can be qualitatively understood in terms of hadron resonance gas model hadrons can carry different quark flavors => different quark flavors are correlated in the hadronic phase quarks are un-bound at high temperatures => no correlations between different quark flavors

  18. Baryon fluctuations and baryon strangeness correlations • Agreement between HRG with modified spectrum and lattice obtained with p4 and asqtad • on Nτ=8, Huovinen, P.P, arXiv:0912.2541 • For baryon-strangeness correlations HISQ results are close to the physical HRG result, • at T>250 MeV these correlations are very close to the ideal gas value

  19. Trace anomaly in HRG and on the lattice Agreement between HRG with modified spectrum and lattice obtained with p4 and asqtad on Nτ=8, Huovinen, P.P, arXiv:0912.2541 HISQ results are close to the s95p-v1 parameterization used in hydro models

  20. Chiral and deconfinement transition again Light quark number fluctuations are sensitive to singular part of the free energy • Light quark number susceptibility shows rapid change in the vicinity of the chiral transition • Inflection points of Polyakov loop and strangeness susceptibility maybe higher than the • chiral transition temperature because they are dominated by the regular part

  21. Conclusions • Lattice discretization effects are large in the staggered fermion formulation at low T these discretization effects can be largely reduced using HISQ action (will be used by HotQCD collaboration in the future) • Chriral transition temperature Tc < 170 MeV, more work is needed to define deconfinement transition temperature • O(N) scaling is confirmed by lattice for the 1st time, the physical point is in the scaling region • At low T thermodynamics can be understood in terms of HRG The deconfinement transition can understood as transition from HRG to quark gluon gas it is gradual and analagous to ionized gas – plasma transition • To study the interplay between chiral and deconfinement aspect of the transition and precisely determine the transition temperature one has to consider thermodynamic quantities that are sensitive to the singular part of the free energy density, e.g. light quark number susceptibility • Many thanks to my collaborators in RBC-BI and HotQCD collaborations, especially to Bazavov, C. DeTar, M. Cheng, P. Hegde, U. Heller,F. Karsch, E. Laermann, C. Miao, S. Mukherjee, C. Schmidt, W. Soeldner, D. Toussaint

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