1. Toward an Improved Determination of Tc with 2+1 Flavors of Asqtad Fermions C. DeTar University of Utah The HotQCD Collaboration July 30, 2007

2. HotQCD Collaboration T. Battacharya (LANL) M. Cheng (Columbia) N. Christ (Columbia) C. DeTar (Utah) S. Gottlieb (Indiana) R. Gupta (LANL) U. Heller (APS) K. Huebner (BNL) C. Jung (BNL) F. Karsch (BNL/Bielefeld) E. Laermann (Bielefeld) L. Levkova (Utah) T. Luu (LLNL) R. Mawhinney (Columbia) P. Petreczky (BNL) D. Renfrew (Columbia) C. Schmidt (BNL) R. Soltz (LLNL) W. Soeldner (BNL) R. Sugar (UCSB) D. Toussaint (Arizona) P. Vranas (LLNL)

3. Physics Goals Accurate determination of Tc –Energy density ~ T^4 sensitive to errors in T Equation of State (zero and nonzero density) –Needed for modeling heavy ion collisions. Spectral Functions Spatial and temporal correlators versus T Transport coefficients of the quark gluon plasma

4. Data Sample Algorithm: –Asqtad 2+1 flavor RHMC Ensembles –Line of constant physics: m_l/m_s = 0.1 –32^3 x 8 ~12000 trajectories each –13 beta values along line of constant physics –32^4 couple hundred trajectories for now I will be focusing on Asqtad results for Nt = 8, m_l/m_s = 0.1 throughout this talk.

5. How to Measure T c “Chiral” phenomena T chiral –Peaks in chiral susceptibilities –Singular at critical point (no ambiguity there) “Deconfinement” phenomena T deconf –Inflection points in ReP, energy density vs T –May be linked at chiral critical point How large are the differences in these measures at the physical quark mass? –Aoki et al (Wuppertal – Budapest) Phys Lett B 643:46 (2006)

6. Sources of Error Algorithm R vs RHMC Finite volume Peak or inflection point determination Statistics (sample size) Extrapolation to physical quark mass and continuum Scale error

7. Asqtad R vs RHMC Differences are very small

8. Chiral susceptibilities 

9. Connected Chiral Susceptibility Finite size effect increases values at low T

10. Disconnected chiral susceptibility Larger volume is important

11. Singlet chiral susceptibility Finite size effect tends to decrease Tc slightly 16^3: 184(2)MeV 32^3: 186(2) Statistical error for this fit model only! Systematic errors to be determined.

12. Renormalized singlet susceptibility (Wuppertal-Budapest) Small difference in peak position

13. Quark number susceptibilities

14. Strange quark number susceptibility It is more difficult to locate an inflection point than a peak.

15. Polyakov Loop Unrenormalized

16. Summary of Tc Determination (Nt=8, 0.1ms) All methods give answers in the range 180- 195 MeV “Chiral” measures tend to give a bit lower Tc than “deconfining” measures

17. Error budget beyond Nt = 8, 0.1ms Extrapolation to physical masses and continuum depends on extrapolation model: Estimated error: a few MeV from previous Asqtad studies Scale error in determination of lattice spacing (theorists can use r1 Tc) Estimated error: 4 MeV

18. Error budget conclusions R vs RHMC: insignificant Finite size: couple MeV Peak or inflection point determination: couple to several MeV Statistics (to be determined) Extrapolation (to be determined) Scale (few MeV)

19. To be Done Complete Nt=8 simulations Finish analysis of all the variables Combine Nt=4,6,8 calculations Extract transition temperature at which bulk quantities show largest fluctuations Is there a difference in temperature for chiral and deconfinement phenomena at the physical quark mass?