1. QCD Thermodynamics: Taylor expansion and imaginary chemical potential Rossella Falcone, Edwin Laermann, Maria Paola Lombardo Extreme QCD 2010 21-23 June 2010 At the Physikzentrum Bad Honnef Rossella Falcone, Talk at Lattice 2010 Work in progress

2. 22/06/2010MpL xQCD20102 Picture: NSAC long range plan

3. 22/06/2010MpL xQCD20103

4. Two complementary approaches to the QCD phase diagram Imaginary chemical potential Taylor expansion 22/06/20104MpL xQCD2010

5. Two complementary approaches to the QCD phase diagram Imaginary chemical potential: main problem, control over analytic continuation 22/06/20105MpL xQCD2010

6. Two complementary approaches to the QCD phase diagram Taylor expansion: main problem, control of the convergence 22/06/20106MpL xQCD2010 Works Inside circle

7. Combine Taylor expansion and imaginary chemical potential : Slope of the (pseudo)critical line Precision thermodynamics Control of the convergence of the  series How do(es) the critical point(s) affect the convergence of the series (R. Gavai, M. Stephanov, M. Wagner talks ) Physics around the kinetic/chemical freezout 22/06/20107MpL xQCD2010

8. Combine Taylor expansion and imaginary chemical potential : Slope of the (pseudo)critical line Precision thermodynamics Control of the convergence of the  series How do(es) the critical point(s) affect the convergence of the series (R. Gavai, M. Stephanov, M. Wagner talks ) Physics around the kinetic/chemical freezout 22/06/20108MpL xQCD2010

9. 22/06/20109MpL xQCD2010

10. 22/06/201010MpL xQCD2010

11. The pseudocritical line 22/06/201011MpL xQCD2010

12. The pseudocritical line 22/06/201012MpL xQCD2010

13. 22/06/2010MpL xQCD201013 Simulations and Results

14. 22/06/201014MpL xQCD2010

15. Thermodynamics and Taylor expansion 22/06/201015MpL xQCD2010

16. 22/06/2010MpL xQCD201016

17. 22/06/201017MpL xQCD2010

18. Phase of the Polyakov loop 22/06/201018MpL xQCD2010

19. Susceptibility of the Polyakov loop 22/06/201019MpL xQCD2010

20. Chiral condensate 22/06/201020MpL xQCD2010

21. The critical line 22/06/201021MpL xQCD2010

22. The critical line, ctd’ 22/06/201022MpL xQCD2010

23. Quark Density 22/06/201023MpL xQCD2010

24. 22/06/201024MpL xQCD2010 Singular behaviour at the End point of the RW transition Nf=4 (D,Elia, di Renzo, Lombardo (2007)) Nf=2 (D’Elia, Sanfilippo(2009)) Nf=3 (de Forcrand, Philipsen (2009)

25. 22/06/201025MpL xQCD2010 Quark density and Taylor expansion

26. 22/06/201026MpL xQCD2010

27. 22/06/2010MpL xQCD201027 Summary: (Preliminary) Results for improved staggered quarks with physical quark masses for - the slope of the critical line for staggered fermions - precision thermodynamics above Tc Combined imaginary chemical potential and Taylor expansion  control over radius of convergence Outlook: Analysis of the freezout region Control over estimates of the endpoint

28. 22/06/2010MpL xQCD201028 Outlook

29. 22/06/201029MpL xQCD2010

30. 22/06/201030MpL xQCD2010

31. 22/06/201031MpL xQCD2010

32. 22/06/201032MpL xQCD2010

33. Singularities limit the radius of convergence This can be computed from the Taylor expansion and observed at purely imaginary  22/06/201033MpL xQCD2010

34. S. Gupta @ Lattice2010 22/06/201034MpL xQCD2010 S. Gupta, Lattice 2010

35. 22/06/2010MpL xQCD201035 Taylor expansion around 

36. Use imaginary  to validate radius of convergence I m a g i n a r y c e m i c a l p o t e n t a l T a y l o r e x p a n s i o n 22/06/201036MpL xQCD2010 Observed radius Of convergence CandiCan Check radius of convergence here!