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QCD Thermodynamics: Taylor expansion and imaginary chemical potential Rossella Falcone, Edwin Laermann, Maria Paola Lombardo Extreme QCD 2010 21-23 June.

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Presentation on theme: "QCD Thermodynamics: Taylor expansion and imaginary chemical potential Rossella Falcone, Edwin Laermann, Maria Paola Lombardo Extreme QCD 2010 21-23 June."— Presentation transcript:

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!


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