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 transcript:

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

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

22/06/2010MpL xQCD20103

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

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

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

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

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

22/06/20109MpL xQCD2010

22/06/201010MpL xQCD2010

The pseudocritical line 22/06/201011MpL xQCD2010

The pseudocritical line 22/06/201012MpL xQCD2010

22/06/2010MpL xQCD Simulations and Results

22/06/201014MpL xQCD2010

Thermodynamics and Taylor expansion 22/06/201015MpL xQCD2010

22/06/2010MpL xQCD201016

22/06/201017MpL xQCD2010

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

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

Chiral condensate 22/06/201020MpL xQCD2010

The critical line 22/06/201021MpL xQCD2010

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

Quark Density 22/06/201023MpL xQCD2010

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)

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

22/06/201026MpL xQCD2010

22/06/2010MpL xQCD 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

22/06/2010MpL xQCD Outlook

22/06/201029MpL xQCD2010

22/06/201030MpL xQCD2010

22/06/201031MpL xQCD2010

22/06/201032MpL xQCD2010

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

S. Lattice /06/201034MpL xQCD2010 S. Gupta, Lattice 2010

22/06/2010MpL xQCD Taylor expansion around 

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!