Maria Paola Lombardo GGI Firenze March 2014

Transcription

1 Dense matter from lattice QCD (?) Maria Paola Lombardo GGI Firenze March 2014

2 The phases of strong interactions Andronic et al 2010 Tojo et al 2011

3 ..and the experimental programs First proposal: Cabibbo and Parisi, 1975 LHC RHIC NICA /FAIR / RHIC II US NSAC Long RangePlan (adapted)

4 (Dense) matter on the lattice QCD, and the lattice Few body physics, nuclear potential and the nuclear equation of state EoS and condensates from first principles in QCDlike models I: fermionic models EoS and condensates from first principles in QCD-like models II: two color QCD Overview of methods and results in QCD The critical point of QCD

5 Fundamental theory of strong interactions QCD, AND THE LATTICE

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7 QCD

8 ..on the lattice

9 Designing a simulation Choice of the discretization Input parameters

10 Dimensional transmutation 1/T a L..and check of the continuumlimit

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12 Option 1:

13 Option 2

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15 FEW BODY RESULTS

16 Wuppertal- Budapest 2013

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19 H dibaryon

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21 Nuclear force from Lattice QCD Phenomenological NN forces have fitting parameters. For hyperon nucleon and nucleon nucleon a factor 3 more However in QCD all interactions are controlled only by the scale parameter and the physical quark masses NN potentials are determined from the equal time Nambu-Bethe-Salpeter wave function

22 Wave function, Schroedinger equation and potential

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25 Fits to phenomenological form

26 Overview of the results

27 Three nucleon forces

28 The short distance repulsion among baryons Aoki, Balog, Weisz 2013 The wave function at short distance Diverges at r = 0 if n1 > 0 Vanishes at r = 0 if n1 < 0 Implies for the short distance potential Attractive if n1 > 0 Repulsive if n1 < 0 In some cases a mismatch was observed between the sign of the potential and these estimates, indicating that the asymptotic behaviour has not been reached yet on the lattice

29 September 2013

30 EoS from lattice nuclear forces Input : NN potentials from zero strangeness sector in flavor SU(3) QCD

31 Ground state energies

32 Ground state energies

33 Mass-radius relation

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35 I. Dense Matter from First Principles QCD-like models and the strong coupling expansion : condensates, equation of state, search for exotic phases II. QCD, and its critical point

36 Observables and EoS

37 GN 2+1, NJL 3+1 FERMIONIC MODELS

38 2+1 Gross-Neveu model Phase diagram in ordinary conditions

39 GN model on the continuum and on the lattice

40 Mean field solution vs lattice results Set S=0 and obtain the critical line Note for T=0 m independence till mc = S0

41 The Phase Diagram of 2+1 GN model : mean field and exact Hands, Kocic, Kogut 1993

42 Condensate and EOS in NJL 3+1 Hands and Walters 2003

43 Diquark condensation

44 From QCD to four fermion models Lattice QCD action with staggered fermions

45 From QCD to four fermion models Cfr Lectures by Massimo Mannarelli Gauge part disappears in the infinite coupling limit

46 From QCD to four fermion models Gauge part disappears in the infinite coupling limit Meson operators

47 Sketch of the calculations (T,m=0) 1) Bosonization Z 2) Mean field Z

48 Results from the strong coupling expansion for finite T and m

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50 TWO COLOR QCD

51 QCD with two colors Pauli Gursey Symmetry: quarks and antiquarks transform according to equivalent reps.

52 Spectrum and condensates Quark propagator SU(2) matrix Mesons and Baryons are degenerate at T,m=0 The degeneracy is lifted at T,m 0 Hands, Kogut, MpL, Morrison 1999

53 Rotation of condensates

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56 Phases of two color QCD? Hands, Skullerud, Kim 2013

57 QCD

58 The sign problem Complex for real m Possibilities for a real determinant: Four fermion models Imaginary m Wilson fermions Two color, isospin density

59 Features of the phase of the determinant MpL, Splittorff, Verbaarschot 2010

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65 All methods work at high T

66 SEARCHING FOR THE QCD CRITICAL POINT

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68 Back to the complex m plane

69 The radius of convergence (?)

70 Has the critical point of QCD being found?? Nt=4 Nt = 6 Nt=8

71 Lower bound on the radius of convergence And freezout point Data from RBC Collaboration Courtesy E. Laermann and C. Schmidt. C. Ratti and MpL QM09 Freezout point

72 Use imaginary m to validate radius of convergence Falcone, Meyer, Laermann, MpL I m a g i n a r y Check radius of convergence here! c e m i c a l p o t e n t a l Candidate Critical point Observed radius Of convergence T ay l o r e x p a n s i o n

73 Alternative estimate of the radius of convergence Laermann, MpL, Meyer 2013

74 Falcone, Laermann, Meyer, MpL A proposal for a better control on the QCD critical point

75 LHC RHIC NICA /FAIR / RHIC II US NSAC Long RangePlan (adapted)