Lattice QCD Results on Strangeness and Quasi-Quarks in Heavy-Ion Collisions

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1 Lattice QCD Results on Strangeness and Quasi-Quarks in Heavy-Ion Collisions Rajiv V. Gavai T. I. F. R., Mumbai, India In collaboration with Sourendu Gupta, TIFR, Mumbai, Phys. Rev. D73, (2006) Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 1

2 Lattice QCD Results on Strangeness and Quasi-Quarks in Heavy-Ion Collisions Rajiv V. Gavai T. I. F. R., Mumbai, India Introduction The Wróblewski Parameter Quasi-quarks Summary In collaboration with Sourendu Gupta, TIFR, Mumbai, Phys. Rev. D73, (2006) Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 1

3 Introduction Fluctuations in conserved charges, B, Q, as promising signals of QGP (Asakawa-Heinz-Müller, PRL 00, Jeon-Koch PRL 00). Quark Number Susceptibilities (QNS) measure these fluctuations. Lattice approach yields these directly from QCD. (Gottlieb et al, 86, 87,.., Gavai et al ) Ratios of the susceptibilities, C K/L χ K χl = σ2 K σ L 2 Phase: both theoretically and experimentally. are robust variables in high T Many aspects studied of QGP can be studied using these, e.g., the Wróblewski Parameter. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 2

4 Introduction Fluctuations in conserved charges, B, Q, as promising signals of QGP (Asakawa-Heinz-Müller, PRL 00, Jeon-Koch PRL 00). Quark Number Susceptibilities (QNS) measure these fluctuations. Lattice approach yields these directly from QCD. (Gottlieb et al, 86, 87,.., Gavai et al ) Ratios of the susceptibilities, C K/L χ K χl = σ2 K σ L 2 Phase: both theoretically and experimentally. are robust variables in high T Many aspects studied of QGP can be studied using these, e.g., the Wróblewski Parameter. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 2

5 Introduction Fluctuations in conserved charges, B, Q, as promising signals of QGP (Asakawa-Heinz-Müller, PRL 00, Jeon-Koch PRL 00). Quark Number Susceptibilities (QNS) measure these fluctuations. Lattice approach yields these directly from QCD. (Gottlieb et al, 86, 87,.., Gavai et al ) Ratios of the susceptibilities, C K/L χ K χl = σ2 K σ L 2 Phase: both theoretically and experimentally. are robust variables in high T Many aspects studied of QGP can be studied using these, e.g., the Wróblewski Parameter. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 2

6 Introduction Fluctuations in conserved charges, B, Q, as promising signals of QGP (Asakawa-Heinz-Müller, PRL 00, Jeon-Koch PRL 00). Quark Number Susceptibilities (QNS) measure these fluctuations. Lattice approach yields these directly from QCD. (Gottlieb et al, 86, 87,.., Gavai et al ) Ratios of the susceptibilities, C K/L χ K χl = σ2 K σ L 2 Phase: both theoretically and experimentally. are robust variables in high T Many aspects studied of QGP can be studied using these, e.g., the Wróblewski Parameter. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 2

7 Nature of QGP Excitations Outstanding question in spite of long history of several investigations: Equation of State : T 3 5T c agrees with weak coupling schemes. Quark Number Susceptibilities : Successful check on them. Screening Masses : T 2T c : Close to Fermi gas of quarks. We address this directly using C (KL)/L = KL K L L 2 L 2, i.e., using the off-diagonal susceptibility χ KL. Physically, create an excitation of quantum number K and ask what else (like L) does it carry. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 3

8 Nature of QGP Excitations Outstanding question in spite of long history of several investigations: Equation of State : T 3 5T c agrees with weak coupling schemes. Quark Number Susceptibilities : Successful check on them. Screening Masses : T 2T c : Close to Fermi gas of quarks. We address this directly using C (KL)/L = KL K L L 2 L 2, i.e., using the off-diagonal susceptibility χ KL. Physically, create an excitation of quantum number K and ask what else (like L) does it carry. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 3

9 Nature of QGP Excitations Outstanding question in spite of long history of several investigations: Equation of State : T 3 5T c agrees with weak coupling schemes. Quark Number Susceptibilities : Successful check on them. Screening Masses : T 2T c : Close to Fermi gas of quarks. We address this directly using C (KL)/L = KL K L L 2 L 2, i.e., using the off-diagonal susceptibility χ KL. Physically, create an excitation of quantum number K and ask what else (like L) does it carry. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 3

10 Quark Number Susceptibility Assuming three flavours, u, d, and s quarks, and denoting by µ f the corresponding chemical potentials, the QCD partition function is Z = DU exp( S G ) Q f=u,d,s Det M(m f,µ f ). (1) Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 4

11 Quark Number Susceptibility Assuming three flavours, u, d, and s quarks, and denoting by µ f the corresponding chemical potentials, the QCD partition function is Z = DU exp( S G ) Q f=u,d,s Det M(m f,µ f ). (1) Defining µ B = µ u + µ d + µ s and µ 3 = µ u µ d, baryon and isospin density/susceptibilities can be obtained as : (Gottlieb et al. 87, 96, 97, Gavai et al. 89) Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 4

12 Quark Number Susceptibility Assuming three flavours, u, d, and s quarks, and denoting by µ f the corresponding chemical potentials, the QCD partition function is Z = DU exp( S G ) Q f=u,d,s Det M(m f,µ f ). (1) Defining µ B = µ u + µ d + µ s and µ 3 = µ u µ d, baryon and isospin density/susceptibilities can be obtained as : (Gottlieb et al. 87, 96, 97, Gavai et al. 89) n i = T V ln Z µ i, χ ij = T V 2 ln Z µ i µ j, i, j = 0, 3, u, d, s Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 4

13 Similarly, Charge (Q), Hypercharge (Y ), Strangeness (S) susceptibilities can be defined. Higher order susceptibilities are defined by χ fg = T V n log Z µ f µ g = n P µ f µ g. (2) (3) Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 5

14 Similarly, Charge (Q), Hypercharge (Y ), Strangeness (S) susceptibilities can be defined. Higher order susceptibilities are defined by χ fg = T V n log Z µ f µ g = n P µ f µ g. (2) These are Taylor coefficients of the pressure P in its expansion in µ. All of these can be written as traces of products of M 1 and various derivatives of M; Evaluated using Gaussian Noise. (3) Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 5

15 Similarly, Charge (Q), Hypercharge (Y ), Strangeness (S) susceptibilities can be defined. Higher order susceptibilities are defined by χ fg = T V n log Z µ f µ g = n P µ f µ g. (2) These are Taylor coefficients of the pressure P in its expansion in µ. All of these can be written as traces of products of M 1 and various derivatives of M; Evaluated using Gaussian Noise. Finite Density Results by Taylor Expansion in µ (3) Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 5

16 Similarly, Charge (Q), Hypercharge (Y ), Strangeness (S) susceptibilities can be defined. Higher order susceptibilities are defined by χ fg = T V n log Z µ f µ g = n P µ f µ g. (2) These are Taylor coefficients of the pressure P in its expansion in µ. All of these can be written as traces of products of M 1 and various derivatives of M; Evaluated using Gaussian Noise. Finite Density Results by Taylor Expansion in µ Theoretical Checks : Resummed Perturbation expansions, Dimensional Reduction, Models of (s)qgp,.. (3) Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 5

17 Similarly, Charge (Q), Hypercharge (Y ), Strangeness (S) susceptibilities can be defined. Higher order susceptibilities are defined by χ fg = T V n log Z µ f µ g = n P µ f µ g. (2) These are Taylor coefficients of the pressure P in its expansion in µ. All of these can be written as traces of products of M 1 and various derivatives of M; Evaluated using Gaussian Noise. Finite Density Results by Taylor Expansion in µ Theoretical Checks : Resummed Perturbation expansions, Dimensional Reduction, Models of (s)qgp,.. We (Gavai & Gupta, PR D 02 ) have argued that λ s = 2χ s χ u + χ d. (3) Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 5

18 Robustness of Ratios C Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 6

19 / Q χ B χ Quenched Partially quenched /N 2 t / Q χ QY χ Quenched Partially quenched /N 2 t Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 7

20 / Q χ B χ Here 1) C B/Q and C (QY )/Q at T = 2T c exhibited as a function of lattice spacing Quenched Partially quenched /N 2 t / Q χ QY χ Quenched Partially quenched /N 2 t Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 7

21 / Q χ B χ Here 1) C B/Q and C (QY )/Q at T = 2T c exhibited as a function of lattice spacing Quenched Partially quenched /N 2 t ) Partially Quenched Dynamical quarks of mass 0.1T c on , corresponding to m ρ /T c = 5.4 and m π /m ρ = 0.3 / Q χ QY χ Quenched Partially quenched /N 2 t Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 7

22 / Q χ B χ Here 1) C B/Q and C (QY )/Q at T = 2T c exhibited as a function of lattice spacing Quenched Partially quenched /N 2 t ) Partially Quenched Dynamical quarks of mass 0.1T c on , corresponding to m ρ /T c = 5.4 and m π /m ρ = 0.3 / Q χ QY χ Quenched Partially quenched /N 2 t ) Valence light and strange quark masses : m up v /T c = 0.03 and m strange v /T c Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 7

23 Some Robust Predictions for various fluctuations thus are : Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 8

24 Some Robust Predictions for various fluctuations thus are : Q χ/χ Y I 3 -S/2 B T/Tc C X/Q as a function of T/T c for X = B, S, Y and I 3 ; For X = S, C/2 shown. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 8

25 Some Robust Predictions for various fluctuations thus are : Q χ/χ Y I 3 -S/2 B T/Tc C X/Q as a function of T/T c for X = B, S, Y and I 3 ; For X = S, C/2 shown. C S/Q and C B/Q exhibit a large change in going from Hadronic phase to QGP. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 8

26 Wróblewski Parameter Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 9

27 1 0.8 λ s Nt = 4 Nf = 2 QCD T/Tc χ/ m A 1 B D C T/Tc Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 10

28 Fluctuation-Dissipation Theorem, Kramers - Krönig relation & a relaxation time approximation = robust observable C s/u λ s. λ s Nt = 4 Nf = 2 QCD T/Tc χ/ m A 1 B D C T/Tc Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 10

29 λ s χ/ m Nt = 4 Nf = 2 QCD T/Tc Fluctuation-Dissipation Theorem, Kramers - Krönig relation & a relaxation time approximation = robust observable C s/u λ s. λ s 0.4 close to T c, in agreement with extractions from experiment ( See, e.g., Cleymans, JPG 28 (2002) 1575.) and our own earlier result in Quenched QCD. Goes down at lower temperature. 2 A 1 B D C T/Tc Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 10

30 λ s Nt = 4 Nf = 2 QCD T/Tc Fluctuation-Dissipation Theorem, Kramers - Krönig relation & a relaxation time approximation = robust observable C s/u λ s. λ s 0.4 close to T c, in agreement with extractions from experiment ( See, e.g., Cleymans, JPG 28 (2002) 1575.) and our own earlier result in Quenched QCD. Goes down at lower temperature. χ/ m A Strongly dependent on m s for T T c. χ BY / 2 us, curves A, D and C with m s /T c = 0.1, 0.75 and 1, hint at kinematic effects in the shape of λ s. 1 B D C T/Tc Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 10

31 Flavour Carriers : Quasi-quarks? Flavour in quark sector assists in identification of relevant degrees of freedom. Excite one quantum number and look for magnitude of another. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 11

32 Flavour Carriers : Quasi-quarks? Flavour in quark sector assists in identification of relevant degrees of freedom. Excite one quantum number and look for magnitude of another. Koch, Majumder and Randrup (PRL 95,182301(2005)) introduced C BS = 3C (BS)/S = 1 + χ us+χ ds χ s, to distinguish models of QGP excitations : C BS 2/3 for sqgp and unity for (ideal) quarks. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 11

33 Flavour Carriers : Quasi-quarks? Flavour in quark sector assists in identification of relevant degrees of freedom. Excite one quantum number and look for magnitude of another. Koch, Majumder and Randrup (PRL 95,182301(2005)) introduced C BS = 3C (BS)/S = 1 + χ us+χ ds χ s, to distinguish models of QGP excitations : C BS 2/3 for sqgp and unity for (ideal) quarks. Charge and Strangeness Correlation offers another similar possibility of being unity, if strangeness is carried by quarks : C QS = 3C (QS)/S = 1 2χ us χ ds χ s. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 11

34 First Results on C BS and C QS : X=Q 1 C XS X=B T/Tc Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 12

35 First Results on C BS and C QS : X=Q 1 C XS X=B T/Tc Note that while both are different from unity below T c, they become close to unity immediately above T c : = Unit strangeness is carried by objects with baryon number -1/3 and charge 1/3 near T c. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 12

36 Variation of m s /T c between 0.1 and 1.0 does not alter the value for T T c, 1, or the T -independence. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 13

37 Variation of m s /T c between 0.1 and 1.0 does not alter the value for T T c, 1, or the T -independence. Natural Explanation of T -behaviour if Strange Excitations with Baryon Number become lighter at T c. T -independence suggests existence of a single one. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 13

38 Variation of m s /T c between 0.1 and 1.0 does not alter the value for T T c, 1, or the T -independence. Natural Explanation of T -behaviour if Strange Excitations with Baryon Number become lighter at T c. T -independence suggests existence of a single one. Similar results in the light quark sector: From e.g., C (BU)/U and C (QU)/U, or C (BD)/D and C (QD)/D, u (d)-flavour is carried by B = 1/3 and Q = 2/3 (-1/3) objects. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 13

39 C (ud)/u T/Tc Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 14

40 C (ud)/u T/Tc Interactions dress up quarks. Close to T c the coupling is presumably not weak, but these flavour linkages seem to persist quasi-quarks. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 14

41 Summary Ratios of Quark Number Susceptibilities, C A/B are robust variables : Depend weakly on the lattice spacing and the sea quark content of QCD in the high temperature phase. C S/Q and C B/Q exhibit a large change in going from Hadronic phase to QGP. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 15

42 Summary Ratios of Quark Number Susceptibilities, C A/B are robust variables : Depend weakly on the lattice spacing and the sea quark content of QCD in the high temperature phase. C S/Q and C B/Q exhibit a large change in going from Hadronic phase to QGP. First full QCD results for the Wróblewski Parameter λ s are in agreement with RHIC and SPS results near T c. Being a robust observable, small lattice cut-off effects expected. Flavour linkages of excitations demonstrate that High Temperature phase of QCD essentially consists of quasi-quarks. Strangeness in Quark Matter, UCLA, Los Angeles, USA, March 29, 2006 R. V. Gavai Top 15

Quark Number Susceptibilities & The Wróblewski Parameter

Quark Number Susceptibilities & The Wróblewski Parameter Rajiv V. Gavai T. I. F. R., Mumbai, India In collaboration with Sourendu Gupta, TIFR, Mumbai Hard Probes 2004, Ericeira, Portugal, November 9, 2004