1. WHOT-QCD Collaboration Yu Maezawa (RIKEN) in collaboration with S. Aoki, K. Kanaya, N. Ishii, N. Ukita, T. Umeda (Univ. of Tsukuba) T. Hatsuda (Univ. of Tokyo) S. Ejiri (BNL) Magnetic and electric screening masses from Polyakov-loop correlations in two-flavor lattice QCD Seminar @ Komaba, Todai, May 7, 2008

2. Contents Introduction Decomposition of Polyakov-loop correlator Numerical simulations in N f =2 lattice QCD Summary Lattice QCD simulation Polyakov-loop correlation  Euclidean-time reflection and charge conjugation Electric and magnetic screening masses are separately extracted from Polyakov-loop correlators Results of screening masses AdS/CFT correspondence Comparison with quenched QCD heavy-quark potential

3. Big Bang RHIC T qq QGP nucleus CSC s-QGP Introduction Study of Quark-Gluon Plasma (QGP) Early Universe after Big Bang Relativistic heavy-ion collision Theoretical study based on first principle (QCD)  Perturbation theory ・ weak coupling at high T limit However  Study of strongly-correlated QGP Lattice QCD simulation at finite ( T,  q ) ・ bulk properties of QGP (p, , T c, …) are well investigated at T > 0. ・ internal properties of QGP are still uncertain. 1)Infrared problem 2)Strong coupling near T ~ T c  /T 4 T / T pc N f = 2, CP-PACS 2001 T c ~ 170 MeV

4. Introduction Polyakov loop: heavy quark at fixed position Heavy-quark free energy, inter-quark interaction, screening effects, … Properties of quarks and gluons in QGP Heavy-quark potentials How they are screened? Q-Q interaction heavy-meson ( J/  ) correlation Q-Q interaction diquark correlation in QGP Electric (Debye) screening Magnetic screening

5. Introduction Screening properties in quark-gluon plasma Electric (Debye) screening mass ( m E ) Heavy-quark bound state (J/,  ) in QGP Magnetic screening mass ( m M ) Spatial confinement in QGP, non-perturbative Attempts so far  from lattice simulations in quenched approximation (Nakamura et al. PRD 69 (2004) 014506)  Supergravity modes in AdS/CFT correspondence (Bak et al. JHEP 0708 (2007) 049) Polyakov-loop correlations in full lattice simulations (N f =2) Our approach

6. Lattice QCD simulation Polyakov-loop correlation Lattice QCD simulation Polyakov-loop correlation

7. Basis of lattice QCD Gluon action Gluon field Quark action Wilson-type quark action ( N f = 2 ) Finite temperature Continuum limit/Thermodynamic limit a << 1/m D << L a → 0 and L → ∞ Debye screening mass m D :

8. Monte Carlo simulations based on importance sampling Configurations {U i } proportional to exp(-S(U)) 500-600 confs. Simulation parameters Action on lattice  /T 4 T / T pc N f = 2, CP-PACS 2001 Quark mass Small m q dependence in  /T 4 Lattice size m D /T ~ O(1) a < 1/m D < L Iwasaki improved gluon action Clover-improved Wilson quark action ( N f = 2 ) improvement of lattice discretization :

9. Static charged quark Polyakov loop Order parameter of confinement-deconfinement PT at N f = 0 Characterizing rapid crossover transition at N f = 2 Pseudo-critical temperature T pc from susceptibility

10. Correlation between Polyakov loops Polyakov-loop correlations Free energy between quark ( Q ) and antiquark ( Q )  Separation to each channel after Coulomb gauge fixing Free energies between Q and Q Normalized free energies (“heavy-quark potential”) V 1, V 8, V 6, V 3* at T >T pc : WHOT-QCD Coll., PRD 75 (2007) 074501

11. Single gluon exchange ansatz (T = 0) (T >T pc ) Heavy-quark potential Higher order (magnetic) contribution?

12. ~ + + : Screened Coulomb form : Single electric gluon exchange Heavy-quark “potential” with gauge fixing m E (A 4 ) : electric mass m M (A) : magnetic mass

13. ~ + + m E (A 4 ) : electric mass m M (A) : magnetic mass Leading-order in g from electric sector Higher-order in g from magnetic sector Heavy-quark “potential” with gauge fixing

14. ~ + + m E < 2m M : electric dominance m E > 2m M : magnetic dominance Inequality between m E and m M is important Which term is dominant at long distance? c.f. perturbative-QCD m E ~ O(gT) >> m M ~ O(g 2 T) at high T limit Magnetic dominance What about the magnitude of m E and m M at T ~ (1-4) T c ? Heavy-quark “potential” with gauge fixing

15. Decomposition of Polyakov-loop correlator Extract electric and magnetic sector from Polyakov-loop correlator Euclidean-time reflection ( T E ) Charge conjugation ( C ) Intermediate states in z-direction Magnetic and electric gluons btw. Polyakov-loops Arnold and Yaffe, PRD 52 (1995) 7208 z 

16. Decomposition of Polyakov-loop operator Polyakov-loop correlator four parts

17. Decomposition of Polyakov-loop operator  Electric sector ○ |A 4 > × |A i >, |A i A i > ××

18.  Evaluate m E and m M in lattice simulation of N f =2 QCD Magnetic sector ○ |A i A i >, |A 4 A 4 > × |A i >, |A 4 > ×

19. Lattice size: Action: RG-improved gauge action Clover improved Wilson quark action Quark mass & Temperature (Line of constant physics) # of Configurations: 500-600 confs. (5000-6000 traj.) Lattice spacing ( a ) near T pc Gauge fixing: Coulomb gauge Two-flavor full QCD simulation Numerical Simulations

20. Correlation functions between Polyakov-loops (heavy-quark potential) C oo (r,T) electric screening mass C ee (r,T) magnetic screening mass

21. Screening masses  Mass inequality: m M < m E  For T > 2T pc, both m M and m E decreases as T increases.  For T pc < T < 2T pc, m M and m E behaves differently.  m E well approximated by the NLO formula Rebhan, PRD 48 3967

22. Screening masses  Mass inequality: m M < m E  For T > 2T pc, both m M and m E decreases as T increases.  For T pc < T < 2T pc, m M and m E behaves differently.  m E well approximated by the NLO formula Rebhan, PRD 48 3967

23. Screening ratio m E < 2m M : electric dominance m E > 2m M : magnetic dominance Heavy-quark potential in color-singlet channel Heavy-quark potential is Electrically dominated Inequality m M < m E < 2m M is satisfied at 1.3T pc < T < 4T pc

24. Comparison with AdS/CFT Screening masses in N=4 supersymmetric Yang-Mills matter Bak et al. JHEP 0708 (2007) 049 Good agreement at T > 1.5T pc Spectra of supergravity modes Lightest T E -odd mode (electric sector) Lightest T E -even mode (magnetic sector) Screening ratio D.O.F btw. SYM and QCD different

25. Comparison with quenched calculation  For T > 1.2T pc, qualitative behavior ( m M < m E ) is the same.  For T < 1.2T pc, as T → T pc m E decreases m M increases Quench m E increases m M decreases N f =2 QCD From in Quenched QCD Nakamura et al, PRD69 (2004) 014506 Order of the phase transition responsible ? From Polyakov-loops in N f =2 QCD this work

26. Comparison with heavy-quark potential Inequality m E < 2m M is satisfied at 1.3T pc < T < 4T pc Heavy-quark potential is dominated by electric screening. Heavy-quark potential of color-singlet channel Heavy-quark potential of color-averaged channel (gauge invariant) mE ⇔ 2mMmE ⇔ 2mM mE ⇔ mMmE ⇔ mM

27. Comparison with heavy-quark potential m 1 eff (V 1 ) ~ m E (C oo ) V 1 (r,T) is electrically dominated m av eff (V av ) ~ m M (C ee ) V av (r,T) is magnetically dominated m M < m E < 2m M is confirmed.

28. Summary Electric and magnetic screening masses in QGP from Polyakov-loop correlator Using Euclidean-time reflection and charge conjugation, the Polyakov-loop correlator can be decomposed: Calculate m E and m M in lattice simulations of N f =2 QCD Temperature dependence: m M < m E < 2m M Heavy-quark potential is electrically dominated. Comparison with AdS/CFT correspondence Good agreement of screening ratio at T > 1.5T pc Comparison with quenched QCD Qualitative agreement at T > 1.2T pc Different behavior at T < 1.2T pc C oo (r,T) couples to |A 4 > electric mass ( m E ) C ee (r,T) couples to |A i A i >, |A 4 A 4 > magnetic mass ( m M )

29. Summary Comparison with heavy-quark potential color-singlet channel is electrically dominated. color-averaged channel is magnetically dominated. m M < m E < 2m M is confirmed. Notice at high temperature! m E ~ O(gT) >> m M ~ O(g 2 T) Future Chiral & continuum limit Single magnetic-gluon exchange in Polyakov-loop correlation? Large statistics

30. Single magnetic-gluon exchanges C eo (r,T) couples to single magnetic gluon |A i > However, signal of C eo is very small Comparison btw. C eo (r,T) and m M obtaind from C ee /( C oo ) 2 C eo will become good probe of m M with high statistics.

31. Buck up slides

32. Comparison with thermal perturbation theory Rebhan, PRD 48 (1993) 48 at 1.5 T pc < T < 4.0 T pc ~ Non-perturbative contributions in NLO: magnetic mass m M  Next-to-leading order PRD 73 (2006) 014513  2-loop running coupling Leading order Next-to-leading order