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Magnetic and electric screening masses from Polyakov-loop correlations in two-flavor lattice QCD

Magnetic and electric screening masses from Polyakov-loop correlations in two-flavor lattice QCD. 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).

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Magnetic and electric screening masses from Polyakov-loop correlations in two-flavor lattice QCD

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  1. Magneticand electric screening massesfrom Polyakov-loop correlationsin two-flavor lattice QCD 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) Seminar @ Komaba, Todai, May 7, 2008

  2. 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 Contents • Introduction • Decomposition of Polyakov-loop correlator • Numerical simulations in Nf=2 lattice QCD • Summary • Lattice QCD simulation • Polyakov-loop correlation

  3. Big Bang T RHIC QGP • Early Universe after Big Bang • Relativistic heavy-ion collision s-QGP nucleus CSC mq Nf = 2, CP-PACS 2001 e /T4 T / Tpc Tc ~ 170 MeV Introduction Study of Quark-Gluon Plasma (QGP) 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,mq) ・bulk properties of QGP (p, e, Tc, …) are well investigated atT > 0. ・internal properties of QGP are still uncertain. • Infrared problem • Strong coupling near T ~ Tc

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

  5. Introduction Screening properties in quark-gluon plasma • Electric (Debye) screening mass (mE) • Heavy-quark bound state (J/Y, U) in QGP • Magnetic screening mass (mM) • Spatial confinement in QGP, non-perturbative Attempts so far • <AmAn> 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) Our approach Polyakov-loop correlations in full lattice simulations (Nf=2)

  6. Lattice QCD simulation • Polyakov-loop correlation

  7. Wilson-typequark action (Nf = 2) Quark action Finite temperature Debye screening mass mD: a << 1/mD << L a → 0and L →∞ Basis of lattice QCD Gluon field Gluon action Continuum limit/Thermodynamic limit

  8. Iwasaki improved gluon action • Clover-improved Wilson quark action (Nf = 2) improvement of lattice discretization : Configurations {Ui} proportional to exp(-S(U)) 500-600 confs. Nf = 2, CP-PACS 2001 e /T4 a < 1/mD < L mD/T ~ O(1) T / Tpc Action on lattice Monte Carlo simulations based on importance sampling Simulation parameters Quark mass Small mq dependence in e /T4 Lattice size

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

  10. Polyakov-loop correlations Free energy between quark (Q) and antiquark (Q) V1, V8, V6, V3* atT >Tpc: WHOT-QCD Coll., PRD 75 (2007) 074501 Correlation between Polyakov loops • Separation to each channel after Coulomb gauge fixing Free energies between Q and Q Normalized free energies (“heavy-quark potential”)

  11. (T >Tpc) (T = 0) Single gluon exchange ansatz Higher order (magnetic) contribution? WHOT-QCD Coll., PRD 75 (2007) 074501 Heavy-quark potential

  12. ~ + + • mE(A4): electric mass • mM(A): magnetic mass • Heavy-quark “potential” with gauge fixing : Single electric gluon exchange : Screened Coulomb form

  13. ~ + + Leading-order in g from electric sector Higher-order in g from magnetic sector • mE(A4): electric mass • mM(A): magnetic mass • Heavy-quark “potential” with gauge fixing

  14. ~ + + c.f. perturbative-QCD mE ~ O(gT)>>mM~ O(g2T)at high T limit Magnetic dominance What about the magnitude of mE and mM at T~ (1-4)Tc? • Heavy-quark “potential” with gauge fixing Which term is dominant at long distance? Inequality between mE and mMis important • mE < 2mM: electric dominance • mE > 2mM: magnetic dominance

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

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

  17. Electric sector ○ |A4> × |Ai>, |Ai Ai > × × Decomposition of Polyakov-loop operator Polyakov-loop correlator four parts

  18. ○ |Ai Ai >, |A4 A4 > × |Ai>, |A4> Magnetic sector × Evaluate mEand mM in lattice simulation of Nf=2 QCD

  19. Numerical Simulations Two-flavor full QCD simulation • 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 Tpc • Gauge fixing: Coulomb gauge

  20. Numerical Simulations Correlation functions between Polyakov-loops (heavy-quark potential) Coo(r,T) electric screening mass Cee(r,T) magnetic screening mass

  21. Screening masses • Mass inequality: mM < mE • For T > 2Tpc, both mM and mE decreases as T increases. • For Tpc < T < 2Tpc, mM and mE behaves differently. • mEwell approximated by the NLO formula Rebhan, PRD 48 3967

  22. Screening masses • Mass inequality: mM < mE • For T > 2Tpc, both mM and mE decreases as T increases. • For Tpc < T < 2Tpc, mM and mE behaves differently. • mEwell approximated by the NLO formula Rebhan, PRD 48 3967

  23. Screening ratio Heavy-quark potential in color-singlet channel • mE < 2mM: electric dominance • mE > 2mM: magnetic dominance Inequality mM < mE < 2mM is satisfied at 1.3Tpc < T < 4Tpc Heavy-quark potential is Electrically dominated

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

  25. Quench Nf=2 QCD • mE increases • mM decreases • mE decreases • mM increases as T → Tpc Comparison with quenched calculation From Polyakov-loops in Nf=2 QCD this work From <AA> in Quenched QCD Nakamura et al, PRD69 (2004) 014506 • For T>1.2Tpc, qualitative behavior (mM < mE) is the same. • For T<1.2Tpc, Order of the phase transition responsible ?

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

  27. m1eff(V1)~mE (Coo) V1(r,T) is electrically dominated maveff(Vav)~mM (Cee) Vav(r,T) is magnetically dominated mM < mE < 2mMis confirmed. Comparison with heavy-quark potential

  28. Coo(r,T) couples to |A4> electric mass (mE) • Cee(r,T) couples to |AiAi>, |A4A4> magnetic mass (mM) 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 mE and mM in lattice simulations of Nf=2 QCD Temperature dependence: mM < mE < 2mM Heavy-quark potential is electrically dominated. Comparison with AdS/CFT correspondence Good agreement of screening ratio at T>1.5Tpc Comparison with quenched QCD Qualitative agreement at T>1.2Tpc Different behavior at T<1.2Tpc

  29. Notice at high temperature! mE ~ O(gT)>>mM~ O(g2T) Large statistics mM < mE < 2mMis confirmed. Summary Comparison with heavy-quark potential color-singlet channel is electrically dominated. color-averaged channel is magnetically dominated. Future • Chiral & continuum limit • Single magnetic-gluon exchange in Polyakov-loop correlation?

  30. Single magnetic-gluon exchanges Ceo(r,T)couples to single magnetic gluon|Ai> However, signal of Ceo is very small Comparison btw. Ceo(r,T)and mM obtaind from Cee/(Coo)2 Ceo will become good probe of mM with high statistics.

  31. Buck up slides

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

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