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Electric and magnetic screening masses from the Polyakov loop correlations

Electric and magnetic screening masses from the Polyakov loop correlations. 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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Electric and magnetic screening masses from the Polyakov loop correlations

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  1. Electric and magnetic screening massesfrom the Polyakov loop correlations 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) LATTICE2008 @ the College of William and Mary, July 14-19, 2008

  2. Introduction Screening properties in quark-gluon plasma • Electric (Debye) screening mass (mE) • Heavy-quark bound state (J/Y, Υ) 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) • Screening masses of QCD in 3D-effective field theory (Hart et al. NPB 586 (2000) 443)

  3. Static quark Potential btw. heavy-quark and heavy-antiquark Our approach Polyakov-loop correlations in full QCD simulation (Nf=2) Polyakov loop: useful probe to study screening effect on the lattice Correlation between Polyakov-loops Screening properties in QGP

  4. : TE -odd Electric sector : TE -even Magnetic sector Decomposition of Polyakov-loop operator Extract electric and magnetic sector from Polyakov-loop correlator • Euclidean-time reflection (TE) Arnold and Yaffe, PRD 52 (1995) 7208 • Intermediate states between Polyakov loops • Charge conjugation (C) Screening masses with C symmetry for each sector

  5. Decomposition of Polyakov-loop operator Polyakov-loop correlators in gauge invariant (GI) form Note , (+,-) and (-,+) correlators are not calculable from PLC in GI form.

  6. Polyakov-loop correlators with gauge fixing (GF) • Fitting correlation functions by a screening Coulomb form • Magnetic sector (TE-even) • Electric sector (TE-odd) Magnetic mass Electric mass

  7. 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

  8. Numerical Simulations Magnetic sector TE-even Polyakov-loop correlators for each quantum number Electric sector TE-odd Screening masses for each sector

  9. Screening masses : Magnetic mass • Magnetic sector (TE-even) • Lightest screening mass • At high T, In weak coupling expansion, Polyakov-loop correlators in magnetic sector (TE-even)become, Two gluon exchanges

  10. Screening masses • Electric sector (TE-odd) • Lightest screening mass • At T > 1.5Tpc, Electric mass ~ In weak coupling expansion, Polyakov-loop correlators in electric sector (TE-odd )become, : one gluon ex. : three gluon ex.

  11. ~ + … Relation to gluon correlators Assuming that electric and magnetic screening masses are defined as, • Electric mass TE-odd PLC with gauge fixing • Magnetic mass TE-even PLC in gauge invariant form Two electric and magnetic exchanges

  12. Magnetic mass can be extracted from • TE-even PLC in gauge invariant form Fit results of mE and mM • Mass inequality: mM < mE • For T > 2Tpc, both mM and mE decreases as T increases. • For Tpc < T < 2Tpc, mM and mE behaves differently.

  13. Quench Nf=2 QCD • mE increases • mM decreases • mE decreases • mM increases 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>1.5Tpc, qualitative behavior (mM < mE) is the same. • For T<1.5Tpc, as T → Tpc Order of the phase transition responsible ? Violation of two-gluon exchange assumption?

  14. Comparison with other calculations Assuming: at Nf=2, T=2LMS Screening ratio • Screening masses from GI correlator in Nf=2 lattice QCD (this work) • Supergravity modes in AdS/CFT correspondence (Bak et al. JHEP 0708 (2007) 049) • Screening masses of QCD in 3D-effective field theory (Hart et al. NPB 586 (2000) 443) Magnitude of masses Difference of D.o.F agreement at T>1.3Tpc

  15. Summary • Electric and magnetic screening masses in QGP from Polyakov-loop correlator with gauge fixing • Using Euclidean-time reflection TE and charge conjugation C, the Polyakov-loop correlator can be decomposed: • Fitting by a screened Coulomb form • Relation to gluon correlators obtained mM and mE Temperature dependence: mM < mE • Comparison with quenched results from <AA> qualitative agreement at T>1.5Tpc • Comparison with AdS/CFT and 3D-EFT agreement of screening ratio at T>1.3Tpc • Electric sector (TE-odd): • Magnetic sector (TE-even): • Electric mass: • Magnetic mass: described by weak coupling expansion

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