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格子 QCD シミュレーションによる QGP 媒質中のクォーク間ポテンシャルの研究

W HOT-QCD Collaboration. 格子 QCD シミュレーションによる QGP 媒質中のクォーク間ポテンシャルの研究. 前沢祐 ( 理研 ) in collaboration with 青木慎也 , 金谷和至 , 大野浩史 ( 筑波大物理 ) 浮田尚哉 ( 筑波大計算セ ) 初田哲男 , 石井理修 ( 東京大学 ) 江尻信司 (BNL) 梅田貴士 ( 広島大学 ). WHOT-QCD Coll. arXive:0907.4203 WHOT-QCD Coll. PoS LAT2007 (2007) 207

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格子 QCD シミュレーションによる QGP 媒質中のクォーク間ポテンシャルの研究

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  1. WHOT-QCD Collaboration 格子QCDシミュレーションによるQGP媒質中のクォーク間ポテンシャルの研究 前沢祐 (理研) in collaboration with 青木慎也, 金谷和至, 大野浩史 (筑波大物理) 浮田尚哉 (筑波大計算セ) 初田哲男,石井理修 (東京大学) 江尻信司 (BNL) 梅田貴士 (広島大学) WHOT-QCD Coll. arXive:0907.4203 WHOT-QCD Coll. PoS LAT2007 (2007) 207 WHOT-QCD Coll. Phys. Rev. D75 (2007) 074501 原子核・ハドロン物理 @ KEK, 2009年8月11—13日

  2. Study of Quark-Gluon Plasma (QGP) • Early universe after Big Bang • Relativistic heavy-ion collision Theoretical study based on first principle (QCD) Lattice QCD simulation at finite (T, mq) Introduction Bulk properties of QGP (p, e, Tc,…)Internal properties of QGP are well investigated. are still uncertain. • Properties of quarks and gluons in QGP • Heavy-quark potential: free energy btw. static charged quarks in QGP • Relation of inter-quark interaction between zero and finite T • Temperature dependence of various color-channels • Heavy-quark potential at finite density (mq) in Taylor expansion method

  3. Properties of heavy-quark potential in quark-gluon plasma • Heavy-quark bound state (J/y, Υ) in QGP • Screening effect in QGP • Inter-quark interaction btw. QQ and QQ Lattice QCD simulations Heavy-quark potential at finite T Heavy-quark potential interaction btw. static quark (Q) and antiquark (Q) in QCD matter • T = 0, • T > 0, string tension (s) decreases, string breaking at rc • At T > Tc, screening effect in QGP 3

  4. Polyakov-line : static quark at x Operator similar to the Wilson-loop at finite T Heavy-quark free energy To characterize an interaction b/w static quarks, T = 0 Heavy-quark potentialBrown and Weisberger (1979) Wilson-loop operator T > 0 Heavy-quark free energyNadkarni (1986) Correlation b/w Polyakov-lines projected to a color singlet channel in the Coulomb gauge Heavy-quark free energy may behave in QGP as: • short r: F1(r,T)~V(r) (no effect from thermal medium) • mid r : screened by plasma • long r : two single-quark free energies w/o interactions 4

  5. a: lattice spacing Nt: lattice size in E-time direction Approaches of lattice simulations at finite T To vary temperature on the lattice, • Fixed Nt approach • Fixed scale approach WHOT-QCD, PRD 79 (2009) 051501. • Changing a (controlled by the gauge coupling (b=6/g2)),fixing Nt Advantages: T can be varied arbitrarily, because b is an input parameter. • Changing Nt , fixing a Advantages: investigation of T dependence w/o changing spatial volume possible. renormalization factor dose not change when T changes.

  6. Results of numerical simulations Heavy-quark potential at T = 0 and T > 0 Heavy-quark potential for various color-channels Heavy-quark potential at finite density (mq) 6

  7. Simulation details Nf = 2+1 full QCD simulations • Lattice size: Ns3 x Nt = 323 x 12, 10, 8, 6, 4 Temperature:T ~ 200-700 MeV (5 points) • Lattice spacing:a = 0.07 fm • Light quark mass*: mp/mr = 0.6337(38) • Strange quark mass*: mK/mK* = 0.7377(28) • Scale setting:Sommer scale,r0 = 0.5 fm *CP-PACS & JLQCD Coll., PRD78 (2008) 011502. 7

  8. Our fit results Heavy-quark potential at T = 0 Data calculated by CP-PACS & JLQCD Coll. on a 283 x 58lattice Phenomenological potential = Coulomb term at short r + Linear term at long r + const. term 8

  9. Heavy-quark free energy at T > 0 At short distance F1(r,T) at anyT converges to V(r) = F1(r,T=0). Short distance physics is insensitive to T. Note: In the fixed Nt approach, this property is used to adjust the constant term of F1(r,T). In our fixed scale approach, because the renormalization is common to all T. no further adjustment of the constant term is necessary. We can confirm the expected insensitivity!

  10. T ~ 200 MeV: F1~V up to 0.3--0.4 fm T ~ 700 MeV: F1 = V even at 0.1 fm Range of thermal effect is T-dependent Debye screening effect Heavy-quark free energy at T > 0 At short distance F1(r,T) at anyT converges to V(r) = F1(r,T=0). Short distance physics is insensitive to T. WHOT-QCD Coll. arXive:0907.4203 WHOT-QCD Coll. Phys. Rev. D75 (2007) 074501

  11. F1(r,T) becomes flat and has no increase linealy. Confinement is destroyed due to a thermal medium effect. Heavy-quark free energy at T > 0 2FQ calculated from Polyakov-line operator Long distance At large r, correlation b/w Polyakov-lines will disappear, F1 converges to 2x(single-quark free energy) at long distance

  12. Results of numerical simulations Heavy-quark potential at T = 0 and T > 0 Heavy-quark potential for various color-channels Heavy-quark potential at finite density mq 12

  13. QQ correlator: • QQ correlator: Heavy-quark potential for various color-channels Interaction for various color-channels are induced in QGP Separation to each color channel Projection of Polyakov-line correlatorsNadkarni (1986) Normalized free energy

  14. Casimir factor Heavy-quark potential for various color-channels QQ potential QQ potential • Temperature increases becomes weak • 1c, 3*c: attractive force, 8c, 6c: repulsive force Single gluon exchange ansatz Consistent with Casimir scaling e.g.)

  15. Results of numerical simulations Heavy-quark potential at T = 0 and T > 0 Heavy-quark potential for various color-channels Heavy-quark potential at finite density (mq) 15

  16. Heavy-quark potential at finite mq Motivation Taylor expansion method in terms of mq /T Properties of QGP at 0 < mq /T << 1 Expectation values at finite mq At mq /T << 1, Taylor expansion of quark determinant detD(mq) where • Early universe after Big Bang • Relativistic heavy-ion collisions • Low density • e.g.mq /Tc ~ 0.1 at RHIC c.f.) sign problem detD becomes complex when mq≠0

  17. Heavy-quark potential at finite mq Heavy-quark potential up to 2nd order with expansion coefficients: QQ potential (1c, 8c)QQ potential (3*c, 6c) Odd term of QQ potential vanishes because of symmetry under mq→ -mq

  18. becomes weak at 0 < mq /T << 1 QQ potential 1cchannel: attractive force 8cchannel: repulsive force

  19. becomes strong at 0 < mq /T << 1 QQ potential 3*cchannel: attractive force 6cchannel: repulsive force

  20. Heavy-quark potential at finite mq QQ potential (1c, 8c) QQ potential (3*c, 6c) Attractive channel in heavy-quark potential Heavy-meson correlation (1c) weak at 0 < mq /T << 1 Diquark correlation (3*c) strong

  21. At short r: F1 at any T converges to heavy-quark potential at T = 0 Short distance physics is insensitive to T. • At mid r : screening effect appears • At long r: F1 becomes flat and has no linear behavior. Correlation b/w Polyakov-lines disappears and F1 converges to 2FQ Summary Properties of quark-gluon plasma Heavy-quark potential (F1(r,T)) defined by free energy btw. static charged quarks Heavy-quark potential at T = 0 and T > 0 Heavy-quark potential for various color-channels Heavy-quark potential at finite density (mq) • 1c, 3*c: attractive force, 8c, 6c: repulsive force Consistent with Casimir scaling based on single gluon exchange ansatz • Taylor expansion in terms of mq /T Heavy-meson correlation (1c) weak Diquark correlation (3*c) strong at 0 < mq /T << 1

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