Quark-Gluon LHC

Transcription

1 Quar-Gluon LHC Stanisław Mrówczyńsi Świętorzysa Academy Kielce Poland & Institute for Nuclear Studies Warsaw Poland LHC wealy couled strongly collectie unstable equilibrates fast 1

2 Relatiistic heay-ion collision Little Bang after free hadrons t hadrons quars & gluons freeze-out hadronization equilibration z before

3 Au-Au RHIC s 1 +1 GeV/NN eeriment 3

4 RHIC s. LHC GeV/NN RHIC s s LHC 3 55 GeV/NN LHC s RHIC Initial temerature i 3 MeV RHIC 7 GeV LHC 3 / 4 1 T. 3 4

5 RHIC s. LHC cont. Asymtotic freedom α s 1π Q 33 N f ln ΛQCD Λ QCD Q #T MeV RHIC LHC T 3 MeV α s.3 T 7 MeV α s. 5

6 RHIC s. LHC cont. Lattice thermodynamics of Quar-Gluon Plasma Ideal EoS 3 1 ε RHIC LHC F. Karsch arxi: [he-lat]. 6

7 7 Mean fields s. collisions [ ] f C t f g t f t r B E r π α 4 g s Transort equation collisions ~ α s mean field ~ α s free streaming In wealy couled lasmas the mean field dominates the dynamics Wealy couled lasmas are strongly collectie

8 Plasma s collectie behaior λ D 1 m D ~ 1 gt screening length V r ~ e r λ r D V r Coulomb screened Debye shere λ D r V ~ ~ 3 1 πλd n T n V if g 3 3 D ~ 3 g T 3 >> g D 1 << 1 In a wealy couled lasma there are many articles in a Debye shere! 8

9 Plasma oscillations charge fluctuation E t r E cos ω t r + ϕ ω ω ~ gt lasma frequency E 9

10 Landau daming E t E cos ω t ω ϕ Resonance energy transfer from electric field to articles with φ 1

11 Instabilities stationary state Instability A t A + δa t δa t e γt fluctuation γ > stable configuration unstable configuration A At A At 11

12 Terminology Plasma instabilities interlay of articles and classical fields Quantum Field Theory no articles no classical fields ~ T hard articles hard ecitations hard modes classical fields highly oulated soft ecitations soft modes ~ 1/ g ~ soft gt 1

13 Plasma instabilities instabilities in configuration sace hydrodynamic instabilities instabilities in momentum sace inetic instabilities instabilities due to non-equilibrium momentum distribution f is not ~ E e T 13

14 Kinetic instabilities longitudinal modes E δρ ~ e i ωt r transerse modes E δj ~ e i ωt r E electric field wae ector ρ charge density j - current 14

15 Transerse modes Instabilities occur due to anisotroy of the momentum distribution Transerse modes are releant for relatiistic nuclear collisions! 15

16 Momentum Sace Anisotroy in Nuclear Collisions Parton momentum distribution is initially strongly anisotroic T T L time L CM after 1-st collisions local rest frame 16

17 17 Seeds of instability j a but current fluctuations are finite δ π δ ν ν t f E d j j ab b a t t t t Direction of the momentum surlus

18 Mechanism of filamentation z F F F F Lorentz force F q B Amere s law j z B j B y y 18

19 Instabilities s. collisions Time scale of collisional rocesses t hard t soft ~ g g 4 ~ 1 ln 1/ gt 1 ln 1/ gt Time scale of collectie henomena t q collec ~ hard scattering: q ~ T soft scattering: q ~ gt 1 g T g << 1 t >> t >> t hard soft collec The instabilities are fast! 19

20 Disersion equation Equation of motion of chromodynamic field A in momentum sace ν ν ν [ g Π ] A ν Disersion equation gluon self-energy det[ g ν ν Π ν ] ω Instabilities solutions with Imω > A Im ~ e ωt Dynamical information is hidden in ν Π. How to get it?

21 Transort theory transort equations fundamental adjoint g D Q { F Q} C g D Q + { F Q } C g D G { F G} C g quars antiquars gluons free streaming mean-field force collisions D ig[ A...] F ν A ν ν A ig[ A A ν ] D ν ν F j [ Q Q G] mean-field generation collisionless limit: C C Cg 1

22 Transort theory - linearization Q Q Q δ + fluctuation stationary colorless state n Q ij ij δ Q Q Q Q δ >> δ >> Linearized transort equations δ + δ δ QG g G Q F g Q D Q F g Q D F D

23 3 Transort theory olarization tensor ' ' 4 Q F d g Q δ A j ν ν Π 4 D δ ] [ G Q Q j δ δ δ g n n n f + + λ + σ σ λ ν λ ν + π Π f i g E d g ] [ 3 3 Π Π Π ν ν ν

24 Diagrammatic Hard Loo aroach Π ν Hard loo aroimation: << 3 ν λ ν g d λ f Π [ g ] 3 σ + λ π E σ + i Π ν ν ν Π Π St. M. & M. Thoma Phys. Re. C

25 Disersion equation Disersion equation det[ g ν ν Π ν ] ε ij ij 1 ij δ Π ω Disersion equation Π ν chromodielectric tensor ω det[ δ ij i j ω ε ij ] ij ij g d ε δ ω π ω + i 3 i f l [1 ω δ lj + l ω j ] / E 5

26 y Disersion equation configuration of interest z Direction of the momentum surlus j j E E Disersion equation ω ε zz ω 6

27 Eistence of unstable modes Penrose criterion H ω C ω ε zz ω d ω 1 dh ω πi H ω dω Im H ω ω ω dω d ln H ω ln H ω πi dω C number of zeros of Hω in C Imω C i Reω φπ φπ + ω ω Re H There are unstable modes if H ω < Anisotroy! 7

28 Unstable solutions f π 1/ 3/ ρσ σ σ 3 e σ α s ρ 6 fm 3 g / 4π. 3 σ.3 GeV ω ε zz ω solution ω ± i γ < γ R J. Randru & St. M. Phys. Re. C

29 9 Hard-Loo dynamics Soft fields in the assie bacground of hard articles Braaten-Pisarsi action generalized to anisotroic momentum distribution: ] [ ~ eff D f C i F D F f d g L F b ab a ψ γ ψ + π ρ ρ ν ν q q Σ + Σ Λ Π ν St. M. A. Rebhan & M. Stricland Phys. Re. D

30 Growth of instabilities 1+1 numerical simulations SU Hard Loo Dynamics total transerse magnetic A 1+1 dimensions a Aa t z Scaled field energy density Anisotroic article s momentum distribution f fiso + ζz m α s dfiso D π d d m ζ D Strong anisotroy ζ 1 γ * - maimal growth rate A. Rebhan P. Romatsche & M. Stricland Phys. Re. Lett

31 Isotroization - articles Direction of the momentum surlus j B F dt F 31

32 Isotroization - fields Direction of the momentum surlus E B P ~ B E ~ fields a a 3

33 Isotroization numerical simulation Classical system of colored articles & fields T ij 3 d π 3 i E j f T yy +T zz / Isotroy: T T + Tyy Tzz / A. Dumitru & Y. Nara Phys. Lett. B

34 Conclusions LHC wealy couled strongly collectie unstable equilibrates fast QGP is not a gas of artons 34