Instabilities Driven Equilibration in Nuclear Collisions

Transcription

1 Instabilities Driven Equilibration in Nuclear Collisions Stanisław Mrówczyńsi Świętorzysa Academy, Kielce, Poland & Institute for Nuclear Studies, Warsaw, Poland 1

2 Evidence of equilibration success of thermal models in describing ratios of article multilicities - chemical equilibrium of the final state n n a b ~ e m a m T b success of thermal models in describing article T sectra - thermal equilibrium of the final state d d m + n ~ e T T T

3 Evidence of equilibration at the early stage Success of hydrodynamic models in describing ellitic flow φ Hydrodynamics + v v t ρ Hydrodynamic requires local thermodynamical equilibrium! dn dϕ π/ π 3 φ

4 Equilibration is fast v ~ ε + y y Eccentricity decays due to the free streaming! ε v t eq. 6 fm/ c time of equilibration U. Heinz and P. Kolb, Nucl. Phys. A7, 69 4

5 Collisions are too slow Time scale of hard arton-arton scattering t hard ~ g 4 1 ln 1/ gt hard scattering ~ momentum transfer of order of T either single hard scattering or multile soft scatterings t eq t hard.6 fm/ c R. Baier, A.H. Mueller, D. Schiff and D.T. Son, Phys. Lett. B539, 46 5

6 Scenarios of fast equilibration Production mechanism of articles obeys equilibrium momentum distributions instantaneous equilibration Schwinger mechanism: d d π m n ~ e ee T T A. Białas, Phys.Lett. B466, W. Florowsi, Acta Phys. Pol. B35, D. Kharzeev & K. Tuchin, he-h/5134 Equilibration is fast because quar-qluon lasma is strongly couled sqgp E.V. Shurya, J. Phys.G3, S11 4 E.V. Shurya & I. Zahed, Phys. Rev. C7, Instabilities drive equilibration - as in the EM lasma 6

7 Instabilities driven equilibration The most imortant contributions St. Mrówczyńsi, Color Collective Effects At The Early Stage Of Ultrarelativistic Heavy Ion Collisions, Phys. Rev. C 49, St. Mrówczyńsi, Color filamentation in ultrarelativistic heavy-ion collisions, Phys. Lett. B 393, P. Romatsche and M. Stricland, Collective modes of an anisotroic quar gluon lasma, Phys. Rev. D 68, Unstable Mode Analysis P. Arnold, J. Lenaghan and G.D. Moore, QCD lasma instabilities and bottom-u thermalization, JHEP 38, 3 Numerical Simulations A. Rebhan, P. Romatsche and M. Stricland, Hard-loo dynamics of non-abelian lasma instabilities, Phys. Rev. Lett. 94, A. Dumitru and Y. Nara, QCD lasma instabilities and isotroization, arxiv:he-h/

8 Instabilities driven equilibration The most imortant contributions cont. St. Mrówczyńsi and M. Thoma, Hard Loo Aroach to Anisotroic Systems, Phys. Rev. D 6, 3611 P. Arnold and J. Lenaghan, The abelianization of QCD lasma instabilities, Phys. Rev. D 7, Effective Action St. Mrówczyńsi, A. Rebhan and M. Stricland, Hard-loo effective action for anisotroic lasmas, Phys. Rev. D 7, 54 4 Heavy-Ion Phenomenology J. Randru and St. Mrówczyńsi, Chromodynamic Weibel instabilities in relativistic nuclear collisions, Phys. Rev. C 68, P. Arnold, J. Lenaghan, G.D. Moore and L.G. Yaffe, Aarent thermalization due to lasma instabilities in quar gluon lasma, Phys. Rev. Lett. 94,

9 Instabilities stationary state Instability A t A + δa t δa t e γt fluctuation γ > stable configuration unstable configuration A At A At 9

10 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 1

11 Kinetic instabilities longitudinal modes E, δρ ~ e i ωt r transverse modes E, δj ~ e i ωt r E electric field, wave vector, ρ charge density, j - current 11

12 Logitudinal modes unstable configuration lasma f, y, z beam Energy is transferred from articles to fields 1

13 Logitudinal modes Electric field decays - daming f, y, z Electric field grows - instability f, y, z article acceleration ω E article deceleration article acceleration ω E article deceleration ω - hase velocity of the electric field wave, - article s velocity E 13

14 Transverse modes Unstable transverse modes occur due anisotroic momentum distribution f f f ê y e ˆ Momentum distribution distribution can monotonously decrease in every direction 14

15 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 15

16 16 Seeds of instability t f E d j j ab b a v δ π δ ν ν Current fluctuations,,,,, t t t t Direction of the momentum surlus

17 Mechanism of filamentation z F v v F v v F F F q v B j z B j B y y 17

18 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? 18

19 Transort theory distribution functions Distribution functions of quars Q, antiquars Q, gluons G, 3 3 matri 8 8 matri Distribution functions are gauge deendent Q, U Q, U 1 Tr[ Q, ] gauge indeendent Baryon current Color current j 3 1 d b Tr [ Q, Q, ] 3 3 π E 3 d 3 g π E { Q, 1 Tr[ Q, ] +...} 3 antiquars & gluons 19

20 Transort theory transort equations fundamental adjoint v D g F Q, v v D + g F Q, D F v v g v G, C g C C 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

21 1 Transort theory - linearization,,, + G g G Q F g Q D Q F g Q D v v v v v v δ δ δ F D,, Q Q Q δ + Linearized transort equations,,, Q Q Q Q δ >> δ >> stationary colorless state fluctuation n Q ij ij δ

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

23 Diagrammatic Hard Loo aroach Π ν Hard loo aroimation: << g d 3 ν λ ν νλ Π g 3 σ + π E σ + i [ ] f λ Π ν ν ν Π, Π 3

24 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 v ε δ ω π ω v + i 3 i f l [1 v ω δ lj + l v ω j ] v / E 4

25 y Disersion equation configuration of interest z Direction of the momentum surlus j,, j, E,, E,,, Disersion equation zz ω ε ω, 5

26 Eistence of unstable modes Penrose criterion H ω C ω ω ω ε zz ω, d ω 1 dh ω πi H ω dω Im H ω ω dω d ln H ω ln H ω πi dω C Re H number of zeros of Hω in C ω i H C Imω ω < Re ω φπ φπ There are unstable modes if + 6

27 Unstable solution 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 and St. M., Phys. Rev. C 68,

28 Growth of instabilities numerical simulation Classical system of colored articles & fields initial fields: Gaussian noise as in Color Glass Condensate initial article distribution: f, ~ δ e y + hard z magnetic hard 1 GeV 3 L 4 fm ρ 1 fm electric A. Dumitru and Y. Nara, arxiv:he-h/5311 8

29 Abelanization V eff [ A a ] A a A a g f abc f ade A b A d A c A e the gauge a a A, Ai t,, y, z Ai a L YM 1 4 g 1 4 f F abc a ν f F ade ν a A b 1 A d B a B A c a A e SU a a g b B A + fabca A c P. Arnold and J. Lenaghan,Phys. Rev. D 7,

30 Abelanization numerical simulation Classical system of colored articles & fields φ L rms Tr[ A ] d L C L d L Tr i[ A y, A z ] Tr[ A ] A. Dumitru and Y. Nara, arxiv:he-h/5311 3

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 and Y. Nara, arxiv:he-h/

34 Conclusion The scenario of instabilities driven equilibration seems to be a lausible solution of the fast equilibration roblem of relativistic heavy-ion collisions 34