Color Instabilities in Quark-Gluon Plasma Stanisaw Mrwczyski Jan - PowerPoint PPT Presentation

Color Instabilities in Quark-Gluon Plasma Stanisław Mrówczyński Jan Kochanowski University, Kielce, Poland & Institute for Nuclear Studies, Warsaw, Poland 1

over 30 years St. Mrówczyński, 1) Stream instabilities of the quark-gluon plasma, Physica Letters B 214 , 587 (1988), Erratum B 656 , 273 (2007) 2) St. Mrówczyński, Plasma Instability at the initial stage of ultrarelativistic heavy-ion collisions, Physics Letters B 314 , 118 (1993)  5) St. Mrówczyński and M. Thoma, Hard loop approach to anisotropic systems, Physical Review D 62 , 036011 (2000)  17) St. Mrówczyński, B. Schenke and M. Strickland, Color instabilities in the quark-gluon plasma, Physics Reports 682 , 1 (2017)  2

Elementary Physics Story on Color Instabilities in Quark-Gluon Plasma 3

Hadrons, Quarks & Gluons baryons mesons      N *      , K , , , n , p , , , , , , ,     q , q q , q , q 4

Confinement Electrodynamics Chromodynamics r energy density     1 1       2 D E , 0, u ED E   8 8 Gauss law r 2 e e         E r V r        const E 4 g 2 r r   4 g 4 g        E r V r r K. Kogut & L. Susskind, Phys. Rev, D 9 , 3501 (1974)   H.B. Nielsen & P. Olesen, Nucl. Phys. B 61 , 45 (1973) 5

Confinement cont.   V r linear 2 2 m c q 0 r Coulomb The potential is studied in spectroscopy of heavy quarkonia. 6

Asymptotic Freedom   12 2  Color charge vanishes at small distances ( Q ) s   2 Q    33 2 N ln     f  2   QCD Sourceless Maxwell equations in a medium   D 0     D E B H   B 0     2    E 0    1 B      2 2 E c t    c t     2  1 D    B 0     H 2  2 c t    c t c phase velocity of EM wave   in vacuum 1  7

Asymptotic Freedom cont. diamagnetic dielectric    1   1 charges are screened   1 paramagnetic paraelectric      1 1 charges are antiscreened ! Quarks of spin ½ produce diamagnetic effect Gluons win! Gluons of spin 1 produce paramagnetic effect G. ’t Hooft, unpublished N. K. Nielsen, Am. J. Phys. 49 , 1171 (1981) 8

Creation of Quark-Gluon Plasma compression of nuclear matter    3 0.12 fm 0 normal nuclear density 1 fm heating up hadron gas  3 ~ T hadron density   m T   natural system of units:  c k B 9

Phase diagram of strongly interacting matter T Quark-Gluon Plasma critical point ~ 180 MeV Hadron Gas Color Superconductor  0     0 3 0 . 12 fm B B baryon density nuclei 10

Schematic phase diagram of water T supercritical vapor critical point g as liquid solid gas & liquid   T 0  triple point density of molecules 11

Relativistic heavy-ion collisions after free hadrons t freeze-out hadrons hadronization equilibration time quarks & gluons z before    An important role of boost invariance 2 2 t z 12

Quark-Gluon Plasma vs. EM Plasma Electromagnetic Quark-Gluon Plasma Plasma Underlying QCD QED Microscopic Theory  g g g g Elementarny Interactions g g g g e e q q quarks, antiquarks electrons, positrons Fermions Constituents Massless gluons photons Gauge Bosons - massive ions 2 g 2 e 1      2     ( Q ) 0 . 1 1 Coupling 4 4 137 13

Ultrarelativistic Quark-Gluon Plasma Plasma constituents – quarks & gluons – are massless! m q  T Temperature T is often the only dimensional parameter.  3 ~ T density: T  1 l ~ inter-particle spacing :  4 ~ T energy density: 4 p ~ T pressure: 14

Weakly Coupled Quark-Gluon Plasma Plasma from the earliest stage of relativistic heavy-ion collisions is assumed to be weakly coupled.   12 Asymptotic freedom formula:  2 ( Q ) s   2   Q  33 2 N ln     f  2   QCD   1 / 4 Dimensional argument: Q  - energy density 15

Plasma manifests collective behavior r   1 1 e D   screening length ~ V ( r ) ~ D m D gT r V ( r ) Coulomb screened Debye sphere 0  r D 4 1 1 3 3     V ~ , n ~ T , n V ~ 1 if g 1 D D D 3 3 3 3 g T g In a weakly coupled plasma, there are many particles in a Debye sphere ! 16

Screening length Poisson equation charge density    e  V ( ) r ( ) r  ( ) r r  e V ( ) r T 0 eV ( ) r eV ( ) r eV ( ) r         e 1 1 1 T   eV ( ) r  T T     ( ) r e 1  T  0    2 e      V ( ) r e ( ) r 0 V ( ) r T Debye mass  1 ~   m e 0 eT D  T 2 d  D   m x 2 V x ( ) m V x ( ) V x ( ) ~ e D D 2 dx  3 0 ~ T 17

Plasma oscillations charge fluctuation       E ( t , r ) E cos( ( k ) t k r ) 0    ( ) k ~ gT p  k 0 plasma or Langmuir frequency E 18

Plasma frequency l Gauss theorem   Q s   ES flux E  E  0 0   charge Q e Sx s   E e x electric field E  0 x x Equation of motion Quark-gluon plasma Harmonic oscillator  e g       2 x x M x F p  3 ~ T   M mSl mass m ~ T plasma frequency    e m  ~ gT  F QE force p p    charge Q   e Sl 19

Landau damping E x    ( t , x ) E cos( t kx ) 0 0   0 v  k Resonance energy transfer from electric field to particles with v = v φ 20

Instabilities stationary state Instability     t   A ( t ) A A ( t ) A ( t ) e 0   0 fluctuation stable configuration unstable configuration A A ( t ) 0 A A ( t ) 0 21

Plasma instabilities instabilities in configuration space – hydrodynamic instabilities instabilities in momentum space – kinetic instabilities instabilities due to non-equilibrium  T  E momentum distribution   f ( p ) ~ exp is not   22

Kinetic instabilities    i ( t kr )  k || E , ~ e longitudinal modes –    i ( t kr )   k E , j ~ e transverse modes – E – electric field , k – wave vector , ρ – charge density , j – current Which modes are relevant for QGP from relativistic heavy-ion collisions? 23

Logitudinal modes unstable configuration f ( p , p , p ) plasma x y z beam p 0 x Energy is transferred from particles to fields. 24

Logitudinal modes Electric field decays - damping Electric field grows - instability f ( p , p , p ) f ( p , p , p ) x y z x y z p x p x   0 0 E E k k x x particle particle particle particle acceleration deceleration acceleration deceleration  p x - particle’s velocity - phase velocity of the electric field wave, 25 k E x

Parton momentum distribution in AA collisions p x ˆ e p y Momentum distribution has a single maximum and monotonously decreases in every direction. Longitudinal unstable modes are irrelevant for relativistic heavy-ion collisions. There are unstable transverse modes. 26

Evolution of Parton Momentum Distribution time p p T T p p L L prolate oblate 27

Seeds of instability  x but current fluctuations are finite  j a ( ) 0   3 1 d p p p      ab p  ( 3 )   j ( x ) j ( x ) f ( ) ( x v t ) 0 a 1 b 2  3 2 2 ( 2 ) E p  x ( , t x )  2 2 2     x ( t t , x x )  x ( , t x ) 1 2 1 2 1 1 1 Direction of the momentum surplus 28

Mechanism of filamentation z Lorentz force F  q  F v B F v v   v v F F j Ampere’s law z   B  j B y  y x 29

Time scale & collisional damping Time scale of collective phenomena 1 1   t ~ ~ ~ gT collec collec gT t collec Frequency of collisions Parton-parton scattering    4 hard ~ g ln 1/ g T hard scattering: q ~ T q    2 soft ~ g ln 1/ g T soft scattering: q ~ gT        2 g 1 hard soft collec The instabilities are fast! 30

Growth of instabilities – 1+1 numerical simulations SU(2) Hard Loop Dynamics total transverse magnetic 1+1 dimensions    A A ( z t , ) Scaled a a field energy density Anisotropic particle’s momentum distribution    f ( p ) f (| p | p ) iso z   df ( p )  2 2   s iso m dpp D  dp 0 γ * - maximal growth rate Strong anisotropy   10 A. Rebhan, P. Romatschke & M. Strickland, Phys. Rev. Lett. 94 , 102303 (2005) 31