The Plasma Physics of the Quark Gluon Plasma

1. What is this stuff and how does it work? The Plasma Physics of the Quark Gluon Plasma Barbara Jacak Stony Brook July 19, 2006

2. Kolb, et al PHENIX RHIC makes fundamentally “new” matter • Pressure built up very rapidly during ion collisions at RHIC • large collective flow, calculate w/hydro • interaction s large, fast thermalization • viscosity small • huge energy loss by fast quarks traversing medium • energy, gluon density large • medium is opaque • baryon production enhanced by • factor of 3 compared to p+p

3. To understand new kind of matter study: • density, temperature • phase • solid, liquid, gas (ideal or not?), plasma • equation of state • screening properties (for plasmas) • transport properties • particle number, energy, momentum, charge • diffusion sound viscosity conductivity

4. QGP plasma properties known, so far Extract from models, constrained by data

5. I. Vitev calculate using an opacity expansion answer: L/mfp ~ 3.5 (model dependent) r≥ 1000 gluons/unit y d+Au Au+Au have probed density by jet quenching interaction of radiated & plasma gluons enhances the amount of radiation

6. proton pion Temperature: hydro, eloss say 380-400 MeV nucl-ex/0410003 Hydro models: Teaney (w/ & w/o RQMD) Hirano (3d) Kolb Huovinen (w/& w/o QGP)

7. need to measure T directly! • Temperature via blackbody radiation • real & virtual g • e+e- also signal any late stage medium modification of hadrons large e+e- background below 1.5 GeV mass, huge g bkgd. strategy: detector upgrades to measure charm & reject decays luminosity to allow measurement as a function of e, m

8. Karsch, Laermann, Peikert ‘99 e/T4 T/Tc Tc ~ 170 ± 10 MeV e ~ 3 GeV/fm3 phase of the new matter? • recall T ~ 400 MeV, e ~ 15 GeV/fm3 • preclude hadronic solid or liquid • also not a normal • hadron gas

9. plasma • ionized gas which is macroscopically neutral • exhibits collective effects • interactions among charges of multiple particles • spreads charge out into characteristic (Debye) length, lD • multiple particles inside this length • they screen each other • plasma size > lD • “normal” plasmas are electromagnetic (e + ions) • quark-gluon plasma interacts via strong interaction • color forces rather than EM • exchanged particles: g instead of g

10. Plasmas exhibit screening • Debye length: distance where influence of an individual charged particle is felt by the other particles in the plasma • charged particles arrange themselves so as to effectively shield any electrostatic fields within a distance lD • lD = e0kT • ------- • nee2 • Debye sphere = sphere with radius lD • number electrons inside Debye sphere is typically large • ND= N/VD= rVD VD= 4/3 plD3 1/2 in strongly coupled plasmas it’s  1

11. Debye screening in QCD: a tricky concept • in leading order QCD (O. Philipsen, hep-ph/0010327) • vv

12. don’t give up! ask lattice QCD Karsch, et al. running coupling coupling drops off for r > 0.3 fm

13. Implications of lD ~ 0.3 fm • can use to estimate Coupling parameter, G • G = <PE>/<KE> but also G = 1/ND • for lD = 0.3fm and e = 15 GeV/fm3 • VD = 4/3 plD3 = 0.113 fm3 • ED = 1.7 GeV • to convert to number of particles, use gT or g2T • for T ~ 2Tc and g2 = 4 • get ND = 1.2 – 2.5  G ~ 1 • NB: for G ~ 1 • plasma is NOT fully screened – it’s strongly coupled! • affects interaction s! • other strongly coupled plasmas behave as liquids, even crystals for G≥ 150 • dusty plasmas, cold atoms+ions , warm dense matter

14. Is the quark gluon plasma just like other plasmas? • NO! • Non-Abelian • charge carriers self-interact • range, shape of strong interaction differ from EM • Relativistic And yet, determining how QGP works requires answering the same questions about plasma properties

15. collective effects a basic feature distinguishing plasmas from ordinary matter • simultaneous interaction of each charged particle with a considerable number of others • due to long range of (electromagnetic) forces • magnetic fields generated by moving charges give rise to magnetic interactions (gives rise to color-magnetic interactions in QGP)

16. strong elliptic flow, scales w/ number of quarks

17. Kolb, et al Equation of State • relationship of thermodynamic properties • e.g. pV = nRT for ideal gas • p = e /3 for ideal QGP • for resonance gas • p > e /3 • generate pressure • rather than make • more resonance elliptic flow of heavier particles: → softer than hadronic EOS!!

18. EOS using transmission in EM plasma EM plasma: x-ray transmission for QGP: we cannot time resolve so must use time integrated transmission & flow strength as we vary T, e, r equivalent to different plasma physics “shots”

19. going from qualitative to quantitative • map p vs. e as a function of collision energy, system size • c, W, X, f flows • & improve hydro. • find critical point • on phase • diagram • Need higher lumi. • → scan and collect statistics forall observables • → cooling improves lumi. at low energy • + Detector upgrades for particle ID

20. how about screening in the QGP? • lattice showed: • screening sets in when r ~ 0.3 fm for charm quarks • but, these are ~ static unlike light partons • indicative of plasma properties? • yes* • * needs more work in both theory & experiment

21. screening masses from gluon propagator Screening mass, mD, defines inverse length scale Inside this distance, an equilibrated plasma is sensitive to insertion of a static source Outside it’s not. Nakamura, Saito & Sakai, hep-lat/0311024 T dependence of electric & magnetic screening masses Quenched lattice study of gluon propagator figure shows: mD,m= 3Tc, mD,e= 6Tc at 2Tc lD ~ 0.4 & 0.2 fm magnetic screening mass is non-zero not very gauge-dependent, but DOES grow w/ lattice size (long range is important)

22. Karsch, Kharzeev, Satz, hep-ph/0512239 40% of J/y from c and y’ decays they are screened but direct J/y not? Probe experimentally: onium spectroscopy

23. Need RHIC II luminosity to sort out! yields in PHENIX from Tony Frawley RHIC Users mtg.

24. STAR yield estimates from Tony Frawley RHIC Users mtg.

25. Transport properties transport in plasmas is driven by collisions • transport of particles → diffusion • transport of energy by particles → thermal conductivity • transport of momentum by particles → viscosity • transport of charge by particles → electrical conductivity • is transport of color charge an analogous question for us?

26. from <r> to r(x,v): Jet tomography • map jet quenching vs. reaction plane • as a function of system size, energy • → parton & energy density gives EOS • → vary pT to probe medium coupling, • see early development of system • golden channel: g-jet correlations • g fixes jet energy • flavor-tagged jets to sort out g vs. q energy loss • need detector upgrades (calorimeter coverage, DAQ) • must have RHIC II high luminosity for: • statistics for clean g-jet (background hadron decay g’s) • multi-hadron correlations • system scan in a finite time cross section is small, so rate is low!

27. radiation vs. collisions? consider leptons in matter • electrons stop in matter • g (bremsstrahlung) radiation • muons have long range • radiation is suppressed by the large mass • dominant energy loss mechanism is via collisions • implication • use heavy quarks as second kind of probe • collisions should be important for c, b quarks is light quark energy loss radiation dominated? EM plasmas → no radiation: blackbody, bremsstrahlung, collisional, recombination

28. we see evidence for both radiation & collisions RAA for heavy mesons via e± from semi-leptonic decays Wicks, et al. nucl-th/0512076 nucl-ex/0607012

29. PHENIX preliminary diffusion = transport of particles by collisions D = 1/3 <v> lmfp = <v>/ 3rs D  collision time →relaxation time Moore & Teaney PRC71, 064904, ‘05 D ~ 3/(2pT) is small! → strong interaction of c quarks larger D → less charm e loss fewer collisions, smaller v2

30. burning questions • what is the role of B decays in electron RAA? • need RHIC II luminosity & upgrades to measure • direct probe of extent & timescale of thermalization? • RHIC II will yield • statistics for v2, pT reach for heavy quarks • allow scan of systems with exclusive decay channels • relative abundance of charmed hadron states inner trackers for PHENIX and STAR

31. Another important transport property is the viscosity • → transport of momentum by particle collisions • found to be (very) small at RHIC

32. sort out via3D hydro + measure v2 vs. v3, v4 scan in system size & energy c, W, X, f flows to separate late stage dissipation from early viscous effects  RHIC II luminosity Kolb, et al data + hydrodynamics → very low viscosity Ideal hydrodynamics (h/S =0) enough to conclude viscosity=0? Deviations → viscous effects? RHIC viscosity has drawn great interest from other fields including string theorists, who conjecture a lower bound h/S ≥ (h/4p) for “QCD”

33. minimum h at phase boundary? seen in strongly coupled dusty plasma B. Liu and J. Goree, cond-mat/0502009 Csernai, Kapusta & McLerran nucl-th/0604032 minimum arises because kinetic part of h decreases with G & potential part increases; measure by density-density correlation

34. PHENIX nucl-ex/0507004 dN/d(Df) STAR PRL95, 152301 (2005) (1/Ntrig)dN/d(Df) M.Miller, QM04 0 p/2 p p/2 p Df challenge: can a jet excite a density wave in the plasma? g radiates energy kick particles in the plasma accelerate them along the jet non-equilibrium process

35. shear generally a phenomenon in crystals but not liquids

36. d+Au Δ2 Au+Au Central 0-12% Triggered Δ1 Δ1 3 particle correlations support cone-like structure pT = 3-4  1-2 GeV/c Need a LOT more statistics to pin down pT ,centrality (&T) dependence of >2 particle correlations! J. Ulery, HP06

37. D. Morrison, SQM’06 other key measurements at RHIC II • elliptic flow at high pT • g elliptic flow • g HBT • map baryon & multi-strange • hadron production • poke at the hadronization • mechanism • probe 2q correlations • in the medium all have large backgrounds require RHIC II luminosity & detector upgrades to reject background & probe as a function of e, m

38. RHIC II will get us • from “oh wow!” • we have found a surprising new form of matter • to “aha!” • here is how it works • how QGP relates to and helps progress in other fields

39. Plasma properties we will measure at RHIC II

40. backup slides

41. QGP energy density • > 1 GeV/fm3 i.e. > 1030 J/cm3 Energy density of matter high energy density: e > 1011 J/m3 P > 1 Mbar I > 3 X 1015W/cm2 Fields > 500 Tesla

42. RAA baryon puzzle… baryons enhanced for pT < 5 GeV/c

43. deposited energy doesn’t thermalize so fast T. Renk Df Dh Dh distribution + longitudinal expansion depopulate Df = p region & shift Mach peak

44. PHENIX preliminary PHENIX preliminary 0-5%

45. use this technique to measure viscosity melt crystal with laser light induce a shear flow (laminar) image the dust to get velocity study: spatial profiles vx(y) moments, fluctuations → T(x,y) curvature of velocity profile → drag forces viscous transport of drag in  direction from laser compare to viscous hydro. extract h/r shear viscosity/mass density PE vs. KE competition governs coupling & phase of matter Csernai,Kapusta,McLerran nucl-th/0604032

46. Hatsuda, et al. Lattice QCD shows qq resonant states at T > Tc, also implying high interaction cross sections Fast equilibration, highopacity (even for charm): how? Molnar multiple collisions using free q,g scattering cross sections doesn’t work! need s x50 in the medium

48. Plasma Coulomb coupling parameter G • ratio of mean potential energy to mean kinetic energy • a = interparticle distance • e = charge • T = temperature • typically a small number in a normal, fully shielded plasma • G = 1/(number particles in Debye sphere) • when G > 1 have a strongly coupled, or non-Debye plasma • many-body spatial correlations exist • behave like liquids, or even crystals when G > 150 • lD < a

49. estimate G using this use l=0.2 fm from electric screening mass e=15 GeV/fm3 from hydro initial conditions constrained by v2 density from dE/dx constrained by RAA put them together: get 0.5 GeV inside Debye sphere FEW particles! ~1 →G ~ 1  quark gluon plasma should be a strongly coupled plasma • As in warm, dense plasma at lower (but still high) T • dusty plasmas, cold atom systems • such EM plasmas are known to behave as liquids! softer than hadronic EOS!!