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Quark Gluon Plasma: The hottest plasma in the world
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outline l Heat nuclei: expect a plasma of quarks and gluons Quantum Chromo Dynamics (QCD) predictions l Create and study it in the laboratory expected QGP signatures useful probes of plasma properties p+p is a crucial benchmark – defines the expected l Surprise! evidence for strong coupling in QGP it is very opaque (“jet quenching”) it is a (~perfect) thermalized fluid it catches even the heavy quarks collective response to deposited energy “shines” brightly
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QCD predicts a phase transition gluons carry color charge gluons interact among themselves theory is non-abelian curious properties at large distance: confinement of quarks in hadrons + +… At high temperature and density: screening by produced color-charges expect transition to gas of free quarks and gluons asymptotic freedom
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Phase diagram of Nuclear Matter As with other material, nuclear matter has many phases. Strong interaction → strong coupling unless very dilute or hot
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non-perturbative QCD – lattice gauge theory T/T c Karsch, Laermann, Peikert ‘99 /T 4 T c ~ 170 ± 10 MeV (10 12 °K) ~ 3 GeV/fm 3 ~15% from ideal gas of weakly interacting quarks & gluons
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plasma l ionized gas which is macroscopically neutral exhibits collective effects l interactions among charges of multiple particles spreads charge out into characteristic (Debye) length, D multiple particles inside this length they screen each other plasma size > D l weakly or strongly coupled depends on density (number of screeners) can behave like a liquid or crystal if strongly coupled l “normal” plasmas are electromagnetic (e + ions) quark-gluon plasma interacts via strong interaction color forces rather than EM, exchange g not non-abelian plasma
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probing a heavy ion collision K p n d, Hadrons reflect (thermal) properties when inelastic collisions stop (chemical freeze-out). we focus on mid-rapidity (y=0) y=1/2 ln[(E+p L )/(E-p L )] CM of colliding system 90° in the lab at collider thermal radiation ( , e + e -, + color-screened QGP pressure builds up Hard scattered q,g (short wavelength) probes of plasma formed
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RHIC at Brookhaven National Laboratory Collide Au + Au ions for maximum volume s = 200 GeV/nucleon pair, p+p and d+A to compare
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The Tools STAR specialty: large acceptance measurement of hadrons PHENIX specialty: rare probes, leptons, and photons
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events viewed by the 4 experiments STAR
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Expected signatures of quark gluon plasma l enhanced strange quark production if T ≥ m s, g + g → s + s l J/ suppression color screening breaks up cc pairs l phase transition signatures if first order: long particle emission time if second order: critical fluctuations in particles l copious thermal radiation l chiral symmetry restoration l jet quenching NB: These were yes/no questions, subject to complicated S/B. But surprises lurk in the properties of the plasma!
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a better way: plasma study by radiated & “probe” particles l as a function of transverse momentum p T = p sin with respect to beam direction) 90° is where the action is (max T, ) p L midway between the two beams! l p T < 1.5 GeV/c “thermal” particles radiated from bulk of the medium “internal” plasma probes l p T > 3 GeV/c jets (hard scattered q or g) heavy quarks, direct photons describe by perturbative QCD produced early→“external” probe
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1 st : benchmark probes in p+p collisions p-p PRL 91 (2003) 241803 Good agreement with pQCD QCD works at RHIC! can use perturbation theory to calculate high p transfer probe production p+p gives baseline prediction for Au+Au 00 mesons are qq bound states produced in the collisions
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peripheral N coll = 12.3 4.0 central N coll = 975 94 jet fragments in Au+Au vs. p+p in central collisions jets are quenched by the plasma
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(colored) q & g lose energy, photons don’t
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jet quenching was expected interaction of radiated gluons with gluons in the plasma greatly enhances the amount of radiation magnitude, p T dependence of observed jet quenching tells us: dN g /dy ~ 1100 or 6 <q < 24 GeV 2 /fm q → transfer from medium to hard gluon per unit path length ^ ^ these are huge!
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Experimenters must ask questions! l What happens to heavy quarks traversing QGP? l Prediction: much less energy loss large quark mass reduces phase space for radiated gluons l Measure via semi-leptonic decays of mesons containing charm or bottom quarks D Au D X e± K
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c,b decays via single electron spectrum compare data to “cocktail” of hadronic decays
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surprise #2: heavy quarks DO lose energy! pQCD: Wicks, Horowitz, Djordjevic, Gyulassy, NuclPhysA784, 426 (2007) Plasmas have collisions among constituents! including it helps larger than expected scattering → stronger coupling BUT – what about e± from B meson decays??!! collisions also increase gluon & u,d quark Eloss e± from heavy quark decay
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Plasmas have collective excitations. Do we? dN/d ~ 1 + 2 v 2 (p T ) cos (2 ) + … “elliptic flow” Almond shape overlap region in coordinate space x y z momentum space
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v 2 is large & reproduced by hydrodynamics large pressure buildup anisotropy happens fast fast equilibration! Surprise #3: must use viscosity ~ 0 “perfect” liquid (D. Teaney, PRC68, 2003) Kolb, et al Hydrodynamics reproduces elliptic flow of q-q and 3q states Mass dependence requires softer than hadronic EOS!!
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Elliptic flow scales with number of quarks transverse KE implication: quarks, not hadrons, are the relevant degrees of freedom when the pressure is built up
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hydrodynamic flow of quarks! Surprise 4: HOW can system thermalize in <0.6 fm/c??? parton scattering insufficient (with pQCD cross section) initial collision of saturated gluon phase? plasma instability (a growing mode transfers energy from particles into wave field)? physics of extremely strong coupling? l long expected, works at RHIC as long as: viscosity per particle ( /S) vanishingly small initial condition: thermalized system in < 0.6 fm/c use QGP equation of state for first few fm/c l NB: learning properties by constraining hydrodynamical calculation + data constraint is standard in plasma physics!
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Strong coupling suggests applying methods of string theory to QGP slide: R. Granier de Cassagnac Policastro,Son, Starinets Maldacena
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AdS/CFT also used to calculate energy loss l Gubser and collaborators l Liu, Rajagopal and Wiedemann l Teaney and Casalderrey-Solana l L. Yaffe and collaborators l Surprise #5: the matter is so strongly coupled that string theorists can have fun with it → large drag force from plasma on heavy quark! NB: this plasma is dominantly made of gluons
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do the heavy quarks equilibrate?? l This is like putting a rock in a stream and watching if the stream can drag it along… l Rate of equilibration gives information on the viscosity of the liquid! Heavy quarks flow!! What do they tell about transport properties of QGP? analogy from J. Nagle
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mechanism of energy loss? nucl-ex/0611018 accepted in PRL Radiative energy loss alone: fails to reproduce v 2 HF. Heavy quark transport model has better agreement with both R AA and v 2 HF. Small relaxation time or diffusion coefficient D HQ inferred for charm. But, agreement with data is not perfect…
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transport: diffusion is related to viscosity l diffusion = brownian motion of particles definition: flux density of particles J = -D grad n l integrating over forward hemisphere: D = diffusivity = 1/3 so D = / 3n D collision time, determines relaxation time data say: it is small! particle concentration = mean free path note: viscosity is ability to transport momentum = 1/3 so D = S → measure D get ! heavy quark + Langevin model → D ~ few times 1/(4 ) NB: /S ≥ 1/(4 from string ↔“QCD” correspondence
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minimum at phase boundary? Csernai, Kapusta & McLerran PRL97, 152303 (2006) quark gluon plasma B. Liu and J. Goree, cond-mat/0502009 minimum observed in other strongly coupled systems – kinetic part of decreases with while potential part increases strongly coupled dusty plasma
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Color screening? the famous J/ suppression J/ bound state of c and cbar quarks) Tests color screening length ( D ) : do bound c + c survive the medium? or does QGP screening kill them? note: it’s not so clear what to expect other observations: strong coupling, collective motion, many collisions…
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suppression at RHIC very similar to that at SPS! why?? more suppressed at y 0 PHENIX PRL98 (2007) 232301 J/ screening length: onium spectroscopy 40% of J/ from and ’ decays they are screened but direct J/ not? Karsch, Kharzeev, Satz, hep-ph/0512239 y=0 y~1.7
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what does non-perturbative QCD say? Lattice QCD shows heavy qq correlations at T > T c, also implying that interactions are not zero Big debate ongoing whether these are resonant states, or “merely” some interactions Color screening – yes! but not fully… Some J/ may emerge intact Hatsuda, et al. J/ is a mystery at the moment! Others may form in final state if c and cbar find each other
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so far we have seen l medium is very opaque to light quarks and gluons to heavy quarks too l system (dominated by gluons) thermalizes very quickly collective hydrodynamic behavior l vanishingly small viscosity i.e. doesn’t support shear stress large cross sections & strong coupling forget about perturbation theory after 0.6 fm/c(!) J/ suppression does not follow the energy density what happens to the energy deposited in the plasma?
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experimental probe of the medium response l study using hadron pairs l high p T trigger to tag hard scattering l second particle to probe the medium Central Au + Au same jet opposing jet collective flow in underlying event
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at high momentum, jets punch through STAR central collisions on away side: same distribution of particles as in p+p but ~5 times fewer! X Phys.Rev.Lett. 97 (2006) 162301
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Surprise #7: particles at lower p T look funny 3<p t,trigger <4 GeV p t,assoc. >2 GeV Au+Au 0-10% preliminary STAR 1 < p T,a < 2.5 < p T,t <4 GeV/c peripheralcentral
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lost energy excites a sound (density) wave? FROM DATA PEAK LOCATION +/-1.23=1.91,4.37 → c s ~ 0.33 (√0.33 in QGP, 0.2 in hadron gas) UNEXPECTED! IS IT RIGHT? relative excitation of sound and diffusion modes in intense study data → sound mode very dominant Gubser, Pufu, Yarom 0706.4307(hep-th) Chesler & Yaffe, 0706.0368(hep-th) strong coupling: try AdS/CFT answer: yes it does!
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Au+Au agrees with p+p at resonances ( ) Enhancement for 0.2 < m ee < 0.8 GeV Also excess → during hadron gas phase Agree at 1.2 < m < 3 GeV and J/ by coincidence (J/ scales as 0 due to scaling as N coll + suppression) Is the medium hot enough to radiate? p+p and Au+Au normalized to 0 region arXiv:0706.3034) measure * → e+e- pairs
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Low mass dilepton excess at RHIC is large submitted to Phys. Rev. Lett arXiv:0706.3034 yield excess grows faster than N large excess below q+q → * → e+e- ? thermal radiation
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R.Rapp, Phys.Lett. B 473 (2000) R.Rapp, Phys.Rev.C 63 (2001) R.Rapp, nucl/th/0204003 low mass enhancement at 150 < m ee < 750 MeV 3.4±0.2(stat.) ±1.3(syst.)±0.7(model) Low-mass: Comparison with theory calculations: min bias Au+Au they include: QGP thermal radiation chiral symmetry restoration A. Toia
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Plasma at RHIC is dense, hot and weird l the quark gluon plasma is strongly coupled l very opaque to fast quarks & gluons, heavy quarks too l viscosity is vanishingly small l thermalization takes < 0.6 fm/c l can apply methods of string theory for QGP properties l partons seem to leave wakes in the plasma l plasma and/or hadron gas shines brightly MYSTERIES: l what is the fate of B quarks in the plasma? l how can the system thermalize so fast? l interaction mechanism for heavy quarks? what’s going on with J/ and color screening? hot gluons show surprising features & their spin is weird too!
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Energy density of matter high energy density: > 10 11 J/m 3 P > 1 Mbar I > 3 X 10 15 W/cm 2 Fields > 500 Tesla QGP energy density > 1 GeV/fm 3 i.e. > 10 30 J/cm 3
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l backup slides
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are J/ ’s regenerated late in the collision? c + c coalesce at freezeout → J/ R. Rapp et al.PRL 92, 212301 (2004) R. Thews et al, Eur. Phys. J C43, 97 (2005) Yan, Zhuang, Xu, PRL97, 232301 (2006) Bratkovskaya et al., PRC 69, 054903 (2004) A. Andronic et al., NPA789, 334 (2007) R. Rapp et al.PRL 92, 212301 (2004) R. Thews et al, Eur. Phys. J C43, 97 (2005) Yan, Zhuang, Xu, PRL97, 232301 (2006) Bratkovskaya et al., PRC 69, 054903 (2004) A. Andronic et al., NPA789, 334 (2007) should narrow rapidity dist. … does it? central peripheral J/ is a mystery at the moment!
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How hot is the medium, anyway? l at RHIC T init ~ 1.5 – 2 T c (~ 300 MeV) indirect! flow, energy loss constrain initial conditions will measure T via radiation of & * → e+e- real photons inclusive/hadron decays QCD direct thermal
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“std” scenario, G(Q 2 =1GeV 2 )=0.4, is excluded by data on >3 sigma level: 2 (std) 2 min >9 Uncertainties from functional from ΔG(x) are not included. Reducing these requires measurement at lower x. Calc. by W.Vogelsang and M.Stratmann Spin of the proton: the surprises continue! arXiv 0704.3599 (accepted for publication)
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must examine lower x Gehrmann-Stirling models GSC: G(x gluon = 0 1) = 1 G(x gluon = 0.02 0.3) ~ 0 GRSV-0: G(x gluon = 0 1) = 0 G(x gluon = 0.02 0.3) ~ 0 GRSV-std: G(x gluon = 0 1) = 0.4 G(x gluon = 0.02 0.3) ~ 0.25 GSC: G(x gluon = 0 1) = 1 GRSV-0: G(x gluon = 0 1) = 0 GRSV-std: G(x gluon = 0 1) = 0.4 charm and bottom identification by displaced vertices , Jet identification with larger acceptance upgrades extend range! NCC direct photons
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baryon puzzle… baryons enhanced for 1.5 < p T < 5 GeV/c
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excess continues to ~ 5 GeV/c STAR
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formation of baryons – coalescence of quarks Greco, Ko, Levai: PRC 68 (2003)034904 Enhancement can be explained by recombination of thermal quarks from an expanding quark gluon plasma. baryons from quark coalescence ►collectively flowing medium focuses them at higher p T ►surplus of energy ahead of fast quark yields extra particle density ►enhances leading baryon in jets speculate:
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Are back-to-back jets there in d+Au? Pedestal&flow subtracted Yes! no medium ↓ no jet quenching
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NA50 and NA60 show suppression in Pb+Pb & In+In suppression follows system size Normal nuclear absorption from p+A data: = 4.18±0.35 mb At CERN (√s = 17 GeV) :
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Is the energy density high enough? 5.5 GeV/fm 3 (200 GeV Au+Au) well above predicted transition! PRL87, 052301 (2001) R2R2 2c Colliding system expands: Energy to beam direction per unit velocity || to beam value is lower limit: longitudinal expansion rate, formation time overestimated
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0 suppressed to high p T, direct at very high p T ?
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The acid test for quark scaling meson (bound state of s+sbar) mass ~ m proton but flows like the mesons PHENIX
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plasma basics – Debye screening l distance over which the 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 of order D D = 0 kT ------- n e e 2 Debye sphere = sphere with radius D l number electrons inside Debye sphere is large N D = N/V D = V D V D = 4/3 D 3 1/2 n e = number density e = charge
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plasma frequency and oscillations l instantaneous disturbance of a plasma → collective motions plasma wants to restore the original charge neutrality electrons oscillate collectively around the (heavy) ions characterized by natural oscillation frequency plasma frequency it’s typically high l restoring force: ion-electron coulomb attraction l damping happens via collisions if e-ion collision frequency < electron plasma frequency pe /2 then oscillations are only slightly damped a plasma condition: electron collision time large vs. oscillation n e e 2 p = ------ m e 0 1/2
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For all distributions described by temperature T and (baryon) chemical potential : dn ~ e -(E- )/T d 3 p Does experiment indicate thermalization? T f ~ 175 MeV
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Strange quarks are indeed enhanced over pp as expected for a hot equilibrated system!
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