QCD theory Formation of quark-gluon plasma in QCD T. Lappi University of Jyvaskyl¨ a,¨ Finland Particle physics day, Helsinki, October 2017 1/16 Outline I Heavy ion collision: big picture I Initial state: small-x gluons I Production of particles in weak coupling: gluon saturation I 2 ways of understanding glue I Counting particles I Measuring gluon field I For practical phenomenology: add geometry 2/16 A heavy ion event at the LHC How does one understand what happened here? 3/16 Concentrate here on the earliest stage Heavy ion collision in spacetime The purpose in heavy ion collisions: to create QCD matter, i.e. system that is large and lives long compared to the microscopic scale 1 1 t L T > 200MeV T T t freezefreezeout out hadronshadron in eq. gas gluonsquark-gluon & quarks in eq. plasma gluonsnonequilibrium & quarks out of eq. quarks, gluons colorstrong fields fields z (beam axis) 4/16 Heavy ion collision in spacetime The purpose in heavy ion collisions: to create QCD matter, i.e. system that is large and lives long compared to the microscopic scale 1 1 t L T > 200MeV T T t freezefreezeout out hadronshadron in eq. gas gluonsquark-gluon & quarks in eq. plasma gluonsnonequilibrium & quarks out of eq. quarks, gluons colorstrong fields fields z (beam axis) Concentrate here on the earliest stage 4/16 Color charge I Charge has cloud of gluons I But now: gluons are source of new gluons: cascade dN !−1−O(αs) d! ∼ Cascade of gluons Electric charge I At rest: Coulomb electric field I Moving at high velocity: Coulomb field is cloud of photons (“equivalent photon approximation”) dN !−1 (when ! 0) d! ∼ ! 5/16 Cascade of gluons Electric charge I At rest: Coulomb electric field I Moving at high velocity: Coulomb field is cloud of photons (“equivalent photon approximation”) dN !−1 (when ! 0) d! ∼ ! Color charge I Charge has cloud of gluons I But now: gluons are source of new gluons: cascade dN !−1−O(αs) d! ∼ 5/16 Initial state is small x I Gluons ending in central rapidity region: multiple splittings from valence quarks I Emission probability αs dx=x =) rapidity plateau for ∆y 1/αs I Many gluons, in fact X 1 n αs N (αs ln ps) ps y ln ps n! ∼ ∼ n ∼ 〉 14 η pp(pp), INEL AA, central /d ch ALICE ALICE 12 N CMS CMS d 〈 UA5 ATLAS 〉 10 PHOBOS PHOBOS part 2 ISR PHENIX 0.155(4) N ∝ 〈 BRAHMS s 8 pA(dA), NSD STAR ALICE NA50 PHOBOS 6 4 ∝ s0.103(2) 2 |η| < 0.5 0 10 102 103 104 s (GeV) NN 6/16 Particle production I Perturbative gluon production dNg 1 (dimensionally) 2 2 4 dy d p d x ∼ pT I Total number of gluons Z dN Z dp d2p g T 2 2 3 dy d p d x ∼ pT I Transverse energy (gauge invariant) Z dN Z dp d2p g T 2 2 2 dy d p d x ∼ pT Something needs to happen to regulate this; either at I Confinement scale: strings, meson/baryon dof’s I Weak coupling scale: saturation =) at high ps 7/16 2 ways of doing weak coupling QCD at small x I Parton picture, Infinite Momentum Frame (IMF) I Measure numbers of partons: parton distributions I Calculate their interactions as pQCD scattering Talk by Paakkinen + Correct physical picture at large x, large pT - But including saturation is hard I Target rest frame picture I Small-x gluons = classical color field I Quantify as eikonal scattering amplitude of probe Talk by Hanninen¨ + Gluon saturation “automatic”: consequence unitarity! - Only high energy: connecting to large-x, pT tricky. 8/16 “EKRT” model: turn this argument quantitative by I Counting final state gluons I Fitting constant κ to data Gluon saturation in IMF: nonlinear interactions Saturation when phase space density of gluons large 2 I Number of gluons xG(x; Q ) 2 I Size of one gluon 1=Q ∼ 2 I Transverse space available πRp I Coupling αs Estimate in terms of gluon numbers Nonlinearities important when 2 2 1 πR αsxG(x; Q ) p ∼ Q2 (LHC kinematics: Solve for Q2 = Q2; “saturation scale” s Qs ≈ 1 .. 2 GeV) 9/16 Gluon saturation in IMF: nonlinear interactions Saturation when phase space density of gluons large 2 I Number of gluons xG(x; Q ) 2 I Size of one gluon 1=Q ∼ 2 I Transverse space available πRp I Coupling αs Estimate in terms of gluon numbers Nonlinearities important when dNg 1 πR2 = κ p dy Q2 (LHC kinematics: Solve for Q2 Q2; “saturation scale” = s Qs ≈ 1 .. 2 GeV) “EKRT” model: turn this argument quantitative by I Counting final state gluons I Fitting constant κ to data 9/16 Target rest frame Example: DIS process γ∗ + A ! X ∗ I γ consists of partons, to first approximation a qq¯ dipole I Partons traverse target gluon field Eikonal (high energy) limit Interaction: Wilson line in target classical color field Z + − a V = P exp ig dx Aa t − Scattering amplitude for dipole probe: 1 (x y) = 1 Tr V y(x)V(y) 1 N − − Nc ≤ 10/16 Gluon saturation in dipole picture: unitarity I Scattering amplitude must satisfy unitarity limit 1 z N ≤ γ∗ (probability < 1) rT 1 z I Two gluon exchange: − σˆ r2xG(x; Q2 1=r2) r P ( ) αs 2 ∼ N ∼ πRp 2 2-gluon exchange wrong when Q2 1 Q2 αsxG(x;Qs ) r2 . s 2 ∼ ∼ πRp Gluon saturation in target rest frame I Degree of freedom is scattering amplitude (not number of partons) I Saturation appears as unitarity constraint =) Built into formalism; does not look dynamical. 11/16 τ = 0: At i i i A = A(1) + A(2) τ=0 ig Aη = [Ai ; Ai ] jτ=0 2 (1) (2) Solve numerically equations of motion for τ > 0 Get energy density, pressure =) plug into hydrodynamics Gluon fields in AA collision Now two colliding nuclei =) two color currents µ µ+ − µ− + J = δ ρ(1)(x)δ(x ) + δ ρ(2)(x)δ(x ) Classical Yang-Mills 2 pure gauges + x− t x i Ai = V (x)@ V y (x) (3) η = cst. (1,2) g (1,2) i (1,2) Aµ = ? τ = cst. V(1,2)(x): same Wilson line (1) (2) z Aµ = pure gauge 1 Aµ = pure gauge 2 (4) Aµ = 0 12/16 τ = 0: Solve numerically equations of motion for τ > 0 Get energy density, pressure =) plug into hydrodynamics Gluon fields in AA collision Now two colliding nuclei =) two color currents µ µ+ − µ− + J = δ ρ(1)(x)δ(x ) + δ ρ(2)(x)δ(x ) Classical Yang-Mills 2 pure gauges + x− t x i Ai = V (x)@ V y (x) (3) η = cst. (1,2) g (1,2) i (1,2) Aµ = ? τ = cst. V(1,2)(x): same Wilson line (1) (2) z At τ = 0: Aµ = pure gauge 1 Aµ = pure gauge 2 i i i A = A(1) + A(2) (4) τ=0 Aµ = 0 ig Aη = [Ai ; Ai ] jτ=0 2 (1) (2) 12/16 Gluon fields in AA collision Now two colliding nuclei =) two color currents µ µ+ − µ− + J = δ ρ(1)(x)δ(x ) + δ ρ(2)(x)δ(x ) Classical Yang-Mills 2 pure gauges + x− t x i Ai = V (x)@ V y (x) (3) η = cst. (1,2) g (1,2) i (1,2) Aµ = ? τ = cst. V(1,2)(x): same Wilson line (1) (2) z At τ = 0: Aµ = pure gauge 1 Aµ = pure gauge 2 i i i A = A(1) + A(2) (4) τ=0 Aµ = 0 ig Aη = [Ai ; Ai ] jτ=0 2 (1) (2) Solve numerically equations of motion for τ > 0 Get energy density, pressure =) plug into hydrodynamics 12/16 Result: initial gluon fields 0.8 2 Bz 2 Ez ] 0.6 2 2 /g B 4 T 2 µ) 2 0.4 ET [(g 0.2 0 0 0.5 1 1.5 2 2 g µτ I Initial condition is longitudinal E and B field, I Depend on transverse coordinate with correlation length 1=Qs =) gluon correlations What was the use of classical approximation? I Enables nonlinear treatment, which makes result finite I No cutoff imposed by hand 13/16 Fluctuating geometry A heavy ion is not smooth: I Nucleon positions fluctuate from event to event I Initial plasma is spatially very anisotropic T [MeV] 200 6 I Interactions/collectivity 4 160 + Temperature/pressure 2 120 gradients 0 80 =) Anisotropic force, -2 acceleration -4 40 momentum anisotropy in -6 0 final state -6 -4 -2 0 2 4 6 14/16 Add nucleon positions and shape Confinement scale physics Model by Monte Carlo Glauber: I Draw positions of nucleons I Nucleon profile Rp ? ∼ I Jargon of the field: Participant nucleons Binary collisions (NN collisions) Understanding collision requires I Consistently combine 0.8 IP-Glasma U+U (Random) 0.7 MC-Glauber MC-KLN 1. QCD particle production 0.6 0.5 2 2. Geometry MC Glauber ε ∼ 0.4 0.3 I Hydrodynamical evolution 0.2 0.1 I Successfully compute 0 100 200 300 400 500 Npart multitude of soft observables next talk Kim 15/16 0.9 0.9 0.9 P P P 0.8 0.8 S 0.8 S S ® ® ® ) ) ) 0.7 0.7 ) 0.7 ) ) 4 4 0.6 4 0.6 0.6 Ψ Ψ Ψ 0.5 0.5 − 0.5 − − 2 2 0.4 2 0.4 0.4 Ψ Ψ Ψ ( ( ( 0.3 0.3 2 0.3 4 8 1 ( ( ( s LHC 2.76 TeV s 0.2 0.2 s 0.2 o o o c Pb +Pb c 0.1 0.1 c 0.1 Conclusions: from­ QCD to heavy­ ion event ­ 0.0 0.0 0.0 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 centrality [%] centrality [%] centrality [%] I Formation of QCD0.8 plasma: 0.8 0.8 P 0.7 η/s =0.20 P 0.7 P 0.7 S S S QCD in nontrivial® regime:η/s =param1 ® ® ) 0.6 ) 0.6 ) 0.6 ) η/s =param2 ) ) 3 0.5 6 0.5 6 0.5 I High gluon phaseΨ spaceη/s =param3 Ψ Ψ 0.4 0.4 0.4 − η/s =param4 − − density: nonperturbative2 0.3 2 0.3 3 0.3 Ψ ATLAS Ψ Ψ ( 0.2 ( 0.2 ( 0.2 6 6 6 I Dynamic phenomena:( pT =[0.5 5.0] GeV ( ( s 0.1 s 0.1 s 0.1 o o o c 0.0 c 0.0 c 0.0 no imaginary­ time lattice! ­ ­ 0.1 0.1 0.1 I But possible in weak0 10 coupling20 30 40 50 60 70 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 centrality [%] centrality [%] centrality [%] (or very strong coupling talk Jokela ) Event plane correlators I Contact with experiments: 0.12 η/s =0.20 RHIC 200 GeV Au +Au η/s =param1 I Combine with confinement pT =[0.15 2.0] GeV 0.10 η/s =param2 2 η/s =param3 / 0.08 scale nuclear geometry ª η/s =param4 4 © 2 v (b) I Spacetime evolution via , 0.06 ª 2 © 2 0.04 hydrodynamics: multiple soft v 0.02 STAR v 2 observables 2 STAR v2 ©4ª/2 0.00 © ª =) Properties of QCD matter 0 10 20 30 40 50 60 70 80 centrality [%] Hydro calculations from Eskola et al =) Momentum harmonics Colors: different viscosity 16/16 Thermalization at weak coupling 10000 -1/2 λ=0 ~x I Initial state classical, L ξ=10 /P T 1000 f (k) 1 1 ξ=4 αs ∼ 100 I Expansion, scattering off Anisotropy: P 10 plane =) occupy λ=1.0 λ =0.5 λ=5.0 λ=10 ? 1 more phase space 0.01 0.1 1 =) f (k) decreases Occupancy: <pλf>/<p> Kurkela, Zhu arXiv:1506.06647 I Kinetic theory for f (k) 1 H αs Kinetic theory simulation in I Major problem is expanding system, initial isotropization anisotropy to a final I Close to isotropy: equilibrium.