QCD Theory 6Em2pt Formation of Quark-Gluon Plasma In

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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

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 ω−1−O(αs) dω ∼

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 ω−1 (when ω 0) dω ∼ →

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 ω−1 (when ω 0) dω ∼ →

Color charge

I Charge has cloud of gluons

I But now: gluons are source of new gluons: cascade dN ω−1−O(αs) dω ∼ 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 √s) √s y ln √s 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 √s 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 †(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:

i i i A = A(1) + A(2) τ=0 ig Aη = [Ai , Ai ] |τ=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 † (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 † (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 ] |τ=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 † (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 ] |τ=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 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: /

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. 2nd order hydro LHC estimate τ 1fm ∼ 1/1