Classicalization, Scrambling and Thermalization in QCD at high energies Raju Venugopalan Brookhaven National Laboratory Galileo Institute School, February 27-March 3, 2020
Outline of lectures Lecture I: Classicalization: The hadron wavefunction at high energies as a Color Glass Condensate Lecture II: The CGC Effective Field Theory Lecture III: From CGC to the Glasma, key features of the Glasma Lecture IV: Thermalization and interdisciplinary connections
The hadron wave-function at high energies The long arm of saturation Ø Description of gluon saturation, geometrical scaling, and matching to pQCD in the CGC EFT Ø Powerful tools to compute n-body correlators and their energy evolution: MV, BK, JIMWLK Ø Precision computations: state of the art for a number of processes in NLO+NLLx 3
Basic idea: emergent saturation scale grows with energy Typical gluon momenta are large Typical gluon k T in hadron/nuclear wave function k T Bulk of high energy cross-sections: a) obey dynamics of novel non-linear QCD regime b) Can be computed systematically in weak coupling in QCD 4
Traditional picture of heavy-ion collisions *@$#! on *@$#! Well known physicist (circa early 1980s)
Standard model of Heavy-Ion Collisions RV, Plenary Talk, ICHEP (2010), arXiv:1012.4699 Glasma Initial sQGP - Color Glass Hadron perfect fluid Gas Overlap Condensates t We will argue that key features of this space-time evolution can be described from first principles in the Regge limit of QCD
Little Bang Big Bang WMAP data (3x10 5 years) Hot Era QGP Inflation CGC/ Glasma Plot by T. Hatsuda 7
Standard model of Heavy-Ion Collisions RV, Plenary Talk, ICHEP (2010), arXiv:1012.4699 Glasma Initial sQGP - Color Glass Hadron perfect fluid Gas Overlap Condensates t Glasma (\Glahs-maa\): Noun : non-equilibrium matter between Color Glass Condensate (CGC) & Quark Gluon Plasma (QGP )
Big Bang vs. Little Bang Decaying Inflaton Decaying Glasma with occupation # 1/g 2 with occupation # 1/g 2 Explosive amplification Explosive amplification of low momentum small of low momentum small fluctuations fluctuations (preheating) (Weibel instabilities) Interaction of fluctutations/inflaton Interaction of fluctutations/Glasma -> thermalization? -> thermalization? Other common features: topological defects, turbulence,…
Forming a Glasma in the little Bang Problem: Compute particle production in QCD with strong time dependent sources
THE LITTLE BANG How can we compute multiparticle production ab initio in HI collisions ? - perturbative VS non-perturbative, Always non-perturbative for questions of strong coupling VS weak coupling interest in this talk! Similar to computations of pair production in strong E&M fields (Schwinger mechanism) and Hawking radiation in the vicinity of a Black Hole
Approaches to multi-particle production in QCD Two “clean” theoretical limits: Ø Holographic thermalization (based on duality of strongly coupled (g 2 N c -> ∞; N c -> ∞) N=4 SUSY YM to classical gravity in AdS 5 ×S 5 ) Ø Highly occupied QCD at weak coupling (g 2 -> 0 ; g 2 f ~ 1) Our focus: non-equilibrium strongly correlated gluodynamics at weak coupling
Particle production in presence of strong time-dependent sources P n obtained from cut vacuum graphs in field theories with strong time dependent sources 13
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N-particle distributions: inclusive multiplicity Gelis, RV ; NPA776 (2006)135 NPA 779 (2006)177 ] [ SK One-point function in the background field Two-point function SK in the background field 15
Inclusive multiplicity to LO in strong fields: O (1/g 2 ) means arbitrary number of insertions of sources 𝜍 In the Schwinger Keldysh formalism, each node of a tree includes a sum over ± Recursive use of this identity shows that sum of all tree diagrams is is the r etarded solution of classical equations of motion with Hence, leading order result for the inclusive multiplicity in the strong fields in a heavy-ion collision is given by solutions of the QCD Yang-Mills equations !
Inclusive multiplicity at NLO in strong fields: O ( g 0 ) ] [ + Product of classical field and Small fluctuation propagator in classical background field 1-loop correction to classical field
QCD factorization of wee gluon distributions of the nuclei Gelis,Lappi,RV (2008) " # 1 Z Z O NLO = G ( ⇥ u, ⇥ v ) T u T v + � ( ⇥ u ) T u O LO 2 u, � � � v u � linear operator of source T u = � ( ⇥ u ) on initial “Cauchy” surface � A ( ⇥ u ) G ( � v ) u, � These 1-and 2-point have logs " # ✓ Λ + ◆ ✓ Λ − ◆ O NLO = ln H 1 + ln H 2 O LO - are resummed to all orders by p + p − the JIMWLK Hamiltonian Quantum fluctuations that cross-talk between QCD factorization ! nuclei before the collision are suppressed
Factorization + temporal evolution in the Glasma ε=20-40 GeV/fm 3 for τ=0.3 fm @ RHIC Scale set by Q S in the nuclei Glasma factorization => universal “density matrices W” Ä “matrix element”
The lumpy Glasma at LO: Yang-Mills equations Collisions of lumpy gluon ``shock” waves Non-equil. computations on lattice: Krasnitz, RV (1998) Krasnitz, Nara, RV (2001) Lappi (2003 ) Leading order solution: Solution of QCD Yang-Mills eqns D µ F µ ν ,a = δ ν + ρ a A ( x ⊥ ) δ ( x − ) + δ ν − ρ a B ( x ⊥ ) δ ( x + ) x ± = t ± z F µ ν ,a = ∂ µ A ν ,a − ∂ ν A ν ,a + gf abc A µ,b A ν ,c
The lumpy Glasma at LO: Yang-Mills equations Collisions of lumpy gluon ``shock” waves Non-equil. computations on lattice: Krasnitz, RV (1998) Krasnitz, Nara, RV (2001) Lappi (2003 ) Leading order solution: Solution of QCD Yang-Mills eqns D µ F µ ν ,a = δ ν + ρ a A ( x ⊥ ) δ ( x − ) + δ ν − ρ a B ( x ⊥ ) δ ( x + ) h ρ a A ( B ) ( x ⊥ ) ρ a A ( B ) ( y ⊥ ) i = Q 2 S,A ( B ) δ (2) ( x ⊥ � y ⊥ ) Q S (x,b T ) determined from saturation model fits to HERA inclusive and diffractive DIS data
The lumpy Glasma at LO: Yang-Mills solutions Glasma energy density and pressure Initial longitudinal pressure is negative: Goes to P L =0 from below with time evolution
The Glasma: colliding gluon shock waves Glasma color fields matched Glasma color fields to viscous hydrodynamics Krasnitz,Venugopalan, Nucl.Phys.B557 (1999) Lappi, Phys.Rev. C67 (2003) Schenke,Tribedy,Venugopalan,PRL108 (2012) Note: 1 fm/c = 3*10 -24 seconds!
The Glasma at NLO: explosive growth of time-dependent fluctuations Gluon pair production contribution One loop corrections to classical field In our previous discussion, we proved the factorization of only static modes in each nucleus (for which the initial Cauchy surface was the backward “Milne” wedge in spacetime) – these correspond to 𝑞 . =0 But for p η ≠ 0 modes, 24
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