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Flux tubes, fluctuations and flow in A+A collisions

Flux tubes, fluctuations and flow in A+A collisions. B. Schenke. Yang-Mills + Viscous hydro. 2+1-D Yang-Mills. Raju Venugopalan. Ridge workshop, INT Seattle, May 7-11, 2012. Forming a Glasma in the little Bang. Mathematical formulation: Quantum field theory in the presence of

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Flux tubes, fluctuations and flow in A+A collisions

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  1. Flux tubes, fluctuations and flow in A+A collisions B. Schenke Yang-Mills + Viscous hydro 2+1-D Yang-Mills Raju Venugopalan Ridge workshop, INT Seattle, May 7-11, 2012

  2. Forming a Glasma in the little Bang Mathematical formulation: Quantum field theory in the presence of strong time dependent sources Gelis, RV: hep-ph/0601209

  3. Bj, DESY lectures (1975) Bj, DESY lectures (1975) The big role of wee glue (Nucleus-Nucleus Collisions at Fantastic Energies) At LHC, ~14 units in rapidity!

  4. Bj, DESY lectures (1975) The big role of wee glue • What is the role of wee partons ? ✔ • How do the wee partons interact and produce glue ? ✔ • Can it be understood ab initio in QCD ? ✔ • Bottom line: described by classical fields with • important role played by particular quantum fluctuations

  5. Lumpy classical configurations Solutions of Yang-Mills equations produce (nearly) boost invariant gluon field configurations: “Glasma flux tubes” Lumpy gluon fields are color screened in transverse plane over distances ~ 1/QS - Negative Binomial multiplicity distribution. “Glasma flux tubes” have non-trivial longitudinal color E & B fields at early times --generate Chern-Simons topological charge

  6. Glasma Initial Singularity sQGP - perfect fluid Color Glass Condensates Hadron Gas Their quantum descendents t • Two kinds of important quantum fluctuations: • Before the collision: pη=0 modes factorized into the wavefunctions • - responsible for energy/rapidity evolution of wavefunctions • After the collision pη ≠ 0; hold the key to early time dynamics • - responsible for decoherence, isotropization, thermalization

  7. Quantum fluctuations in classical backgrounds: I Gelis,Lappi,RV: 0804.2630, 0807.1306,0810.4829 Suppressed Factorized into energy evolution of wavefunctions JIMWLK factorization: pη=0 (small x !) modes that are coherent with the nuclei can be factorized for inclusive observables W’s are universal “functional density matrices” describing distribution of large x color sources ρ1 and ρ2 of incoming nuclei; can be extracted from DIS or hadronic collisions

  8. Initial conditions for quantum evolution For large nuclei, general considerations about the color structure of higher dimensional representations of color charge density ρa probed give as an initial condition for evolution (MV model) μ2 = Color charge squared per unit area ~ A1/3 Other (sub-leading in A) contributions to these initial conditions Jeon, RV Dumitru,Jalilian-Marian,Petreska

  9. Solution of B-JIMWLK hierarchy B-JIMWLK hierarchy of correlators contains all leading info on charge, rapidity and transverse positions of n-gluon correlations in incoming wavefunctions Correlator of Light-like Wilson lines Tr(V(0,0)V^dagger (x,y)) Rummukainen,Weigert (2003) Dumitru,Jalilian-Marian,Lappi,Schenke,RV, PLB706 (2011)219

  10. increasing seed size increasing seed size 2500 2500 Quantum fluctuations in classical backgrounds: II Romatschke,Venugopalan Fukushima,Gelis,McLerran pη ≠ 0 (generated after collision) modes grow exponentially Quant. fluct. grow exponentially after collision As large as classical field at 1/Qs ! Parametrically suppressed Exponentiate and resum these

  11. increasing seed size 2500 The first fermi: a master formula Also correlators of Tμν • From solutions of B-JIMWLK • Gauge invariant Gaussian spectrum • of quantum fluctuations • 3+1-D solutions of • Yang-Mills equations • This is what needs to be matched to viscous hydrodynamics, event-by-event • Expression computed recently-numerical evaluation in progress Dusling,Gelis,RV

  12. “Jet quenching” in the Glasma Energy-Energy correlators a laBasham, Brown, Ellis, Love Other interesting dynamics such as sphaleron transitions (think Chiral Magnetic Effect) and anomalous viscosity (Asakawa,Bass,Muller)

  13. From nuts to soup: I. constraining initial conditions First understand e+p and p+p: Global analysis of HERA data thus far performed only in the IP-Sat, b-CGC and rcBK saturation models - more detailed JIMWLK analysis is desirable and likely 2 Unintegrated proton gluon dist. from dipole cross-section: kT factorization: compute inclusive dist. of produced gluons at given impact par. :

  14. Bartels,Golec-Biernat,Kowalski Kowalski,Teaney Kowalski,Motyka,Watt The IP-Sat model MV model extended to small x + impact parameter dependence Average gluon radius of the proton extracted from HERA diffractive data Χ2 ~ 1 fits to HERA inclusive,diffractive and exclusive small x data with few parameters

  15. IP-Sat: from HERA to RHIC/LHC Levin,Rezaiean Tribedy, RV: 1011.1895, 1112.2445 e+p constrained fits give good description of p+p data p+p Impact parameter dependence (constrained by HERA diffractive data) important for good agreement with data

  16. Lumpy nuclei: constrained by (limited) DIS data Kowalski, Lappi, RV (2008)

  17. From nuts to soup: II. the IP-Glasma model Schenke,Tribedy,RV:1202.6646 A. Construct color charge distributions, event-by-event: • Positions of nucleons sampled from the Woods-Saxon distribution of each nucleus A • and B • IP-Sat provides QS2(x,bT) for each nucleon – proportional to color charge squared • per unit area g2μp2(details, see T. Lappi, arXiv:0711.3039) • Add all g2μp2 (xT) to obtain g2μA2 (xT) and g2μB2 (xT) • Sample ρA,Ba from local Gaussian distribution for each nucleus: This gives the random static source distribution for event-by-event multi-particle production

  18. From nuts to soup: II. the IP-Glasma model Schenke,Tribedy,RV:1202.6646 B. Solve Yang-Mills equations for two color sources: Matching Yang-Mills across τ=0 gives: These depend non-trivially on the initial color charge configurations in the nuclei 2 1 Yang-Mills eqns. are solved numerically using a lattice discretization to determine Tμν (xT,τ) – same ingredient as in hydro Pure gauge configurations:

  19. Some “hydro initial conditions” in the literature Compilation by B. Schenke

  20. Granularity of initial distributions IP-Glasma Flow MC-KLN These models do not include KNO/NBD multiplicity fluctuations MC-Glauber Dumitru,Nara

  21. Fluctuating energy distributions from event-by-event solutions of Yang-Mills eqns. Schenke,Tribedy, RV, arXiv:1202.6646 Dynamical quantum fluctuations in energy/# of gluons event-by-event Gelis,Lappi,McLerran,arXiv: 0905.3234 Lappi, Srednyak, RV, arXiv: 0911.2068

  22. Flow distributions Schenke,Tribedy, RV, arXiv:1202.6646 First study: may be feasible extract essential physics on how quantum field fluctuations generate flow

  23. Summary • Ab initio framework for multi-particle production in heavy ion collision • Missing ingredient, the “spectrum of initial quantum fluctuations” computed • recently. • IP-Glasma framework (matching Yang-Mills evolution event-by-event to • viscous hydrodynamics) developed. • Has important consequences for initial eccentricities and related flow • moments -- more detailed analyses in the works

  24. Fluctuating energy distributions from event-by-event solutions of Yang-Mills eqns. Tribedy, RV 1112.2445 Dynamical quantum fluctuations in energy/# of gluons event-by-event

  25. IP Glasma-initial eccentricities and temporal evolution

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