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Flux tubes, fluctuations and flow in A+A collisions
Raju Venugopalan
Ridge workshop, INT Seattle, May 7-11, 2012
2+1-D Yang-MillsYang-Mills + Viscous hydro
B. Schenke
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
The big role of wee glue
Bj, DESY lectures (1975)
At LHC, ~14 units in rapidity!
(Nucleus-Nucleus Collisions at Fantastic Energies)
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
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
Color Glass
Condensates
Initial
Singularity
Glasma sQGP - perfect fluid
Hadron Gas
t
Their quantum descendents
Two kinds of important quantum fluctuations:
a)Before the collision: pη=0 modes factorized into the wavefunctions - responsible for energy/rapidity evolution of wavefunctions
a)After the collision pη ≠ 0; hold the key to early time dynamics - responsible for decoherence, isotropization, thermalization
Quantum fluctuations in classical backgrounds: I
JIMWLK factorization: pη=0 (small x !) modes that are coherent with the nuclei can be factorized for inclusive observables
Factorized into energy evolution of wavefunctionsSuppressed
Gelis,Lappi,RV: 0804.2630, 0807.1306,0810.4829
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
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 conditionsJeon, RVDumitru,Jalilian-Marian,Petreska
Solution of B-JIMWLK hierarchy
Correlator of Light-like Wilson lines Tr(V(0,0)V^dagger (x,y))
B-JIMWLK hierarchy of correlators contains all leading info on charge, rapidity and transverse positions of n-gluon correlations in incoming wavefunctions
Rummukainen,Weigert (2003)
Dumitru,Jalilian-Marian,Lappi,Schenke,RV, PLB706 (2011)219
Quantum fluctuations in classical backgrounds: IIRomatschke,VenugopalanFukushima,Gelis,McLerran
increasing seed size
2500
Quant. fluct.grow exponentiallyafter collision
As large as classical field at 1/Qs !
pη ≠ 0 (generated after collision) modes grow exponentially
Exponentiate and resum theseParametrically suppressed
The first fermi: a master formula
Gauge invariant Gaussian spectrum of quantum fluctuations
From solutions of B-JIMWLK
3+1-D solutions of Yang-Mills equations
Also correlators of Tμν
Expression computed recently-numerical evaluation in progressDusling,Gelis,RV
This is what needs to be matched to viscous hydrodynamics, event-by-event
“Jet quenching” in the Glasma
Energy-Energy correlators a la Basham, Brown, Ellis, Love
Other interesting dynamics such as sphaleron transitions (think Chiral Magnetic Effect)and anomalous viscosity (Asakawa,Bass,Muller)
From nuts to soup: I. constraining initial conditions
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
First understand e+p and p+p:
Unintegrated proton gluon dist. from dipole cross-section:
2
kT factorization: compute inclusive dist. of produced gluons at given impact par. :
The IP-Sat model
MV model extended to small x + impact parameter dependence
Bartels,Golec-Biernat,KowalskiKowalski,Teaney Kowalski,Motyka,Watt
Χ2 ~ 1 fits to HERA inclusive,diffractive and exclusive small x data with few parameters
Average gluon radius of the proton extracted from HERA diffractive data
IP-Sat: from HERA to RHIC/LHCLevin,RezaieanTribedy, RV: 1011.1895, 1112.2445e+p constrained fits give good description of p+p data
p+p
Impact parameter dependence (constrained by HERA diffractive data) important for good agreementwith data
Lumpy nuclei: constrained by (limited) DIS dataKowalski, Lappi, RV (2008)
From nuts to soup: II. the IP-Glasma modelSchenke,Tribedy,RV:1202.6646
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 g2μA
2 (xT) and g2μB2 (xT)
Sample ρA,Ba from local Gaussian distribution for each nucleus:
A. Construct color charge distributions, event-by-event:
This gives the random static source distribution for event-by-event multi-particle production
From nuts to soup: II. the IP-Glasma modelSchenke,Tribedy,RV:1202.6646
B. Solve Yang-Mills equations for two color sources:
Pure gauge configurations:
1 2
Matching Yang-Mills across τ=0 gives:
These depend non-trivially on the initial color charge configurations in the nuclei
Yang-Mills eqns. are solved numericallyusing a lattice discretization to determine Tμν (xT,τ)
– same ingredient as in hydro
Some “hydro initial conditions” in the literature
Compilation by B. Schenke
Granularity of initial distributions
IP-Glasma
MC-KLN
MC-Glauber
Flow
These models do not include KNO/NBDmultiplicity fluctuations
Dumitru,Nara
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: 0905.3234Lappi, Srednyak, RV, arXiv: 0911.2068
Flow distributions
First study: may be feasible extract essential physics on how quantum field fluctuations generate flow
Schenke,Tribedy, RV, arXiv:1202.6646
Summary
Ab initio framework for multi-particle production in heavy ion collision-Missing ingredient, the “spectrum of initial quantum fluctuations” computedrecently.
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
Fluctuating energy distributions from event-by-event solutions of Yang-Mills eqns.
Dynamical quantum fluctuations in energy/# of gluons event-by-event
Tribedy, RV1112.2445
IP Glasma-initial eccentricities and temporal evolution