1

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