J.Velkovska

1
EoS working group
Convenors Steffen A. Bass
Helen Caines
Julia Velkovska

1. Physics topics in the EoS domain bulk properties
   of hot and dense QCD matter
2. What observables are sensitive to this physics?
3. What have we learned so far ?
4. What are the machine, detector and theoretical
   requirements for future advance ?

2
Physics Questions to be addressed

1. The nature of the transition cross-over or phase
   transition
2. Thermodynamics of the bulk
3. Is the system thermalized ?
4. If yes, how is thermalization achieved and on
   what timescale ?
5. Can we determine the temperature ?
6. What is the EoS ?
7. Character of the medium and dissipative effects
   viscosity, heat capacity, speed of sound,
   diffusion coefficients
8. Hadronization
9. Freeze-out

3
Is there a phase transition ?

• Lattice calculations crossover at m b 0
• Data even-by-event net charge and ltpTgt
  fluctuations exclude critical fluctuations at a
  sharp phase boundary
• Caveat unclear if charge fluctuations in QGP can
  survive hadronization

4
Cross-over and critical point

• Cross-over implications Making QGP is a not a
  Yes/No question ( no sharp boundary between
  hadrons and QGP)
• Goal at RHIC
• Produce matter
• with initial T above the cross-over
• Study its properties
• Where is the tri-critical point ?
• Range of estimates from lattice ( sensitive to
  quark masses used in calculation) , not as
  certain as the calc. of Tc
• mb endpoint/ Tc 1 (Gavai, Gupta), 2
  (Fodor,Katz), 3 (Ejiri et al)
• mbfreezout 450 MeV (AGS) --? 30 MeV (RHIC)
• m bfreezout Tc corresponds to sqrt(s) 25 GeV
  ( accessible to RHIC but not LHC)
• Vary sqrt(s) gt look for enhancement in
  event-by-event fluctuations in ltpTgt and baryon
  number
• Needs energy scan gt luminosity.

• Krishna Rajagopal (Panic05 talk)

5
Lattice Equation of State

• Energy density and pressure deviations from
  ideal gas

6
Lattice EoS
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Can we determine the EoS experimentally ?

• Connection of the thermodynamic properties of
  QGP determined from lattice to the data needs to
  take into account the dynamical effects of the
  finite nuclear collision system
• Microscopic (for the initial state) and
  macroscopic (hydrodynamics) transport models
  describe the collective dynamics EoS is used as
  an input, local thermal equilibrium is assumed at
  all stages, system evolution is computed gt
  results compared to data
• Observables identified particle spectra and
  collective flow

8
Hydro compared to data
p
p
elliptic flow
PHENIX white paper, nucl-ex/0410003
pT spectra
9
Is thermalization achieved ?

• Characteristic mass dependence of elliptic flow
  reproduced by hydrodynamics
• Elliptic flow develops in the early stage of the
  collisions gt early thermalization t 0.6-1 fm/c
• NEED QGP EoS to describe p /p splitting of v2
  but most calculations use ideal gas EoS 1st
  order phase transition. Is this why HBT doesnt
  work ?

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How is thermalization achieved ?

• cannot be addressed by hydrodynamic calculations
• requires microscopic transport progress on
  transport coefficients
• Key observables elliptic flow and nuclear
  modification factors of D and B mesons gt need
  luminosity
• Topic better addressed after detector upgrades
• Phenix Si vertex detector PID in Aerogel/TOF
• Star heavy flavor tracker PID in large area TOF

11
Current status of charm flow measurements
Need detector upgrades statistics
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Temperature of the medium

• Initial Thermal photos
• Difficult measurement . First results from
  Phenix.
• Freeze-out
• Chemical
• Wealth of data on particle ratios
• Described by statistical models
• System appears in chemical equilibrium (including
  strangeness)
• Kinetic vs chemical freeze-out
• Low-pt W spectra with 5 error bars data on
  tape maybe sufficient
• Do we need RHIC II for these measurements?
• EM working group says yes need energy scan to
  disentangle the various contribution to the
  direct photon spectra

13
QGP EoS from thermal g hadron multiplicities

• correlating thermal g slopes hadron
  multiplicities (measure of s)
• Evolution of the effective of degrees of
  freedom, g(s,T), with centrality
• Different behaviour for QGP EoS and hadron gas EoS

DEnterria, Perossounko

• The system maybe too got in 200 GeV AuAu to
  observe a step in the
• effective degrees of freedom vs T
• Proposed smaller species and lower energies
  needs RHIC II luminosity to be doable on a
  reasonable timescale
• However scepticism that 1) such steps exist 2)
  calculation correctly relates observable T with
  the T in hydro

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Properties of the medium beyond ideal
hydrodynamics
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How perfect is the QGP fluid ?

• Ideal Hydro h 0 reproduces the main bulk
  properties observed. Is this enough to conclude
  that the viscosity is 0?
• Deviations from hydro in peripheral collisions,
  intermediate and high pT, away from mid-rapidity
  signal viscous effects and/or incomplete
  thermalization
• Theoretical work on viscous hydro in progress
• Hybrid models hydrohadronic include viscosity
  in the hadronic stage.
• Need to disentangle the two. Spectra and flow
  measurements including multi-strange particles
  and heavy flavor. Detector upgrades needed for
  improved charm flow measurements.
• Can we get the answer from Lattice ?

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Lattice and Viscosity

• Karsch

• Not ab initio lattice calculation hard to do for
  transport coefficients
• What is the viscosity? Answer not coming from
  Lattice

17
UU to test Hydro limit

• Central UU collisions (nose-on-nose) to increase
  the initial energy density
• Surface/volume decreased
• Possible with EBIS
• Could be possible
• before LHC

• Kuhlman, Heinz

18
A method to extract Viscosity

• Stankus

viscosity is a dissipative effect drive local
equilibrium towards global equilibrium. So
higher viscosity means lower v2, and also lower
v3, v4, etc. (v1 is a special case, since it
obeys a sum rule).
v3
v2

• Colliding asymmetric systems will allow us access
  to odd values of vn
• Is v3 more sensitive than v2 to viscosity?
• Need AB running with statistics comparable to
  Run4/5
• Takes advantage of RHIC flexibility (better than
  LHC?)

• Currently work on 3-D hydro and hydroviscosity
• Need to combine Hydro with cascade with Reco

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3D picture of the collisions
BRAHMS, PRL88,202301(2002)
PHOBOS, nucl-ex/0407012

• Hirano

• Need 3D hydro cant assume Bjorken expansion
• Ideal 3D hydro does not reproduce the data
  viscosity incorporated through cascade
• Assymetric system running detector capabilities
  at forward rapidity to constrain models

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Diffusion coefficients

• Charm v2 and Raa linked to charm diff coeff
• Charm number fluctuation liked to diffusion coeff
• Need direct charm identification smaller error
  bars

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Speed of sound insight from jets?
star
phenix

• A dip in the away-side jet at intermediate pT
• Mach shockwaves, Cherenkov radiation
• Access to speed of sound and color di-electric
  constant
• Multi-particle correlations gt need statistics
• Tagged jets shrinking of cone for heavy flavor
  jets gt detector upgrades luminosity

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hadronization

• Hydro/reco/pQCD
• Raa, v2, baryon/meson ratios with PID to high-pt
• Multi-strange baryons need more statistics that
  run4
• phi flows but needs more stat to test flow per
  quark
• Charm - better to do a direct PID to study flow
  and Raa.
• Correlations with identified leading particles
  including multi-strange and charm
• Baryon vs charge transport to test baryon
  junctions
• PID upgrades needed, luminosity to get the
  correlation measurements and the heavy flavor
  measurements

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Summary

• We have learned a great deal about the bulk
  properties of QCD matter from the present data.
  In many cases the theory is catching up.
• Need energy and species scans to turn off QGP
  and follow the evolution of the EoS. Asymmetric
  collisions maybe of help to guide and constrain
  the theory.
• Key physics questions EoS, thermalization,
  viscosity, hadronization
• Key observables are (mostly) in the heavy flavor
  sector, but the more abundant species need to be
  re-measured in different systems/energy
• Detector requirements PID and vertex upgrades,
  forward capabilities
• Machine requirements Many measurements can be
  done with design luminosity, but to accomplish
  the species and energy scans in a reasonable
  time, we need RHIC II luminosity

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Summary II
EoS forward measurements energy and species
scans

• Note1 These ellipses mark the
• Beginning ( not the end of the outlined
  measurements)
• Note2 We need to communicate between the two
  writing groups

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People who contributed talks in the EoS working
group F.Karsch, W. Fischer,T. Hirano, D.
Teaney, V. Greco, D. dEnterria, S.Panitkin, R.
Witt, A. Kuhlman, P. Stankus, J. Thomas, L. Ruan,
G. van Nieuwenhuizen, M. Lamont, A. Milov, E.
Kistenev many others contributed discussions
in the meetings and/or mailing list
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Back-up slides
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Models for Thermalization

• cannot be addressed by hydrodynamic calculations
• requires microscopic transport progress on
  transport coefficients
• Mrowczynski, Lenaghan and Strickland Dumitru,
  Nara plasma instabilities - signature would be
  EM radiation along beam axis in the 0.1 to 1 GeV
  range
• Heavy-quark EFT (van Hees Rapp)
• Multi-gluon processes in a PCM (C. Greiner Z.
  Xu)
• Classical fields particle degrees of freedom
  (Molnar)
• Brueckner-type many-body calculations (Mannarelli
  Rapp)
• Critical opacity at the phase transition
  (Aichelin Gastineau)

• need more ideas/groups
• timescale unknown

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Recombination and charm flow
V2 of electrons

• Direct charm better

V.G. et al., PLB595 (04) 202
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Recent Reco progress

• Higher fock states now included
• Resonances now included
• Neither have big effect

• breaking of the scaling at high pT
• to be test

• Greco

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HBT and Energy scan

• No peak seen in data so far.

• Energy scan could find the soft point
• need comparison to next generation of
• hybrid and micro models

• Panitkin