QGP hydro + hadronic cascade model: Status report
Tetsufumi HiranoDept. of Physics
The Univ. of Tokyo
RCNP, Oct. 29-30, 2007RCNP, Oct. 29-30, 2007
TH, U.Heinz, D.Kharzeev, R.Lacey and Y.Nara, PLB636(2006)299; in preparationTH, U.Heinz, work in progress.
Outline
Introduction Momentum Space (elliptic flow)
Mass ordering of v2(pT) revisited Violation of mass ordering for mesons Soft EOS in CGC case?
Configuration Space (femtoscopy) Source functions from hydro + cascade 1D, 3D (rside, rout, rlong)-directions
Summary
Motivation
• To understand the QGP in H.I.C., one needs to develop a dynamical framework. • One example of agreement btw. data and theory is not sufficient. (Concerning accidental reproduction)• One needs to improve his/her model continuously toward establishment of the “observational QGP physics”.
Mechanism of Mass Ordering?
STAR white paper (’05) PHENIX white paper (’05)
Lines: Results from Ideal hydro
A Hybrid Approach: QGP hydro + hadronic cascade
0collision axis
time
Au Au
QGP fluid
Initial condition:•Transverse Glauber•Longitudinal “BGK triangle”QGP fluid:•3D ideal hydrodynamics (Hirano)•massless free u,d,s+ggas + bag const. •Tc = 170 MeV
Hadron gas:•Hadronic cascade, JAM1.09 (Nara)•Tsw = 169 MeV
hadron gasTH et al.(’06)
(1D) Bass, Dumitru (2D) Teaney, Lauret, Shuryak, (3D) Nonaka, Bass, Hirano et al.
Pseudorapidity Distribution
Tune initial parameterswith Tth = 100MeVto reproduce dN/deta.Then, switch to hadroniccascade below T=Tsw.Caveat: Rejecting in-coming particles at Tsw
pT spectra for pi, K, and p
Reasonable reproduction of yields and spectrain low pT region (pT<~1.5 GeV/c)
TH et al. (in preparation).
v2(pT) for pi, K, and p
OK!
Fail to reproduce data due to(absence of) fluctuation of geometryMiller&Snelling (’03), Bhalerao&Ollitrault(’06)Andrade et al (’06),Drescher&Nara (’07)Browniowski et al(’07)
TH et al. (in preparation).
Hydro + Cascade at Work in Forward Rapidity Regions
Adapted from S.J.Sanders (BRAHMS) @ QM2006
Origin of Mass Ordering
Mass ordering behaviorresults from hadronicrescatterings.Not a direct signal of “perfect fluid QGP”Interplay btw. ideal QGP fluid and dissipative hadron gas
TH and M.Gyulassy; TH et al. (in preparation).
b=7.2fm
b=7.2fm
Why they shift oppositely?
protonspions
pT
v 2(p
T)
v 2
<pT>
must decrease with proper timev2 for protons can be negativeeven in positive elliptic flow
TH and M.Gyulassy, NPA769,71(06) P.Huovinen et al.,PLB503,58(01);TH et al, in preparation
MESON FLOW
What happens to strangeness sector?
Additive Quark Model in Transport Codes (JAM/RQMD/UrQMD)
For cross sections without exp. data,
Expected to be very small for phi, Omega, etc.
Distribution of Freeze-Out Time
b=2.0fm
(no decay)
TH et al. (in preparation).
Early kinetic freezeout for multistrange hadrons: van Hecke, Sorge, Xu(’98)
-meson case
in pT < 1 GeV/c
Just after hadronization Final results
T = Tsw = 169 MeV
b=7.2fm b=7.2fm
TH et al. (in preparation).
Caveat: Published PHENIX data obtained in pT>~1GeV/c for mesons This is NOT obtained within ideal hydrodynamics.
What happens if -meson follows radial flow?
Of course, mass ordering is seen in hydro calculations
CGC INITIAL CONDITIONS
CGC Initial Condition
•Unintegrated gluon distributiona.la. Kharzeev, Levin, and Nardi•Gluon production via kT factorization formula •Count deposited energy in dV at (0,x,y,s), 0 = 0.6fm/c
Transverse profile: Entropy density
Longitudinal Profile:Brodsky-Gunion-Kuhn triangle
Color Glass CondensateGlauber-BGK type
sx(fm) s
x(fm)
ene.
dens
ity
ene.
dens
ity
Two Hydro Initial Conditions Which Clear the “First Hurdle”
1. CGC model Matching I.C. via e(x,y,) 2.Glauber model (as a reference) Npart:Ncoll = 85%:15%
Centrality dependence Rapidity dependence
Kharzeev,Levin, and NardiImplemented in hydro by TH and Nara
v2(Npart) from CGC + QGP Fluid + Hadronic Gas Model
Glauber: Early thermalization Discovery of Perfect Fluid QGPCGC: No perfect fluid? Additional viscosity
required in QGP
Important to understand initial conditions much better for making a conclusion
TH et al.(’06)
Adil, Gyulassy, Hirano(’06)
Large Eccentricity from CGC Initial Condition
xx
yy
Pocket formula (ideal hydro): v2 ~ 0.2 @ RHICOllitrault(’92)
Hirano and Nara(’04), Hirano et al.(’06)Kuhlman et al.(’06), Drescher et al.(’06)
Soft QGP EoS
Soft EOS?(equilibrium)orViscosity?(non-eq.)
Soft EoS reduces v2
as it should
Summary of flow part
A QGP fluid with hadronic rescatteringOrigin of mass ordering for v2(pT)
Radial flow effect, not “mass effect”.Violation of mass ordering for mesons
Mass ordering itself is not a direct signal of perfect fluidity! Interplay btw. QGP fluids and hadron gases.
CGC I.C. is “eccentric”. Soft EOS is needed within ideal hydrodynamics.
Femtoscopy fromHydro + CascadeFrom momentum space
to configuration space
Source Imaging
Primed in PCMS(P = 0)
Source Imaging:Inverse problem from C to D with a kernel K
No more Gaussian parametrization!
Source Imaging:Inverse problem from C to D with a kernel K
No more Gaussian parametrization!
Koonin-Pratt eq.:
Source function and normalized emission rate
(Brown&Danielewicz (’97-))
Distribution of the Last Interaction Point from Hydro + Cascade
Blink: Ideal Hydro, Kolb and Heinz (2003)
x-t x-y
px ~ 0.5 GeV/c for pions•Long tail ( decay? elastic scattering?)•Positive x-t correlation
1D Source Function from Hydro + Cascade
0.48 < KT <0.6 GeV/c0.2 < KT <0.36 GeV/c
•Angle averaged source function•Broader than PHENIX data•Almost no KT dependence PHENIX data•Significant effects of hadronic rescatterings
KT=PT/2
Omega Decay or Not?
Switch off omega decay by hand in hadronic cascade Long tail still seen. Soft elastic scattering of pions?
b=5.8fm
3D Source Function from Hydro + Cascade (preliminary!)
side out long
•Source function in PCMS•1fm-slice in each direction •0.2<KT<0.4 GeV/c, || < 0.35, +-+, --- pairs•Red: Without rescattering, Black: With rescattering•No longer Gaussian shape (Lines: Gaussian)•Broaden by hadronic rescatterings
Summary of Femtoscopy
1D- and 3D-source functions from a dynamical model (QGP hydro + hadronic cascade)Significant rescattering effects are seen.Source function is no longer Gaussian.Long tail in 1D source function is described
within hadronic rescatterings.KT dependence?
Outlook
Pair-angle dependence of source function in non-central collisions
Other pairs (K, p, ,…) correlation to investigate interaction
(with Ohnishi-san)Just get started. Many other things to
do…