rapidity equilibration in d + au and au + au systems
Post on 11-Jan-2016
37 Views
Preview:
DESCRIPTION
TRANSCRIPT
Vienna 11 Aug 05 1
Rapidity equilibration in d + Au and Au + Au systems
Rapidity equilibration in d + Au and Au + Au systems
Georg WolschinHeidelberg University
Theoretical Physics
Georg WolschinHeidelberg University
Theoretical Physics
Vienna 11 Aug 05 2
TopicsTopics
Relativistic Diffusion Model for R(y;t) with
three sources for d +Au, Au + Au at RHIC energies
Net protons dn/dy and produced charged particles dn/d at 200 A GeV
Importance of the equilibrated midrapidity
source in d+Au compared to Au+Au Conclusion
Vienna 11 Aug 05 3
Relativistic Diffusion ModelRelativistic Diffusion Model
GW, EPJ A5, 85(1999), 2 sources;
Phys. Lett. B 569, 67 (2003), 3 sources
Nonequilibrium-statistical description of the distribution function R(y,t) in rapidity space,
y = 0.5 · ln((E + p)/(E − p)).
k=1: target-likek=2: proj.-like
k=3: central distr.
Vienna 11 Aug 05 4
Relativistic Diffusion Model for R(y,t)Relativistic Diffusion Model for R(y,t)
• Nonequilibrium-statistical approach to relativistic many-body collisions
• Macroscopic distribution function R(y,t) for the rapidity y
-The drift function (y-yeq)/y
determines the shift of the mean rapidity towards the equilibrium value
- The diffusion coefficient D accounts for the broadening of the distributions due to interactions and particle creations. It is related
to y via a dissipation-fluct.
Theorem, but enhanced due to longitudinal
expansion.
Vienna 11 Aug 05 5
Dissipation-fluctuation relation in y- space
Dissipation-fluctuation relation in y- space
The rapidity diffusion coefficient Dy is calculated fromy and the equilibrium temperature T in the weak-coupling limit as
Note that D ~ T|y as in the Einstein relation of Brownian motion.
The diffusion coefficient as obtained from this statistical consideration
is further enhanced (Dyeff) due to collective expansion.
GW, Eur. Phys. Lett. 47, 30 (1999)
Vienna 11 Aug 05 6
Linear RDM in y- spaceLinear RDM in y- space
The rapidity relaxation time y determines the peak positionsThe rapidity diffusion coefficient Dy determines thevariances.
Note that D ~ T|y as in the Einstein relation of Brownian motion
In a moments expansion and for function initial conditions, the mean values become
and the variances are
<y3(t)>=yeq[1-exp(-t/y)]
Vienna 11 Aug 05 7
Linear RDM in y-spaceLinear RDM in y-space
The equilibrium value yeq that appears in the drift functionJ(y) = -(yeq-y)/y (and in the mean value of the rapidity) is
obtained from energy- and momentum conservation in thesubsystem of participants as
y eq.12ln
.m 1t ey b .m 2
t ey b
.m 2t ey b .m 1
t ey b
with the beam rapidity yb, and transverse masses
mkt mk
2 p kt 2
yeq = 0 for symmetric systems but ≠ 0 for asymmetric systems
mk = participant masses (k=1,2)
Vienna 11 Aug 05 8
Linear RDM in y-spaceLinear RDM in y-space
Analytical RDM-solutions with -function initial conditions at the beam rapidities ±yb in the two-sources model
are obtained as
R( ),y 0 = .12
y yb y yb
In the 3-sources model, a third (equilibrium) term appears.Is there evidence for a 3-sources-approach? Yes
Vienna 11 Aug 05 9
RDM: time evolution of the rapidity density for net protons
RDM: time evolution of the rapidity density for net protons
• Time evolution for 200 A GeV/c S+Au, linear model; function initial conditions
• Selected weighted solutions of the transport eq. at various values of ty
• The stationary solution (Gaussian) is approached for t/Y »1
Vienna 11 Aug 05 10
Central Collisions at AGS, SPSCentral Collisions at AGS, SPS
Rapidity density distributions evolve from bell-shape to double-hump as the energy increases from AGS (4.9 GeV) to SPS (17.3 GeV)
Diffusion-model solutions are shown for SPS energies:
The data clearly show the drift
Vienna 11 Aug 05 11
Central Au+Au @ RHIC vs. SPSCentral Au+Au @ RHIC vs. SPS
• BRAHMS data at SNN=200
GeV for net protons• Central 10% of the cross
section• Relativistic Diffusion Model
for the nonequilibrium contributions
• Discontinuous transition to local statistical equilibrium at midrapidity may indicate deconfinement.
GW, PLB 569, 67 (2003) and Phys. Rev. C 69 (2004)
Vienna 11 Aug 05 12
3-sources RDM for Au+Au3-sources RDM for Au+Au Incoherent superposition of nonequilibrium and equilibrium solutions of the transport equation
yields a very satisfactory representation of the data Disontinuous evolution of the distribution functions with time towards the local thermal equilibrium
distribution
N eq≈ 56 baryons (22 protons)
N1,2≈ 169 baryons (68 protons)
GW, Phys. Lett. B 569, 67 (2003); Phys. Rev. C 69, 024906 (2004)
dN ,y t intdy = .N 1 R 1 ,y t int
.N 2 R 2 ,y t int.N eq R eq( )y
Vienna 11 Aug 05 13
Au+Au at 62.4/200 A GeVAu+Au at 62.4/200 A GeV
RDM-prediction for 62.4 A GeV
(the lower RHIC energy measured by BRAHMS; data analysis is underway)
Dashed areas are thermal equilibrium results with longitudinal expansion
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
GW, hep-ph/0502123, submitted to Phys. Lett. B
Vienna 11 Aug 05 14
Produced particles in the 3 sources RDM:
Charged-hadron (pseudo-) rapidity distributions
Produced particles in the 3 sources RDM:
Charged-hadron (pseudo-) rapidity distributions
PHOBOS data at SNN=130, 200 GeV for charged hadronsCentral collisions (0-6%)
Total number of particles in the 3 sources: 448:3134:448 @ 130 GeV 551:3858:551 @ 200 GeV
Most of the produced charged hadrons at RHIC are in the equilibrated midrapidity region(78%)
M. Biyajima et al., Prog. Theor. Phys.Suppl. 153, 344 (2004)
Vienna 11 Aug 05 15
d+Au 200 GeV charged hadrons:
PHOBOS data d+Au 200 GeV charged hadrons:
PHOBOS data PHOBOS data in
centrality bins
Use 3-sources-RDM with initial particle creation at beam- and equilibrium (yeq)values of the rapidity in the analysis.
10
20
30
40
0B.B. Back et al., PHOBOS collab. 、Phys. Rev. C, in press
(nucl-ex/0409021)
= -ln(tan(/2))
Vienna 11 Aug 05 16
d+Au 200 GeV charged hadrons:
RDM-analysis d+Au 200 GeV charged hadrons:
RDM-analysis
bk
2.5334.8486.1777.2588.1958.494
1: 0-20 %
2: 20-40%
3: 40-60 %
4: 60-80 %
5: 80-100 %
bmax=8.49 fm
Nk
12.7410.2376.7444.3272.0087.372
Min.bias
y eqj
0.9440.760.5640.3470.1690.664
NGlk
13.58.95.42.91.66.6
B.B.Back et al.
Vienna 11 Aug 05 17
d+Au 200 GeV charged hadrons:
RDM-analysis d+Au 200 GeV charged hadrons:
RDM-analysis In the RDM-analysis,determine in particularthe importance of theMoving equilibrium(gluonic) source
Data: B.B. Back et al., PHOBOS coll. 、Phys. Rev. C
Data are for= -ln(tan(/2)) ≈
y GW, M.Biyajima,T.Mizoguchi, N.Suzuki, hep-ph/0503212
Vienna 11 Aug 05 18
d+Au 200 GeV charged hadrons:
RDM-analysis d+Au 200 GeV charged hadrons:
RDM-analysis Mean value and variance ofthe 3 sources for particle production:
Dashed: d- and Au-likeSolid: equilibrated midrapidity sourceTop: total no. of particles
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Vienna 11 Aug 05 19
Convert to pseudorapidity spaceConvert to pseudorapidity space
The conversion from rapidity (y-) to pseudorapidity space requires the knowledge of the Jacobian
The mean transverse momentum is taken to be 0.4 GeV/c.
The average mass is approximated by the pion mass (0.14 GeV) in the central region. In the Au-like region, it is ≈ 0.17 GeV.
[ < m >≈ mp · Z1/N1ch +m · (N1ch − Z1)/N1ch ≈ 0.17GeV ]
Vienna 11 Aug 05 20
d+Au 200 GeV RDM-analysis d+Au 200 GeV RDM-analysis
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Data: PHOBOS coll.Phys. Rev. C, in press
GW, MB,TM,NS, hep-ph/0503212
Vienna 11 Aug 05 21
d+Au indiv. Distributions in the RDM
d+Au indiv. Distributions in the RDM
Data: PHOBOS coll. Phys. Rev. C, in press
GW, MB,TM,NS
Vienna 11 Aug 05 22
d+Au 200 GeV RDM-analysis d+Au 200 GeV RDM-analysis
Full lines:RDM-results with2-minimization
Data: PHOBOS coll.Phys. Rev. C, in press
GW, MB,TM, NS
Vienna 11 Aug 05 23
d+Au 200 GeV time developmentd+Au 200 GeV time development
• The mean values of all three -distributions approach eq for large
times
• The actual collision stops before full equilibrium is reached
Num. Calc. By T. Mizoguchi
Vienna 11 Aug 05 24
Compare d+Au/Au+Au 200 GeV
central source Compare d+Au/Au+Au 200 GeV
central source
Vienna 11 Aug 05 25
Heavy Relativistic SystemsHeavy Relativistic Systems
Parameters for heavy relativistic systems at AGS, SPS and RHIC energies. The beam rapidity is expressed in the c.m. system. The ratio int/y determines how fast the net-baryon system equilibrates in rapidity space. The effective rapidity width coefficient is y
eff, the longitudinal expansion velocity vcoll.
*At 62.4 GeV, yeff will need adjustment to
forthcoming data.
Vienna 11 Aug 05 26
ConclusionConclusion
The Relativistic Diffusion Model with 3 sources describes rapidity distributions for net protons in central Au + Au at RHIC.
The centrality dependence of pseudorapidity distributions for produced charged hadrons in d+Au and Au+Au collisions at RHIC energies (200A GeV) is also accurately described in the RDM.
For produced particles, the equilibrated central source carries 78% of the charged-particle content in Au+Au central collisions, but only 17% in d+Au collisions.
This thermalized central source may be interpreted as indirect evidence for a locally equilibrated quark-gluon plasma.
top related