Hadronic Signals of Deconfinement at RHIC
Berndt Müller
Duke University
Riken-BNL “Discovery”
Workshop
May 14-15, 2004
Hadrons encode essential
properties of the partonic
phase of dense, hot matter
created in RHI reactions.
Special thanks to…
•
•
•
•
•
M. Asakawa
S.A. Bass
R.J. Fries
C. Nonaka
T. Renk
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PRL 90, 202303
PRC 68, 044902
PLB 583, 73
PRC 69, 031902
nucl-th/0404015
DUKE PHYSICS
What would it really take…?
Question (from a friend):
What would it take to
convince you that the
quark-gluon plasma
has been discovered
at RHIC?
Answer – If we could show that:
• Hadrons are emitted in universal
equilibrium abundances;
• Hadrons are produced by
recombination of quarks;
• Hadrons show clear evidence of
collective flow (v0 and v2);
• Flow pattern is not universal for
hadrons, but universal for the
constituent quarks.
Chemical equilibrium – not new, but…
Tch does not grow from SPS to RHIC !
Equilibrium fits work…
• Chemical equilibrium fits
work, except where they
should not (resonances
with large rescattering).
RHIC Au+Au @ 200 GeV
– Tch = 160 10 MeV
– µ B = 24 5 MeV
(STAR Preliminary)
Central Au-Au v s=200 GeV
STAR Preliminary
5
Strangeness in Au+Au at RHIC
The strangeness “enhancement” is less than at SPS energy,
as expected from chemical equilibrium paradigm!
(sss)
(qss)
(qqs)
Conclusions (1)
• Clear evidence for a universal hadronization
temperature Tch = Tc is seen in RHIC data;
• Already visible at SPS, but only RHIC data make
the evidence compelling;
• Strangeness equilibration is critical discriminator
between phase space dominance (pp, e+e-) and
equilibration (AA).
Issues to be clarified…
• Are hadron abundances described by universal parameters
[Tc = Tc = Tc( )] or by A- and ECM-dependent parameters
describing chemical freezeout conditions?
• If the hadron abundances are determined by equilibrium at
Tc, then only the deviations from equilibrium should be
non-universal. Do the data confirm this?
• Can these deviations from equilibrium be quantitatively
described by microscopic models of final-state hadronic
rescattering (e.g. by UrQMD)?
Hadronization mechanisms
Recombination was predicted in the 1980’s – but a surprise after all
q q
q
q
q
qq q
Recombination
Baryon
1
Meson
Fragmentation
Baryon
Meson
1
pM
2 pQ
pB
3 pQ
Recombination “wins” …
… always for a thermal source
Fragmentation
still wins for a
power law tail
Baryons compete
with mesons
Recombination of thermal quarks
Relativistic formulation using hadron light-cone frame:
w (r , p)
E
dN M
d 3P
dN
E 3B
d p
d
Quark distribution function at “freeze-out”
P u
(2 )3
P u
d
(2 )3
dxw ( R, xP )w ( R, (1 x) P )
M ( x)
2
,
dxdx ' w ( R, xP )w ( R, x ' P ) w ( R, (1 x x ') P )
, ,
For a thermal distribution, w( r , p )
exp( p u / T )
hadron wavefunctions can be integrated out, eliminating the
model dependence of predictions.
B
( x, x ')
2
Recombination vs. Fragmentation
Recombination:
E
dN M
d 3P
d
P u
(2 )3
dxw ( R, xP )w ( R, (1 x) P )
M ( x)
,
1
Fragmentation:
dN h
E 3
d P
Recombination…
w (r , xP ) w (r , (1 x) P ) exp
P u /T
Meson
w (r , xP ) w (r , x ' P ) w (r , (1 x x ') P ) exp
P u /T
Baryon
P u dz
d
(2 )3 0 z 3
w (r , 1z P )D
h
( z)
…always wins over fragmentation for an exponential spectrum (z<1):
exp( P u / T )
exp( P u / zT )
… but loses at large pT, where the spectrum is a power law ~ (pT) -b
2
Recombination & statistical model
In stat. model, hadron distributions at freeze-out are given by:
d 3 Ni
E 3
d P
fi P u
gi
2
3
fi P u P d
exp P u
B
Bi
with
s
Si
I /T 1
1
I i
For pt
, hadron ratios are identical to those in recombination!
(only determined by hadron degeneracy factors & chem. pot.)
recombination provides a microscopic basis for the apparent chemical
equilibration among hadrons at (moderately) large pt
But: The elliptic flow velocity is approximately additive in valence quark
number, showing partonic, rather than hadronic origin of the elliptic flow.
Recombination vs. Fragmentation
Fries, Bass,
Nonaka, BM
RAA
T = 170 MeV
v- = 0.55c
Greco, Ko,
Levai
CP
Suppression: Baryons vs. mesons
pT (GeV/c)
baryons
mesons
behaves like meson ?
(also -meson)
Conclusions (2)
• Strong evidence for dominance of hadronization by
quark recombination from a thermal, deconfined
phase comes from:
– Large baryon/meson ratios at moderately large pT;
– Compatibility of measured abundances with statistical
model predictions;
– Collective flow (v0) still visible at large pT.
•
-meson is an excellent test case (if not from KK
).
Parton Number Scaling of Elliptic Flow
In the recombination regime, meson and baryon v2 can be obtained
from the parton v2 :
2v
pt
2
p
2
v 2M pt
1 2 v 2p
pt
2
3v 2p
2
and v 2B pt
pt
3
3 v 2p
1 6 v 2p
pt
3
Neglecting quadratic and cubic terms, a simple scaling law holds:
v
M
2
pt
2v
p
2
pt
2
and v
B
2
pt
3v
p
2
pt
3
pt
3
2
3
Hadron v2 reflects quark flow !
Conclusions (3)
• Recombination model works nicely for v2:
– v2(pT) curves for different hadrons
collapse to universal curve for
constituent quarks;
– Saturation value of v2 for large pT is
universal for quarks and agrees with
expectations from anisotropic energy
loss;
– Vector mesons ( , K*) permit test for
influence of mass versus constituent
number (but note the effects of hadronic
rescattering on resonances!)
HG
QGP
Issues to be clarified…
meson
A
The “pQCD approach”
to parton recombination
A
Double parton scattering:
T. Ochiai, Prog. Theor. Phys. 75 (1986) 1184
DPS
SPS
16
1/ 3
A
zpT2
2
s
Baryon enhancement by two-quark scattering and di-quark
formation is possible, but does not naturally imply a
statistical ratio of hadron yields (baryons vs. mesons).
Recombination from a thermal quark ensemble does!
2
Hadron-hadron correlations
The fly in the ointment… ?
“Jet”-like
correlations
persist in the
recombination
regime, for
baryons and
mesons!
How serious is this?
• Not a “theorist’s excuse”:
– Existing recombination models are based on the
assumption of a one-body quark density. Two-hadron
correlations are determined by quark correlations,
which are not included (except by Hwa et al.).
• Two- and multi-quark correlations are a natural result of jet
quenching by energy loss of fast partons.
• Incorporation of quark correlations is straightforward, but
introduces many new parameters: C(p1, p2).
Parton correlations ...
…provide a simple way out?
• Parton correlations trivially translate into hadron
correlations.
• Soft-hard recombination naturally gives such correlations.
• Parton correlations even in the thermal regime?
T. Trainor
Two-point velocity
correlations among
1-2 GeV/c hadrons
awa
y-si
de
sam
e-si
de
Correlations - formalism
2-meson production:
dN MM
d 3 P1d 3 P2
Wn ( p1 ,
V2
1
1
1
2
2
3
3
d
q
d
q
(
q
)
(
q
)
W
P
q
,
P
q
,
P2
1
2
1
2
4
1
1
1
1
6
(2 )
2
2
2
, pn )
w( pi ) 1
n
dN MM
3
d 3 Pd
P2
1
V2
2 1
2 1
w
P
w
P2
1
6
(2 )
2
2
Cqq pi , p j
i j
1 2C0
4Cqq
1
q2 , P2
2
q2
Partons with pairwise
correlations
1 1
P1 , P2
2 2
Meson-meson, baryon-baryon, baryon-meson correlations
CBB
9Cqq , CMB
6Cqq , CMM
4Cqq
Model studies are in progress; please stay tuned…
Conclusions – at last!
How the Q(G)P (“a deconfined phase of QCD matter”) was
discovered at RHIC:
Hadrons are emitted in universal equilibrium abundances;
Most hadrons are produced by recombination of quarks;
Hadrons show evidence of collective flow (v0 and v2);
Flow pattern (v2) is not universal for hadrons, but
universal for the constituent quarks.
T H E EN D
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