D. Porok

J/Ψ-suppression in the
hadron resonance gas
Dariusz Prorok
Institute of Theoretical Physics
University of Wroclaw
Wroclaw, 17 February 2014
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All began in the early 1989...
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Why J/Ψ ?
J/Ψ suppression as a signal for the QGP appearance in a
heavy-ion collision.
T. Matsui and H. Satz, Phys. Lett. B178, 416 (1986)
V (r) = σ · r −
α
,
r
T =0
In the QGP (T ≥ Tc ):
r
r
α
V (r) = σ · rD 1 − exp −
− exp −
rD
r
rD
rD = rD (T ) - screening radius
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Basic ingredients of our model
I
Hadron resonance gas exists from the beginning (i.e. from t0 ),
the gas consists of all particles from PDG up to 2 GeV.
I
The gas expands longitudinally and transversally.
I
J/Ψ disintegration is due to inelastic scattering with
constituents of the gas.
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Sketch of a central collision
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Solution of hydro equations for n0B = 0
G. Baym, B. L. Friman, J. P. Blaizot, M. Soyeur and W. Czyż,
Nucl. Phys. A407, 541 (1983)
I
In the z = 0 plane the transverse expansion proceeds in the
form of the rarefaction wave which moves inward with the
sound velocity cs .
I
Inside the temperature/density is constant (radial velocity
vr = 0), in the narrow stripe of the rarefaction wave it
decreases rapidly (radial velocity increases).
I
In the z 6= 0 plane and the moment t the transverse √
expansion
looks the same as in z = 0 but at the moment τ = t2 − z 2 .
Longitudinal velocity vz = z/t.
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z = 0 plane
Figure: View of an AA collision at impact parameter b. The region where
the nuclei overlap has been hatched and its area equals Sef f .
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J/Ψ inelastic scattering in a hadron gas
Inspired by J. P. Blaizot and J. Y. Ollitrault, PRD39, 232 (1989),
generalized in:
DP and L. Turko, PRC 64, 044903 (2001)
J/Ψ + hi −→ D + D̄ + X
l
X
∂f
~ = −f
+ ~v · ∇f
∂t
Z
i=1
p
E = M 2 + p~ 2 ,
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ν
d3 q
i pν q
fi (~r, ~q, t)σi vrel
3
(2π)
EE 0
q
E = m2i + ~q 2
0
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Formal solution of the kinetic equation
f (~r, p~, t) = f0 (~r − ~v (t − t0 ), p~)
( Z
l Z
t
X
0
× exp −
dt
t0
i=1
ν
d3 q
0
0
i pν q
f
(~
r
−
~
v
(t
−
t
),
~
q
,
t
)σ
v
i
i
rel
(2π)3
EE 0
)
p~ - momentum of J/Ψ
~v =
p
~
E
- velocity of J/Ψ
f0 (~r, p~) - initial distribution of J/Ψ at t0 = 1 fm
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Hadron distributions in the presence of a flow
fi (~r, ~q, t) =
(2si + 1)
1
n ν
o
3
(2π~c) exp qν u (~r,t)−µi (~r,t) ± 1
T (~
r,t)
µi (~r, t) = Bi µB (~r, t) + Si µS (~r, t)
uν (~r, t) =
1
(t, 0, 0, z) ,
τ
T (~r, t) = T (z, t) = T (0, τ ) ,
µB(S) (~r, t) = µB(S) (z, t) = µB(S) (0, τ )
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J/Ψ survival factor in the hadron gas
R 2 R 3
d pT d r F(~r, y, p~T , t)|t=∞
NHRG (y, b) = R 2 R 3
d pT d r F(~r, y, p~T , t)|t=t0
F(~r, y, p~T , t) = MT cosh(y) · f (~r, p~T , pL = MT sinh(y), t)
f0 (~r, p~) = f0 (~s) · g0 (pT ) · h0 (y) ,
f0 (~s) =
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~s ∈ Sef f
TA (~s)TB (~s − ~b)
TAB (b)
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J/Ψ survival factor in the hadron gas, cont.
NHRG (y, b) =
1
R
dpT MT g0 (pT )
× exp
Z
Z
tfinal
−
dt
t0
dpT MT g0 (pT )
l Z
X
i=1
pν qiν
d3 q
f
(~
q
,
t)σ
v
i
i rel,i
(2π)3
EEi0
tf inal - average time of leaving the hadron medium by J/Ψ with
the velocity ~v and produced in a collision at impact parameter b
σi = σb for i = baryon,
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σi = 23 σb for i = meson
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Full survival factor of J/Ψ
Possible J/Ψ disintegration in the nuclear matter (pA data):
NNA ∼
= exp {−σb ρ0 hLi}
th
NJ/Ψ
= NNA · NHRG
Only ∼ 60% of J/Ψ measured are directly produced during
collision, so the realistic J/Ψ survival factor should read
N = 0.6 · NJ/ψ + 0.3 · Nχ + 0.1 · Nψ0 .
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J/Ψ suppression at SPS
J/Ψ experimental survival factor only for midrapidity, y ≈ 0
exp
NJ/Ψ
=
AB
Bµµ σJ/ψ
AB
σDY
pp
Bµµ σJ/ψ
pp
σDY
Theoretical predictions: DP and L. Turko, PRC 64, 044903 (2001).
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J/Ψ suppression for Pb-Pb @ 17.2 GeV
pp
pp
Figure: J/Ψ survival factor times Bµµ σJ/ψ
/σDY
for n0B = 0.25 fm−3
and Tf.o. = 140 MeV: σb = 4 mb (solid) and σb = 5 mb (dashed).
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J/Ψ suppression at RHIC
J/Ψ experimental survival factor = J/Ψ nuclear modification
factor
exp
NJ/Ψ
≡ RAA =
AA
dNJ/Ψ
dy
pp
dNJ/Ψ
Ncoll · dy
Theoretical predictions: DP, L. Turko and D. Blaschke, Phys.Lett.
B690, 352 (2010).
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J/Ψ suppression for Cu-Cu @ 200 GeV
Figure: J/Ψ survival factor as a function of rapidity for a given centrality.
Curves correspond to n0B = 0, σb = 4 mb and Tf.o. = 150 MeV, circles
are the PHENIX data.
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J/Ψ suppression for Cu-Cu @ 200 GeV
Figure: J/Ψ survival factor as a function of rapidity for a given centrality.
Curves correspond to n0B = 0, σb = 4 mb and Tf.o. = 150 MeV, circles
are the PHENIX data.
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J/Ψ suppression for Au-Au @ 200 GeV
Figure: J/Ψ survival factor as a function of rapidity for a given centrality.
Curves correspond to n0B = 0, σb = 4 mb and Tf.o. = 150 MeV, circles
are the PHENIX data.
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J/Ψ suppression for Au-Au @ 200 GeV
Figure: J/Ψ survival factor as a function of rapidity for a given centrality.
Curves correspond to n0B = 0, σb = 4 mb and Tf.o. = 150 MeV, circles
are the PHENIX data.
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J/Ψ suppression at RHIC @ 200 GeV
Figure: J/Ψ survival factor as a function of centrality for mid (solid) and
forward (dashed) rapidity. Curves correspond to n0B = 0, σb = 4 mb and
Tf.o. = 150 MeV, symbols are the PHENIX data.
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Conclusions
1. Up to RHIC energies the observed J/Ψ suppression might be
explained without QGP.
2. In this model suppression at y 6= 0 is stronger than for y = 0,
as it is observed at RHIC.
3. It seems that geometry of the collision is responsible in great
part for the pattern of J/Ψ suppression observed at SPS and
RHIC.
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Sto Lat Ludwik!
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How to obtain T (t), µB (t) and µS (t)?
Inside the rarefaction wave only the Bjorken longitudinal expansion:
s(t) =
s0 t0
,
t
nB (t) =
n0B t0
,
t
nS = 0 .
Expressing left sides as corresponding densities in the Grand
Canonical Ensemble:
s = s(T, µB , µS ) ,
nB = nB (T, µB , µS ) ,
nS = nS (T, µB , µS )
and solving at each moment t the above equations, one obtains
T (t), µB (t) and µS (t).
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Sound velocity in the hadron gas
T (t) ∼
= T0 ·
t0
t
c2s (T0 )
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=⇒
putting Tf.o. one obtains tf.o.
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Initial state scattering of gluons
J. Hufner, Y. Kurihara and H. J. Pirner, PL B215, 218 (1988)
S. Gavin and M. Gyulassy, PL B214, 241 (1988)
J. P. Blaizot and J. Y. Ollitrault, PL B217, 392 (1989)
The form proposed by S. Gupta and H. Satz, PL B283, 439
(1992):
(
)
p2T
2pT
g(pT ) = 2 AB · exp − 2 AB
hpT iJ/Ψ
hpT iJ/Ψ
hp2T iAB
J/Ψ - the mean squared transverse momentum of J/Ψ gained
in an A-B collision
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Taking into account the shadowing
E. G. Ferreiro et al., arXiv:0903.4908 with
http://phenix-france.in2p3.fr/software/jin/index.html
I
Fits to PHENIX d-Au data chose the extrinsic scheme with
the EPS08 model and σabs = 3.6 mb.
I
AuAu (y) ≡ RF erreiro (| y |, σ
NNS
abs = 0)
dAu
I
th
AuAu · N
NJ/Ψ−AuAu
= NNA · NNS
HRG
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J/Ψ suppression with shadowing included
Figure: J/Ψ survival factor as a function of rapidity. Curves correspond
to n0B = 0, σb = 3.6 mb and Tf.o. = 150 MeV, circles are the PHENIX
data for Au-Au @ 200 GeV.
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J/Ψ suppression with shadowing included
Figure: J/Ψ survival factor as a function of rapidity. Curves correspond
to n0B = 0, σb = 3.6 mb and Tf.o. = 150 MeV, circles are the PHENIX
data for Au-Au @ 200 GeV.
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NA50 announcement
Bσ(J/ψ) / σ(DY)2.9-4.5
Phys. Lett. 477, 28 (2000)
40
Pb - Pb 1996
35
Pb - Pb 1996 with Minimum Bias
Pb - Pb 1998 with Minimum Bias
30
25
20
15
10
5
0
0
20
40
60
80
100
120
140
ET (GeV)
Figure 6: Comparison between our data and several conventional calculations of J/ψ
suppression.
Figure: Evidence for deconfinement of quarks and gluons from the J/Ψ
suppression pattern measured in Pb-Pb collisions at the CERN-SPS
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Definitions
Rapidity
Pseudorapidity
Z
N=
3
Z
p) =
d p~ f (~
1 E + pL
1 1 + vL
ln
= ln
2 E − pL
2 1 − vL
θ
1 p + pL
η = − ln tan
= ln
2
2 p − pL
y=
Z
2
Z
d pT Ef =
dy
Z
dy
d2 pT
d2 N
2πpT dpT dy
d2 N
mT cosh(y) − µ
= E · f = A mT cosh(y) exp −
2πpT dpT dy
T
mT =
q
m2 + p2T ,
E = mT cosh(y),
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pL = mT sinh(y)
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