the j/ as a probe of quark-gluon plasma erice 2004 luciano maiani università di roma “la...
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The J/ as a probe of Quark-Gluon Plasma Erice 2004
Luciano MAIANI
Università di Roma “La Sapienza”.
INFN. Roma.
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 2
Overview
• Confinement means that the heavy quarks in a c-cbar pair feel a constant attractive force (i.e. a linearly rising potential)
• In the deconfined phase, the attractive force between c and c-bar is screened by the Quark-Gluon Plasma (QGP)
• charmonia bound states “melt”, more and more with rising temperature;
• The onset of J/ suppression in relativistic heavy ion collisions (starting from the J/s from the decay of higher charmonia) would signal the formation of QGP
T. Matsui and H. Satz Phys. Lett. B178, 416 (1986); See R. Vogt, Phys. Rep. 310, 197 (1999).
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 3
Overview (cont’d)
• However, we must control the “other” sources of absorption (nuclear, hadronic);
• several calculations of dissociation cross-section have been performed:
See e.g.:
L. Maiani, F. Piccinini, A.D. Polosa, V. Riquer,hep-ph/0402275; hep-ph/0408150
M.C. Abreu et al., Phys. Lett. B450, 456 (1999); M.C. Abreu et al., Phys. Lett. B477, 28 (2000). Latest analysis: http://na50.web.cern.ch/NA50/
•I will report on our calculation:
•and apply the results to the SPS, NA50 data
,...),h(;DD/Jh(*)
(*)
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 4
Overview (cont’d)
• This will be a “bottom up” presentation: from low temperature rising to high temperature (slowly!);
• 1st lecture: an elementary introduction to the basic concepts;
• 2nd lecture: results of calculations, application to the data.
• The main question:
– DID QGP SHOW UP AT THE SPS?
• Our analysis says:
– YES, MOST LIKELY !!
– But we want to know better...– And to study QGP more, at RHIC, LHC, ...
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 5
Lecture 1: summary
1. A simple view of the collisions
2. Does the fireball thermalise?
3. Hadron gas
4. Hagedorn gas: limiting temperature vs. phase transition
5. The Polyakov loop and Lattice QCD results
6. Debye screening of charmonia
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 6
time
Which is which ?How can we tell ?
The energy of the surviving nuclear fragments seen by the Zero Degree Calorimeter in NA50 gives a measure of the impact parameter b !
Wounded nucleons
J. Bjorken, Phys. Rev. D27, 140 (1983)
U. Wiedemann, CERN Academic Training 20041. Snapshots of relativistic heavy ion collision in the c.o.m.
before...
after...
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 7
Bjorken’s estimate of the energy density of the fireball
Nucleon number/unit area (increases with centrality)
Longitudinal dimension
1.0
0.6
0.8
fm
g(b) for Pb-Pb
)fm12l()c
fm1(fm/GeV6.2
0
3
)fm4l()c
fm1(fm/GeV8.1
0
3
For central Pb-Pb collision:
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 8
12. Does the fireball thermalize?
fireballtheofensiondim
)fm025.0(fm10mb40 131
Average initial density: 1000 particles/100 fm3== 10 fm-3
If the initial particles are pions (?)Cross section: 40mb=4fm-2
GeV55.0E4.1s
EE2cosd
)cos1(EE2cosds
211
1
21
1
1
2222
22
finin2J
M)Ms(
M)s(BW
)]s(BW[BBM
)1J2(16)s;finin(
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 9
Does the fireball thermalize? (cont’d)
• Hadrons at freeze-out are thermal, T=170-180 MeV
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 10
• Antinori, Quark 2004Thermal fits on the contrary don’t do badly at
all. ....... relative particle abundances are found to be
close to those expected at thermodynamical equilibrium for a grand-canonical system, even for the rare multi-strange particles. ...
....we do not seem to be able to observe a system of hadrons with a temperature beyond a maximum value of the order of 170 MeV.
Does the fireball thermalize?
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 11
3. Bottom up approach: the hadron gas
All free particles.Interaction is introduced in the form of new particles, e.g. etc.
i
ii
Zln),T(Vn
Zln),T(VU
)ee1ln(zln
)zln)2(
pdV(dm)m(Zln
)mm(N)1J2()m(
)p(E
i
i3
3
i ich
ii
+: fermions; -: bosons.
Boltzmann limit: exps <<1lnz ≈ ee
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 12
Resonance gas
Neff
T
)T(N
0
eff
Not only pions !!In spite of higher mass, higher resonances contribute to the energy density at temperatures around 150 MeV because of increasing multiplicities
3
Neff (see later)
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 13
4. In the prehistory of modern hadron theory...
Exponentially increasing density of hadronic levels
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 14
Hagedorn bootstrap leads to an exponentially increasing density of hadronic levels
HT
mkem
•TH=Hagedorn temperature ≈ maximum pT observed in hadronic high-energy reactions ≈ 150 MeV;•K=3 preferred;
T
mT
m
k eemZ H
Z cannot exist for T>TH;Hadron matter cannot exist at temperatures >TH
•Exponentially rising density of hadronic resonances is also a property of the (confined) quark model, e.g. Bag Model•What about experiment?
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 15
J. Letessier and J. Rafelski, “Hadrons and Quark Gluon Plasma”, Cambridge Monogr. Part. Phys. Nucl. Phys. Cosmol. 18 (2002).
Hagedorn’s thermodynamics
)mm()m(i
i
)mm(3)m(tot NOTE:
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 16
Varying the Hagedorn Temperature
C= 0.7, mo= 0.66 GeV, T=158 MeV, orC= 1.66, mo= 0.88 GeV, T=173 MeVgive very similar results for m<1.5 GeV
)T
mexp(
)mm(
C)m(
H
2/32
0
2
TH must be consistent with observed temperatures at freeze-out!!
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 17
Interpretation of the Hagedorn temperature
2/1
c0
x
0
2/1
2/1
c0
x
)(E
2/1x
)(E
2/3
)(E
2e)x(dx
)(E
2e)x(dxe)x(dx
c0c0
N. Cabibbo and G. Parisi, Phys. Lett. 59B, 67 (1975) (and Erice ’75).
Use non-relativistic, Boltzmann approx.: critical behaviour is determined by the high masss part of the spectrum, m>>T
.]rege)x(dx)(A[V
dme)m()mm(
C
)2(
VZln
x
)(E
2/32/1
c
)(m2/3
2/32
0
22/3H
c0
c
c=1/TH
E0 >> m0
reg.= terms regular at c
.reg)(AV
Zln 2/1
c
H In conclusion: 2/1
c)(
Rather than a limiting temperature...a second order phase transition!
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 18
5. Order parameter for deconfinement
The order parameter for the deconfinement transition is the Wilson- Polyakov loop
)T/Fexp(LQQ
•F= free energy of a pair of static point sources (heavy quarks) at distance r•confinement: F~ r ∞, L0 (T<Tc)•de-confinement: F 0 , L0 (T<Tc)
F. Karsch, Lattice QCD at High Temperature andDensity arXiv:hep-lat/0106019
Chiral symmetry restored too
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Finite Temperature Lattice QCD
163
)3(N
n)34)(8
7(28)n(N
T3
NT
30N
QGP,eff
ffQGP,eff
4eff4
2
effBoltzmannStefan
3fm/GeV6.1
NOTE:
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6. Debye screening of charmonia
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TD
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 22
(1S), M= 3097 MeV(2S), M= 3686 MeVAbove threshold:(3.77), M= 3770.0 2.4 MeVY(4.04), M= 4040 10 MeV
c0(1P), M= 3415 MeVc1(1P), M= 3510 MeVc2(1P), M= 3556 MeV
=0
= 357 MeV(T=178 MeV)
(3.77)’
3.5
rcr
2
C
Ceff
er
)e1()r(V
)r(Vrm
1m2V
2mc=2.64 GeV= 0.192GeV2
c=0.471
DD
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Erice. Sept. 1, 2004. L. MAIANI. Lez.1 23
Summing up
• The fireball produced in collisions with low energy density is ~ a pion gas at some T;
• Increasing , e.g. by increasing c.o.m. energy and/or centrality, T increases and higher resonances are produced;
• Increasing temperature becomes difficult because more and more energy goes in exciting resonances rather then increasing kinetic energy, i.e. T: dT/d ~(-c)3/2, as we approach the limiting Hagedorn temperature;
• When hadron bags are in contact, bags fuse and quarks and gluon are liberated
• A cartoon representing this:
/T4
TTHag~Tc~180 MeVHadron gas
Quarks & gluons
~ 2/30(16+21/2nf)~16
Hagedorn gasc and ’ start fusing