+
/e e
1
arXiv:0705.1591 [nucl.th]
2
B.S.
PLB 1983
Sometime ago it was noted that:
“The ratio of the production rates (/+-) and ( o, /+-) from quark
gluon plasma is independent of the space time evolution of the fireball”.
Universal Signal :
d 
4 
d x
d 
4 
d x

 


 O( 2T 4 )
 O( s n1  s  )T 4



R      2   s n1  s 


Only a function of universal constants.
(1)
(2)
(3)
3
Light from QGP
B.S.
PLB 1983
q

q

R  / + - = const( , s
qq + -~ T4
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Thermal Photons
Invariant yield of thermal photons can be written as
 d 2 R  4
d 2 N
 d x
    2
2
d pT dy i Q , M , H i  d pT dy i
i

Q  QGP
M  Mixed (coexisting phase of QGP and hadrons)
H  Hadronic Phase
d 2 R 

2
d pT dy i
is the static rate of photon production  convoluted
over the space time expansion.

Rem  d 2 N d 2 pT dy

y 0
 d 2 N * 
 2

 d pT dy  y 0
5
Thermal photons from QGP :
q q  g


q q g q q
using hard thermal loop approximation. Again,
gq  gq , qq  qq , qq q  q
&
gq q  g
 s  ~ Compton & Annihilati on
Resumming ladder diagrams in the effective theory
Thermal photons from hadrons :
(i)    (ii)    (with , , ,  and a1, in the
intermediate state) (iii)    (iv)   ,   
and    &
Similarly from strange meson sector
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Dileptons
Rather similar to photons, dileptons can be efficient probe for QGP –
again not suffering from final state interactions.
One has to subtract out contributions from:
(a) Drell–Yan process,
(b) Decays of vector mesons within the life time of the fireball
(c) Hadronic decays occurring after the freeze out.
Invariant transverse momentum distribution of thermal dileptons (e+e- or
virtual photons, *):
d 2 N *
 
2
d pT dy i Q , M , H

i
 d 2 R * 
2 4
 2

dM
d x
2 
 d pT dydM i
integrated over the invariant mass region:
2m  M  1.05 GeV

qq   *     s
2

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Dileptons from light vector mesons (, ) &  (Hadronic Sector) :
fV2 MV
d 2 R *
2

f [
]
2 2
3 BE
2
2 2
2
dM d pT dy
2
( M  mV )  ( MV )
s
1
1

x (1  )]
8 1  exp(( wo  M ) /  )

Consistent with e+e-
V(,,f) data
fV(V) : coupling between electromagnetic current and vector
meson fields
mV and V are the mass and width of the vector V
and w0 are the continuum threshold above which the
asymptotic freedom is restored.
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Isentropic expansion :
4
2

dN
Ti 3 i 
45 (3)RA2 4a dy
 ( i , r ) 
0
1 e
r  RA

v( i , r )  0;
Hydrodynamics takes care of the evolution
of the transverse motion.
9
The number density as a function of temperature. Effect
of mass modification and width modification is shown.
10
Photons at SPS
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Thermal Photon reproduce WA98 data
12
Di-electrons at SPS
13
Photons at RHIC
(J. Phys. G 2007, J. Alam, J. Nayak, P.Roy,
A. Dutt-Mazumder, B.S.)
14
Thermal Photon reproduce PHENIX data
15
Di-electrons at RHIC
16
Photons at LHC
17
Di-electrons at LHC
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RESULTS from the ratio:
 d 2 R
Rem   2
 d pT dy
d
2
R *

d pT dy 


2

The variation of Rem (the ratio of the transverse momentum spectra of
photons and dileptons) has been studied for SPS, RHIC and LHC. We
argue that simultaneous measurements of this quantity will be very useful
to determine the value of the initial temperature of the system formed after
heavy ion collisions. We observe that Rem reaches a plateau beyond
PT=0.5 GeV. The value of Rem in the plateau region depends on Ti but
largely independent of Tc, vo, Tf and the EOS.
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Ratio (Rem) at SPS
 d 2 R
Rem   2
 d pT dy
d
2

R * d 2 pT dy 



20
Ratio (Rem) at RHIC
 d 2 R
Rem   2
 d pT dy
d
2

R * d 2 pT dy 



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Ratio (Rem) at LHC
 d 2 R
Rem   2
 d pT dy
d
2

R * d 2 pT dy 



22
Ratio (Rem) for pQCD processes
FILTERING OUT pQCD PHOTONS
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Ratio (Rem) vs. Initial Temperature
 d 2 R
Rem   2
 d pT dy
d
2

R * d 2 pT dy 



24
arXiv:0705.1591 [nucl.th]
OBSERVATIONS:
1. The medium effect on Rem is negligibly small
2. Hydrodynamic effects such as viscosity, flow get sort of
erased out by observing the ratio, Rem
3. Equivalently, model dependent uncertainties also get
cancelled out through Rem
4. Contributions from Quark Matter increase with the
increase of the initial temperature –
a) thermal photons mostly for hadronic phase at SPS
b) thermal photons from RHIC and more so from LHC
originate from QGP
5. Rem flattens out beyond pT ~ 0.5GeV
6. In the plateau region: RemLHC > RemRHIC>RemLHC
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OBSERVATIONS, contd.
WHY & HOW
Rem (in Born approx.) =>
2

T
S  4 2 s
 (M 2 )
At the end Rem still remains by far and large model independent:
SPS => RHIC => LHC
Thus Rem is a universal signal of QGP,
model independent and unique.
26
We see that  is a function of the universal constants and the
temperature. Because of the slow (logarithmic) variation as with
temperature, one can assume
s  T2
In an expanding system, however, Rem involves the superposition of
results for all temperatures from Ti to Tf, so the effective (average)
temperature, Teff will lie between Ti and Tf and Rem  Teff2
This explains:
LHC
em
R
 R
RHIC
em
R
SPS
em
It is also interesting to note that for s = 0.3, T=0.4GeV,
(M)2 ~ 1 (Mmax=1.05, Mmin=0.28), we get: Rs~ 260.
This is comparable to Rem obtained in the present calculation.
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WHAT DO WE EXPECT at LHC
 d 2 R
Rem   2
 d pT dy
d
2

R * d 2 pT dy 



28
Photons and di-electrons in the ALICE experiment
TRD: Electron-pairs
PHOS: Photons
29
PMD
photons
PMD
Modules
MUON arm
-pairs
Muon
chambers
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LOOKING FORWARD TO THE VERIFICATION OF
THE UNIVERSAL SIGNATURE:
+
/e e as well as


/ 
at the Large Hadron Collider
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