1

/e+e-

arXiv:0705.1591 [nucl.th]

2

3

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 :

Only a function of universal constants.

)( 424

TOxd

d

44

)( T1nOxd

dss

(1)

(2)

ss nR 1 2

(3)

B.S.PLB 1983

4

B.S.PLB 1983

R / + - = const( , sq

q

Light from QGP

qq + -~ T4

5

Invariant yield of thermal photons can be written as

i Q QGP

M Mixed (coexisting phase of QGP and hadrons)

H Hadronic Phase

is the static rate of photon production convoluted

over the space time expansion.

xddypd

Rd

dypd

Nd

iHMQi i TT

4

,,2

2

2

2

iT dypd

Rd

2

2

0

2

2

022 *

yTyTem dypd

NddypdNdR

Thermal Photons

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Thermal photons from QGP :Thermal photons from QGP :

using hard thermal loop approximation. Again,

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

gqq

gqgqqqqqqqqqgqgq & , ,

~s onAnnihilati &Compton

qqgqq

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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, *):

integrated over the invariant mass region:

xddMdydMpd

Rd

dypd

Nd

iHMQi i TT

42

,,22

2

2

2 *

*

sqq 2*

GeVMm 05.12

Dileptons

8

Dileptons from light vector mesons (, ) & (Hadronic Sector) :

])()(

[ 2

*

2222

2

3

2

22

2

VV

VVBE

T MmM

Mff

dypddM

Rd

)] (1 x )/)exp((1

1

8

1 s

Mwo

Consistent with e+e- V() 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.

9

Isentropic expansion :

dy

dN

aRT

Aii

4)3(45

22

43

ARri

e

r

1

),( 0

0; ),( rv i

Hydrodynamics takes care of the evolutionof the transverse motion.

10

The number density as a function of temperature. Effect of mass modification and width modification is shown.

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Photons at SPS

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Thermal Photon reproduce WA98 data

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Di-electrons at SPS

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Photons at RHIC

(J. Phys. G 2007, J. Alam, J. Nayak, P.Roy, A. Dutt-Mazumder, B.S.)

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Thermal Photon reproduce PHENIX data

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Di-electrons at RHIC

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Photons at LHC

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Di-electrons at LHC

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RESULTS from the ratio:RESULTS from the ratio:

2*

22

2

dypdRd

dypdRd

R TT

em

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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2*

22

2

dypdRd

dypdRd

R TT

em

Ratio (Rem) at SPS

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2*

22

2

dypdRd

dypdRd

R TT

em

Ratio (Rem) at RHIC

22

2*

22

2

dypdRd

dypdRd

R TT

em

Ratio (Rem) at LHC

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Ratio (Rem) for pQCD processes

FILTERING OUT pQCD PHOTONS

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2*

22

2

dypdRd

dypdRd

R TT

em

arXiv:0705.1591 [nucl.th]

Ratio (Rem) vs. Initial Temperature

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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, Rem3. Equivalently, model dependent uncertainties also get

cancelled out through Rem4. 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 > Rem

RHIC>RemLHC

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OBSERVATIONS, contd.WHY & HOW

Rem (in Born approx.) => )M(

T 4

2

2s2

S

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.

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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

T 2s

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 T 2

effemR

This explains: SPSem

RHICem

LHCem RRR

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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2*

22

2

dypdRd

dypdRd

R TT

em

WHAT DO WE EXPECT at LHC

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Photons and di-electrons in the ALICE experiment

PHOS: Photons

TRD: Electron-pairs

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Muon chambersPMD

Modules

PMDphotons

PMDphotons

MUON arm -pairs

MUON arm -pairs

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/e+e- as well as

at the Large Hadron Collider

LOOKING FORWARD TO THE VERIFICATION OFTHE UNIVERSAL SIGNATURE: