1 /e + e - arxiv:0705.1591 [nucl.th]. 2 3 sometime ago it was noted that: “the ratio of the...
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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
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
6
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
7
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.
19
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.
25
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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