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Interference of thermal photons from quark and hadronic phases in relativistic
collisions of heavy nuclei
Dinesh K. SrivastavaVariable Energy cyclotron Centre,
Kolkata
In collaboration with Rupa Chatterjee
In-medium photon self energy: Directly related to the in-medium vector spectral densities!
Direct photons are penetrating probes for the bulk matter produced in nuclear collisions, as they do not interact strongly. They have a large mean free path.
hadronic phaseqgp phase
mixed phasepre-equilibrium phase
freeze-out surface
z
t
Penetrating probes: emitted at all stages then survive unscathed ( αe<< αs).
“Historians” of the heavy ion collision: encode all sub-processes at all times
Direct PhotonsDifferent Sources – Different Slopes
Rate Photons are result of convolutions of the emissions from the entire history of the nuclear collision, so we need rates and a model for evolution.
Hydrodynamics. Cascades. Fire-balls. Cascade+Hydro..
Complete O(aS) for QGP & Exhaustive Hadronic Reactions for hadrons
DKS, PRC 71 (2005) 034905.
Hydrodynamics, QGP + rich EOS for hadrons& accounting for the prompt photons
Chatt erjee, DKS, & Jeon; PRC 79 (2009) 034906.
Thermal Photons from Au+Au@RHIC
d’Enterria & Peressounko,EPJC 46 (2006) 451.
Photons from Passage of Jets through QGP
Fries, Mueller, & DKS, PRL 90 (2003) 132301.
The “bremsstrahlung” contribution will be suppressed due to E-loss.
FMS Results: Comparison to Data
for pT < 6 GeV, FMS photons give significant
contribution to photon spectrum: 50% @ 4 GeV.Fries, Mueller, & DKS, PRC 72 (2005) 041902( R).
Identical point sources at positions r1 and r2.
Single particle momentum distribution:
Two particle momentum distribution:
kd
dN3E
23
1321 kd kd
dNEE
232
131
23
132121 kd
dNE
kddN
Ekd kd
dN E E)k,C(k
Two particle correlation:
r1
r2
x1
k1
k2
ΔR
x2
Quantum statistical correlation
)/2kk(K
,kkq
2T1TT
2T1TT
sinhsinhkkq 22112z1zlong ykyk TT
KKq
q)-(cos k2kkk
k-k
T
TTout
212T1T2T2
1T2
2T2
1T2
)ψ-cos(ψ k2kkk
)ψ-(ψcos1k2k
T
ToutTside
212T1T2T2
1T2
212
2TT1
K
Kqqq
qout
qside
qlong
k1
k2
q
qout
qside
qlong
R side
R long
Rout
k1
k2
q
The corresponding radii are obtained by approximating C as:
R i2= 1/<q i
2>, where i = out, side, and
long, and the average is performed over the distribution (C − 1). One can show that Rout – Rside is a measure of the duration of the emission.
1950
1960
1980
1994
2004
gggggg
pp pp
had
ron
icel
ectr
om
agn
etic
astronomy intermediate energies
relativistic energies
relativistic energies
intermediate energies
Chronology of intensity correlation experiments
200A GeV Au+Au@RHICgg intensity correlation
C(qout,qside=qlong=0)
C(qlong,qout=qside=0)
C(qside,qout=qlong=0) Rside (K1T)
qout=qlong=0
Rlong (K1T) qout=qside=0
Rout (K1T) qside=qlong=0
DKS, PRC 71 (2005) 034905.
5.5A TeV Pb+Pb@LHCgg intensity correlation
C(qout,qside=qlong=0)
C(qlong,qout=qside=0)
C(qside,qout=qlong=0) Rside (K1T)
qout=qlong=0
Rlong (K1T) qout=qside=0
Rout (K1T) qside=qlong=0
DKS, PRC 71 (2005) 034905.
The two-photon correlation
function for average photon
momenta 100 < KT < 200 MeV/c
(top) and 200 < KT < 300 MeV/c
(bottom). The solid line shows
the fit result in the fit region
used (excluding the p0 peak at
Qinv mp0 ) and the dotted line
shows the extrapolation into
the low Qinv region where
backgrounds are large.
M. M. Aggarwal et al., [WA98 collaboration] PRL 93, 022301 (2004)
Intensity Interferometry of Thermal Photons @SPS
A one-dimensional analysis of the correlation function C is performed in terms of the invariant momentum difference as follows:
DKS, PRC 71 (2005) 034905.
WA98 measures Rinv as 8.34 ± 1.7 fm and 8.63 ± 2.0 fm, respectively
For y1=y2=0 and y1=y2=0, qside=qlong=qinv=0,but qout=k1T-k2T .ne.0
2long
2side
2out
2
21212T1T
220
221inv
2inv
2invinv
qqq q where,
)]-cos(-)y-[cosh(y k2k
q q- )k -(k- q
/2Rq - exp 2
1 1 )C(q
pre-equilibrium contributions are easier identified at large pT.
window of opportunity above pT = 2 GeV.
at 1 GeV, need to take thermal contributions into account.
short emission time in the PCM, 90% of photons before 0.3 fm/c
hydrodynamic calculation with τ0=0.3 fm/c allows for a smooth continuation of emission rate
Bass, Mueller, & DKS, PRL 93 (2004) 16230
Outward correlation function of thermal photons for 200A GeV Au+Au collision at RHIC
The outward, sideward, and longitudinal correlation functions for thermal photons produced in central collision of gold nuclei at RHIC taking t0 = 0.2 fm/c. Symbols denote the results of the calculation, while the curves denote the fits.
Correlation function in the two phases can be approximated as
2αi,αi, |ρ|0.51)C(q
]Rq 0.5 [ exp I 2i,
2iii,
where,
i=out, side, and longa= quark matter (Q) or hadronic matter (H)
DKS and R. Chatterjee; arXiv: 0907.1360
i=out, side, and longa= quark matter (Q) or hadronic matter (H)
)dNdN /(dNI
)dNdN /(dNI
HQHH
HQQQ
The final correlation function can be approximated as:
)]R (q cos |ρ| |ρ| 2
|ρ| |ρ| 0.5[1)C(q
iHi,Qi,
2H i,
2Qi,i
DRi stands for the space-time separation of the two sources.
Ro,Q = 2.8, Ro,H = 7.0, DRo =12.3,
Rs,Q ≈ Rs,H = 2.8, DRs ≈ 0.,
Rℓ,Q = 0.3, Rℓ,H = 1.8, DRℓ ≈ 0.
(all values are in fm.)DKS and R. Chatterjee; arXiv: 0907.1360
DKS and R. ChatterjeearXiv: 0907.1360
The outward, sideward, and longitudinal correlation functions for thermal photons produced in central collision of lead nuclei at LHC taking t0 = 0.2 fm/c. Symbols denote the results of the calculation, while the curves denote the fits.
RHIC
RHIC
RHIC
LHC
LHC
LHC
TC dependence of the outward correlation function @RHIC
t0 dependence of the outward and longitudinal correlation functions at RHIC.
The side-wardcorrelation is only marginallyaffected and isnot shown.
DKS and R. Chatterjee, Phys. Rev. C 80, 054914
(2009)
Transverse momentum dependence of fraction of thermal photons from quark matter (IQ) and hadronic matter (IH) at RHIC and LHC energy.
Monte Carlo calculation of intensity correlation
reactionplane
qoutqside
qlong
= 0°
= 90°
Rside (large)
Rside (small)
Future directions
E. Frodermann & U. Heinz; arXiv: 0907.1292
Elliptic Flow of Thermal Photons:Measure Evolution of Flow !
Elliptic Flow of Thermal Photons:Measure Evolution of Flow !
Chatterjee, Frodermann, Heinz, and DKS,PRL 96 (2006) 202302.
Early timesLa
te ti
mes
Adul
t life
Hadron intensity interferometry is sensitive only to the last moments of the collision dynamics.
Photons are emitted throughout the evolution of the system.
In relativistic heavy ion collisions, we have photons from quark matter and hadronic matter.
We report the first ever prediction of interference between thermal photons from quark matter and the hadronic matter.
If measured, this will give size of the system in the quark phase and the hadronic phase, relative contributions from the two phases and the life-time of the emitting source.
Similar results are expected at 40-60 MeV/A at the superconducting cyclotron energies.
Simultaneous measurements of elliptic flow and the angle dependent interferometry would be very valuable.
THANK YOU
Quark Matter 2005 - Zbigniew Chajęcki for the STAR Collaboration
37
Typical results for pion intensity interferometry
Pion HBT radii from different systems and at different energies scale with (dNch/dη)1/3
RHIC/AGS/SPS Systematics<kT>≈ 400 MeV (RHIC) <kT>≈ 390 MeV (SPS)
Lisa
, Pra
tt, S
oltz
, Wie
dem
ann,
nuc
l-ex/
0505
014
STAR DATA (pp,dAu,CuCu,AuAu@62GeV - prelim.)
The outward, sideward, longitudinal correlation function for thermal photons produced in central collision of Pb nuclei at CERN SPS.
DKS, PRC 71 (2005) 034905.
The outward, sideward, longitudinal radii for thermal photons produced in central collision of Pb nuclei at CERN SPS.
DKS, PRC 71 (2005) 034905.
Emission amplitude
2211 ikxiφikxiφ eeee ρ(k) 2
1A(k)
phase of source
real function, characterizes the source strength
bosons / fermions
21cos12)(3
ffxkkrkd
dNSingle particle distribution function
212
3 φφΔx k cos 1 ρ(k)kd
dN
x1-x2
0e 21 iφiφIncoherent emission
23 (k)kd
dN
212112212211 iφiφxikxikiφiφxikxik2121 ee)ρ(k )ρ(k
2
1)k ,A(k
Two particle emission amplitude
Two particle distribution function
Δx k cos 1 )ρ(k)ρ(kkd kd
dN 22
21
23
13
k1-k2
Δx kcos 1),( 21 kkC
Correlation function
r1
r2
x1
k1
k2
ΔRx2
Quantum statistical correlation
2.3 )( 1 ~ )( xkiexxdkC
If instead of two discrete sources, one has a distribution of sources, ρ(x ), then averaging over the distribution, one finds that the correlation function measures the Fourier transform of the source distribution:
Spatial evolution of a central collision in the nucleus-nucleus centre of mass frame obtained with BUU calculation for the system 181Ta+197Au at 40A MeV.
x (fm
)
z (fm)
g
pro
du
ctio
n r
ate
(a
.u.)
Production rate of photons with an energy of 30 MeV as a function of the incompressibility K of nuclear matter obtained with BUU calculations for the system 181Ta+197Au at 40A MeV and b= 5 fm.
Time (fm/c)
Inclusive hard photons at qlab=900. Thermal (solid squares) and direct (sold circles).
Eg (MeV)
(cou
nts/
MeV
)
G. Martinez et al.; Physics Letters B 349, 23 (1995).
IdIt
Dr
Initial compression
2nd compression r
Inte
nsit
y
r(r) r(q)
r(r -Dr) r(q) X eiqDr
Id r(r) + It r(r -Dr) r(q) X (Id+It
eiqDr)
C12(q) = 1 + l exp(- q2R2 - q02t2) Igg(q)
Igg(q) = Id2 + It
2 + 2 Id It cos(qDr)
The correlation function
F. M. Marques et al., Phys. Rept. 284, 91 (1997)
Fits to the interferometry data; showing interference between two sources.
Q (MeV)
C 12