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 phasemixed 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

Chatterjee, 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:

kddN

3E

23

1321 kd kd

dNEE

232

131

23

132121 kd

dNE kd

dNEkd 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

K

Kqq)-(cos k2kkk

k-k

T

TTout

212T1T2T2

1T2

2T2

1T2

)ψ-cos(ψ k2kkk

)ψ-(ψcos1k2k

T

ToutTside

212T1T2T2

1T2

212

2TT1

KKqqq

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

hadr

onic

elec

trom

agne

tic

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 1=2=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 21 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, aa

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

Ri stands for the space-time separation of the two sources.

Ro,Q = 2.8, Ro,H = 7.0, Ro =12.3,

Rs,Q ≈ Rs,H = 2.8, Rs ≈ 0.,

Rℓ,Q = 0.3, Rℓ,H = 1.8, Rℓ ≈ 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 !

Chatterjee, Frodermann, Heinz, and DKS,PRL 96 (2006) 202302.

Early timesLate

tim

es

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 strengthbosons / 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

21)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

x1k1

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 p

rodu

ctio

n ra

te (

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

r

Initial compression

2nd compression r

Inte

nsit

y

(r) (q)

(r -r) (q) X eiqr

Id (r) + It (r -r) (q) X (Id+It eiqr)

C12(q) = 1 + exp(- q2R2 - q02t2) Igg(q)

Igg(q) = Id2 + It

2 + 2 Id It cos(qr)

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