Elliptic flow of thermal photons

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Elliptic flow of thermal photons
Rupa Chatterjee
Variable Energy Cyclotron Centre
Kolkata
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In relativistic heavy
ion collisions a high energy density matter
Quark-Gluon Plasma (QGP) may be formed.
Various signals have been proposed which
probe this new phase of matter.
In particular photons (and dileptons) measure the
properties of this plasma in a relatively clean
manner, since such electro-magnetically
interacting particles do not take part in strong
interactions and only weakly interact with the
system.
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Photons are emitted from every stage of
the collision, from pre-equilibrium stage,
from quark matter, and from hadronic matter.
The thermal photon emission from the QGP and the
hadronic phase are obtained by integrating the
rates of emission over the space-time
history of the fireball. E dNg /
d3p?exp (-pm .um/T ) d4x Where,
pm( pT coshY, px , py , pTsinhY )
gt4-momentum of the photons umgT(cosh h ,
Vx(x,y) ,Vy(x,y) , sinh h ) gt4-velocity of
the flow field d4xt dt dx dy dh
gt4-volume element
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Also Y rapidity (0 as mid-rapidity region)
htanh-1(z/t)
gt space-time rapidity t t2
z21/2 gtproper time
gT1/1 VT21/2 gt Lorentz factor
VT Vx2 Vy 2 1/2 gtradial flow
velocity And pT px2 py 2 1/2
gttransverse momentum Where, pxpTcosf
and pypTsinf Taking the azimuthal angle for
transverse momenta as f (in the reaction plane )
we can write pm.um gT
pTcosh(Y-h)pxvxpyvy
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z 0 plane
Reaction plane
y

y
f
f
x
x
Impact parameter b
Overlap region
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Spatial asymmetry
Initial spatial anisotropy
INPUT
Final momentum anisotropy
High pressure
OUTPUT
Low pressure
Momentum asymmetry
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• ELLIPTIC FLOW or AZIMUTHAL FLOW is
• nothing but the system,s response to the initial
• spatial anisotropy.

• The azimuthal asymmetry in the distribution of
• thermal photons , defined in terms of the
  coefficients
• vn
• dN(b)/d2pTdy dN(b)/2ppTdpTdy12v2(pT,b)cos(2f)
• 
  2v4(pT,b)cos(4f) ..
• 
  

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Initial parameters for AuAu collision at 200
AGeV Initial time t0 0.2 fm Initial entropy
density (s0) 351 fm-3 Initial baryon number
density (n0) 0.40 fm-3 Impact parameter b 7
fm Freeze-out energy density (ef ) 0.075
GeV/fm3 Initial energy density aNWN
(1-a)NBC where, a0.25 NWN (x,y,b)
Number of wounded nucleons NBC
(x,y,b) Number of binary collisions
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b0.0fm b3.0 fm b5.4 fm b7.0 fm b8.3 fm b9.4
fm b10.4 fm
b10.4fm b9.4 fm b8.3 fm b7.0 fm b5.4
fm b3.0 fm b0.0 fm
dN/d2pTdy (1/GeV2)
Transverse momentum pT (GeV)
The yield is maximum for central collision ( b0
fm) and it goes down as we move towards
peripheral collisions with increase of impact
parameter b.
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b 7 fm
QGP Hadronic Total
dN/d2pT dy (1/GeV2)
Transverse momentum pT (GeV)
At high values of transverse momenta (pT) the
yield from the QGP dominates over the yield from
hadrons. As pT gets lower, the yield from the
hadrons makes a significant contribution to the
total emission of thermal photons.
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• Constant energy density contours for eeq, eh
  and ef , along y(x0) (solid curves) and x
  (y0) (dashed curves).
• Where,
• eq 1.6 GeV/fm3
• eh 0.444 GeV/fm3
• ef 0.075 GeV/fm3

nucl-th/0511079
t (fm)
nucl-th/0511079 Rupa Chatterjee, Evan S.
Frodermann, Ulrich Heinz and Dinesh K.Srivastava
.
The difference between the solid and the dashed
curves get pushed to larger x or y as the energy
density decreases or the time increases. Both
the curves are identical for 0 impact parameter .
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nucl-th/0511079 Rupa Chatterjee, Evan S.
Frodermann, Ulrich Heinz and Dinesh K.Srivastava
.
Fluid velocity along the constant energy
density contour for eeq(for QGP phase), eeh
(for mixed phase) and eef (for hadronic phase )
for x (y0) (dashed curve) and y (x0) (solid
curve) .
.
Velocities ( zero at initial time t0 ) which
start differing over extended volume by the end
of the QGP phase, become almost identical at the
end of hadronic phase.
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v2(QM) is small at higher pT (due to absence of
transverse flow at early times) and gradually
build up as pT (and temperature) decreases .
After reaching a peak value (around 1.5 GeV) v2
decreases again as pT ? 0. Elliptic flow of
hadronic photons is much larger than v2(QM). The
hadronic contribution to the photon spectrum is
increasingly suppressed below the QGP
contribution once pT exceeds 1.5- 2.0 GeV.
Hence the overall photonic v2 is larger than pure
QM contribution and also decreases for large pT ,
approaching the v2 of the QM photons in -spite
of the larger elliptic flow of the hadronic
photons .
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nucl-th/0511079

• v2 for thermal photons from 200 AGeV AuAu
  collision is
• shown by the red curve.
• .Quark and hadronic contributions to v2 are shown
  separately.
• v2 for pion is also shown in comparison with
  hadronic v2.
• pion v2 tracks the hadronic v2.

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nucl-th/0511079
Impact parameter dependence of the elliptic flow
Impact parameter are chosen to roughly correspond
to collision centralities of 0-10(b3 fm),
10-20(b5.4 fm), 20-30(b7 fm), 30-40 (b8.3
fm), 40-50 (b9.4 fm), and 50-60 (b10.4) .
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Initial entropy density dependence of
the elliptic flow is shown. Initial entropy
densities are taken In steps of 100, 200,..,1000
fm-3. With rise in initial entropy density the
flow also increases. Higher v2 at LHC!
so1000 fm-3
so351 fm-3
Elliptic flow co-efficient v2
so100 fm-3
Transverse momentum pT (GeV)
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Summary Conclusions

• We have presented a first calculation of
  elliptic flow
• of thermal photons, emitted from relativistic
• collisions of heavy ions.
• The azimuthal flow revealed by the thermal
  photons
• shows a rich structure and sensitivity to the
  evolution
• of the expansion dynamics as well as the rates
  of
• emission from the hadronic and quark matter .
• v2 of thermal photons from hadronic matter
  tracks the
• v2 of pions, while v2 of thermal photons from
  the quark matter tracks the v2 of quarks.

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• v2shows a strong dependence on the impact
  parameter of the collisions as the relative
  contributions of the hadronic and quark matter
  depend on it.

My collaborators for this work- Evan S.
Frodermann and Ulrich Heinz The Ohio State
University, USA Dinesh K. Srivastava, VECC
Kolkata
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Thank you
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