1. High Energy Photons from Relativistic Heavy Ion Collisions
Dinesh Kumar Srivastava
Variable Energy Cyclotron Centre
Kolkata
Motivation
The PCM: Fundamentals & Implementation
Photon Production in the PCM
Medium Effects: Jet-Photon Conversion (FMS Photons)
Intensity Interferometry of Photons
Elliptic Flow of Thermal Photons
WHEPP 2006, Bhubaneswar.

3. Photon Production in the PCM
Part #1:
Photon Production in the PCM
Light from cascading partons in relativistic heavy-ion collisions
- S.A. Bass, B. Mueller and D.K. Srivastava, Phys. Rev. Lett. 90 (2003)
Semi-hard scattering of partons at SPS and RHIC: A study in contrast
-S. A. Bass, B. Mueller, and D. K. Srivastava, Phys. Rev. C 66 (2002) (R)
Intensity interferometry of direct photons in Au+Au collisions - S.A. Bass, B. Mueller and D.K. Srivastava, Phys. Rev. Lett. 93 (2004)
Dynamics of the LPM effect in Au+Au Collisions at 200 AGeV - T. Renk, S.A. Bass and D.K. Srivastava, nucl-th/ , Phys. Lett. B. (in press)

4. Basic Principles of the PCM
Goal: provide a microscopic space-time description of relativistic heavy-ion collisions based on perturbative QCD
Degrees of freedom: quarks and gluons
Classical trajectories in phase space (with relativistic kinematics)
Initial state constructed from experimentally measured nucleon structure functions and elastic form factors
An interaction takes place if at the time of closest approach dmin of two partons
System evolves through a sequence of binary (22) elastic and inelastic scatterings of partons and initial and final state radiations within a leading-logarithmic approximation (2N)
Binary cross sections are calculated in leading order pQCD with either a momentum cut-off or Debye screening to regularize IR behavior
Guiding scales: initialization scale Q0, pT cut-off p0 / Debye-mass μD

5. Initial State: Parton Momenta
flavour and x are sampled from PDFs at an initial scale Q0 and low x cut-off xmin
initial kt is sampled from a Gaussian of width Q0 in case of no initial state radiation
virtualities are determined by:

6. Parton-Parton Scattering Cross-Sections
g g  g g
q q’  q q’
q g q g
q qbar q’ qbar’
g g  q qbar
q g q γ
q q  q q
q qbar  g γ
q qbar  q qbar
q qbar  γ γ
q qbar  g g
a common factor of παs2(Q2)/s2 etc.
further decomposition according to colour flow
Biswanath Layek working on including heavy quarks.

7. Initial and Final State Radiation
Probability for a branching is given in terms of the Sudakov form factors:
Space-like branchings:
Time-like branchings:
Altarelli-Parisi splitting functions included:
Pqqg , Pggg , Pgqqbar & Pqqγ

8. Collision Rates & Numbers
# of collisions lo
full
q + q
70.6
274
q + qbar
1.3
38.52
q + g
428.3
2422.6
g + g
514.4
4025.6
b=0 fm
Lifetime of interacting phase: ~ 3 fm/c
Partonic multiplication due to the initial & final state radiation increases the collision rate by a factor of 4-10
Are time-scales and collision rates sufficient for thermalization?

9. Photon Production in the PCM
Relevant processes:
Compton: q g q γ
Annihilation: q qbar  g γ
Bremsstrahlung: q* q γ
Photon yield very sensitive to parton-parton rescattering

10. What Can We Learn From Photons?
Photon yield directly proportional to the # of hard collisions
Primary-primary collision contribution to yield is < 10%
Emission duration of pre-equilibrium phase: ~ 0.5 fm/c
Photon yield scales with Npart4/3

11. Photons: pre-equilibrium vs. thermal
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

12. HBT Interferometry: Formalism
Correlation between two photons with momenta k1 and k2 is given by:
with S(x,k) the photon source function for a chaotic source
use Wigner function scheme (Hansa code by Sollfrank & Heinz)
emission vertices of a semiclassical transport are not valid Wigner fnct.
need to smear out emission vertices xi by ħ/pi
results are given in terms of outward, sideward & longitudinal correlators

13. Photons: HBT Interferometry
pt=2 GeV: pre-thermal photons dominate, small radii
pt=1 GeV: superposition of pre- & thermal photons: increase in radii

14. Landau-Pomeranchuk-Migdal Suppression
The LPM effect accounts for the suppression of radiation due to coherence effects in multiple scattering f e b
the radiated parton e is assigned a formation time: kt a d c
if the radiating parton d suffers a collision before tform has elapsed, then the radiation of parton e and it’s daughters does not take place
likewise for parton f with respect to e …

15. LPM: Reaction Dynamics
gluon pt distribution
high pt: harder slope, enhanced particle production
low pt: suppression of particle production

16. Photon Production: LPM & Comparison to Data
PCM without LPM:
overprediction of photon yield
PCM with LPM:
photon yield for pt < 6 GeV strongly reduced
strong pt dependence of LPM suppression
good agreement with data

17. Photons via Jet-Plasma Interactions
Part #2:
Photons via Jet-Plasma Interactions
R.J. Fries, B. Mueller, & D.K. Srivastava, PRL 90, (2003),
R.J. Fries, B. Mueller, & D. K. Srivastava, PRC 72, (R) 2005,
See also: S.Turbide, C. Gale, S. Jeon, and G. Moore, PRC 72, (2005).
Dileptons via Jet-Plasma Interactions
S. Turbide, C. Gale, D. K. Srivastava, & R. J. Fries, (to be published), hep-ph/

18. Photon Sources Hard direct photons EM bremsstrahlung
Thermal photons from hot medium
Jet-photon conversion
Turbide, Gale & Rapp, PRC (2004)

20. Jet-Plasma Interactions
Plasma mediates a jet-photon conversion:
Jet passing through the medium:
large energy loss: jet quenching
electromagnetic radiation (real and virtual photons) from jet-medium interactions
suppressed by αEM; negligible as a source of additional jet quenching
can escape without rescattering
use as probe of energy loss?
visible among other sources of electromagnetic signals?

21. QGP-induced EM Radiation
Annihilation and Compton processes peak in forward and backward directions:
One parton from hard scattering, one parton from the thermal medium; Cutoff p,min > 1 GeV/c.
Photon carries momentum of the hard parton.
Jet-photon conversion.

22. Jet-photon Conversion: Rates
Annihilation and Compton rates:
Thermal medium:

23. Photons from jet-plasma interaction

25. FMS Results: Comparison to Data
Calibrate pQCD calculation of direct and Bremsstrahlung photons via p+p data:
For pt<6 GeV, FMS photons give significant contribution to photon spectrum: 4 GeV
Fries, Mueller, & Srivastava, PRC 72, (R) 2005

26. FMS: Centrality Dependence and Jet-quenching
Centrality dependence well described
Effect of energy-loss on jets before conversion ~ 20% (Turbide et al).

27. FMS Photons: Further Confirmations
S. Turbide and C. Gale, hep-ph/

28. Azimuthal Anisotropy of FMS Photons
S. Turbide, C. Gale, and R. J. Fries, hep-ph/

30. Jet-plasma or jet-thermal dileptons

34. Application: Monitoring Jet Quenching
Full jet reconstruction not possible at RHIC:
Measure suppression of single inclusive hadron spectra (compare to p+p baseline)
Better: photon-tagged (Wang & Sarcevic) or dilepton –tagged jets (Srivastava, Gale, & Awes):
q+g  q+: recoil photon knows the initial energy of the jet
Measure energy loss of quark as a function of quark energy E
Photons from jet-photon conversion provide a third, independent measurement. (FMS)
Better handle on the L dependence of energy loss
Jet-photon conversion is background for photon tagged jets

35. Elliptic flow of thermal photons
Part #3:
Elliptic flow of thermal photons
Elliptic Flow of Thermal Photons in Relativistic Heavy Ion
Collisions,
Rupa Chatterjee, Evan S. Frodermann, Ulrich Heinz, and D.K. Srivastava, nucl-th/
Photons are emitted from every point in space and time unlike hadrons which come out only from freeze-out surface, when the fluid element is at 100 MeV !

36. Nuclear Fluid Dynamics
Transport of macroscopic degrees of freedom
Based on conservation laws: μTμν=0, μjμ=0
For ideal fluid: Tμν= (ε+p) uμ uν - p gμν and jiμ = ρi uμ
Equation of State needed to close system of PDE’s: p=p(T,ρi)
assume local thermal equilibrium
Initial conditions (i.e. thermalized QGP) required for calculation
Simple case: scaling hydrodynamics
assume longitudinal boost-invariance
cylindrically symmetric transverse expansion
no pressure between rapidity slices
conserved charge in each slice

37. Collective Flow: Overview
Directed flow (v1, px,dir)
spectators deflected from dense reaction zone
sensitive to pressure
Elliptic flow (v2)
asymmetry out- vs. in-plane emission
emission mostly during early phase
strong sensitivity to EoS
Radial flow (ßt)
isotropic expansion of participant zone
measurable via slope parameter of spectra (blue-shifted temperature)

40. Elliptic Flow: Theory & Experiment
Data from STAR & PHENIX
Good agreement between hydro and pt-differential data
Data saturates for high pt
Kolb & Heinz hep-ph/
Hydro+Micro:
strong sensitivity to QGP EoS
includes proper flavour dynamics
self-consistent freeze-out
D. Teaney, J. Lauret, E. Shuryak
nucl-th/

41. Does v2 Reflect Parton Flow?
Recombination model suggests that hadronic v2 reflects parton v2 :
P. Soerensen, UCLA & SQM2003
measurement of partonic v2 !

42. Contours of Constant Energy Density

43. For central
collisions
these will
be identical.

44. Eliiptic Flow of Thermal Photons

45. Centrality Dependence : Elliptic Flow of Thermal Photons

46. Summary Photon Production in the PCM:
Photon yield very sensitive to parton rescattering
LPM effect needed for proper description of reaction dynamics
HBT experimentally challenging, but feasible with high statistics data sets
calculable in the framework of PCM and hydrodynamics
short emission duration in pre-equilibrium phase: small radii at high pt
larger source at later times due to emission of thermal photons
Contd. ..

47. First ever direct peep into QGP & Hadronic Phases
Photon Production via Jet-Medium Interactions:
jet-photon conversion may contribute up to 4 GeV to photon yield
results compatible with PHENIX data (centrality dependence, RAA)
analogous process for virtual photons: contribution to dilepton production
azimuthal asymmetry of the initial shape of hot & dense fluid.
Elliptic Flow of Thermal Photons:
Large p_T; QGP, small p_T; hadronic phase!
First ever direct peep into QGP & Hadronic Phases