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High Energy Photons from Relativistic Heavy Ion Collisions

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)

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High Energy Photons from Relativistic Heavy Ion Collisions

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  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.

  2. 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) 082301 • 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) 061902 (R) • Intensity interferometry of direct photons in Au+Au collisions- S.A. Bass, B. Mueller and D.K. Srivastava, Phys. Rev. Lett. 93 (2004) 162301 • Dynamics of the LPM effect in Au+Au Collisions at 200 AGeV- T. Renk, S.A. Bass and D.K. Srivastava, nucl-th/0505059, Phys. Lett. B. (in press)

  3. 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 dminof 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

  4. 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:

  5. Parton-Parton Scattering Cross-Sections • a common factor of παs2(Q2)/s2 etc. • further decomposition according to colour flow • Biswanath Layek working on including heavy quarks.

  6. 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

  7. Collision Rates & Numbers 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?

  8. 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

  9. 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

  10. 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

  11. 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

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

  13. 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 tformhas elapsed, then the radiation of parton e and it’s daughters does not take place • likewise for parton f with respect to e …

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

  15. 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

  16. Photons via Jet-Plasma Interactions R.J. Fries, B. Mueller, & D.K. Srivastava, PRL 90, 132301 (2003), R.J. Fries, B. Mueller, & D. K. Srivastava, PRC 72, 041902 (R) 2005, See also: S.Turbide, C. Gale, S. Jeon, and G. Moore, PRC 72, 014906 (2005). Dileptons via Jet-Plasma Interactions S. Turbide, C. Gale, D. K. Srivastava, & R. J. Fries, (to be published), hep-ph/0601042 Part #2:

  17. Photon Sources • Hard direct photons • EM bremsstrahlung • Thermal photons from hot medium • Jet-photon conversion Turbide, Gale & Rapp, PRC 69 014903 (2004)

  18. 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?

  19. 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.

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

  21. Photons from jet-plasma interaction

  22. 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: 50% @ 4 GeV Fries, Mueller, & Srivastava, PRC 72, 041902 (R) 2005

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

  24. FMS Photons: Further Confirmations S. Turbide and C. Gale, hep-ph/0512200

  25. Azimuthal Anisotropy of FMS Photons S. Turbide, C. Gale, and R. J. Fries, hep-ph/0508201.

  26. Jet-plasma or jet-thermal dileptons

  27. 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

  28. 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/0511079. 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 !

  29. 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

  30. 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)

  31. 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/0204061 • Hydro+Micro: • strong sensitivity to QGP EoS • includes proper flavour dynamics • self-consistent freeze-out D. Teaney, J. Lauret, E. Shuryak nucl-th/0110037

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

  33. Contours of Constant Energy Density

  34. For central collisions these will be identical.

  35. Eliiptic Flow of Thermal Photons

  36. Centrality Dependence : Elliptic Flow of Thermal Photons

  37. 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. ..

  38. Photon Production via Jet-Medium Interactions: • jet-photon conversion may contribute up to 50% @ 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

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