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) Intensity Interferometry of Photons Elliptic Flow of Thermal Photons WHEPP 2006, Bhubaneswar.

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 AGe. V - T. Renk, S. A. Bass and D. K. Srivastava, nucl-th/0505059, Phys. Lett. B. (in press)

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 leadinglogarithmic approximation (2 N) • Binary cross sections are calculated in leading order p. QCD with either a momentum cut-off or Debye screening to regularize IR behavior • Guiding scales: initialization scale Q 0, p. T cut-off p 0 / Debye-mass μD

Initial State: Parton Momenta • flavour and x are sampled from PDFs at an initial scale Q 0 and low x cut-off xmin • initial kt is sampled from a Gaussian of width Q 0 in case of no initial state radiation • virtualities are determined by:

Parton-Parton Scattering Cross-Sections gg gg q q’ q g q qbar q’ qbar’ g g q qbar q g q γ qq qq q qbar g γ q qbar γ γ q qbar g g • a common factor of παs 2(Q 2)/s 2 etc. • further decomposition according to colour flow Biswanath Layek working on including heavy quarks.

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

Collision Rates & Numbers b=0 fm # 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 • 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?

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

What Can We Learn From Photons? • Primary-primary collision contribution to yield is < 10% • Emission duration of preequilibrium phase: ~ 0. 5 fm/c • Photon yield directly proportional to the # of hard collisions • Photon yield scales with Npart 4/3

Photons: pre-equilibrium vs. thermal Øpre-equilibrium contributions are easier identified at large pt: Øwindow of opportunity above pt=2 Ge. V Øat 1 Ge. V, need to take thermal contributions into account Øshort emission time in the PCM, 90% of photons before 0. 3 fm/c Øhydrodynamic calculation with τ0=0. 3 fm/c allows for a smooth continuation of emission rate

HBT Interferometry: Formalism Ø Correlation between two photons with momenta k 1 and k 2 is given by: Ø with S(x, k) the photon source function for a chaotic source Ø use Wigner function scheme (Hansa code by Sollfrank & Heinz) Ø emission vertices of a semiclassical transport are not valid Wigner fnct. Ø need to smear out emission vertices xi by ħ/pi Ø results are given in terms of outward, sideward & longitudinal correlators

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

Landau-Pomeranchuk-Migdal Suppression The LPM effect accounts for the suppression of radiation due to coherence effects in multiple scattering f b e kt a c • the radiated parton e is assigned a formation time: d • 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 …

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

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

Part #2: 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

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

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 jetmedium interactions • suppressed by αEM; negligible as a source of additional jet quenching Ø can escape without rescattering Øuse as probe of energy loss? Ø visible among other sources of electromagnetic signals?

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

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

Photons from jet-plasma interaction

FMS Results: Comparison to Data Calibrate p. QCD calculation of direct and Bremsstrahlung photons via p+p data: For pt<6 Ge. V, FMS photons give significant contribution to photon spectrum: 50% @ 4 Ge. V Fries, Mueller, & Srivastava, PRC 72, 041902 (R) 2005

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

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

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

Jet-plasma or jet-thermal dileptons

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): ü q+g q+ : recoil photon knows the initial energy of the jet ü Measure energy loss of quark as a function of quark energy E • Photons from jet-photon conversion provide a third, independent measurement. (FMS) ü Better handle on the L dependence of energy loss ü Jet-photon conversion is background for photon tagged jets

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 Me. V !

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

Collective Flow: Overview • Directed flow (v 1, px, dir) – spectators deflected from dense reaction zone – sensitive to pressure • Elliptic flow (v 2) – asymmetry out- vs. in-plane emission – emission mostly during early phase – strong sensitivity to Eo. S • Radial flow (ßt) – isotropic expansion of participant zone – measurable via slope parameter of spectra (blue-shifted temperature)

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

Does v 2 Reflect Parton Flow? Recombination model suggests that hadronic v 2 reflects parton v 2 : P. Soerensen, UCLA & STAR @ SQM 2003 Ø measurement of partonic v 2 !

Contours of Constant Energy Density

For central collisions these will be identical.

Eliiptic Flow of Thermal Photons

Centrality Dependence : Elliptic Flow of Thermal Photons

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

Photon Production via Jet-Medium Interactions: • jet-photon conversion may contribute up to 50% @ 4 Ge. V 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!