Light from Cascading Partons

1
Light from Cascading Partons in Relativistic
Heavy-Ion Collisions
Steffen A. Bass
Duke University

• Motivation
• The PCM Fundamentals Implementation
• Photon production in the PCM
• Medium Effects Jet-Photon Conversion (FMS
  Photons)

2
A brief history of the PCM

• concept developed by Klaus Kinder-Geiger and
  Berndt Mueller in 1991 (Nucl.Phys.B369600-654,199
  2 )
• original implementation VNI by KKG was not
  further maintained after his untimely death in
  the crash of Swissair 111
• newly revised and improved implementation VNI/BMS
  by SAB, B. Mueller and D.K. Srivastava
• various (simplified) implementations from other
  groups available as well MPC, ZPC, gromit

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 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

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 pas2(Q2)/s2 etc.
• further decomposition according to color flow

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?q?

7
Parton Fusion (2?1) Processes

• in order to account for detailed balance and
  study equilibration, one needs to account for the
  reverse processes of parton splittings
• explicit treatment of 3?2 processes (D. Molnar,
  C. Greiner)
• glue fusion

• qg ? q
• gg ? g

work in progress
8
Hadronization

• requires modeling parameters beyond the PCM
  pQCD framework
• microscopic theory of hadronization needs yet to
  be established
• phenomenological recombination fragmentation
  approach may provide insight into hadronization
  dynamics
• avoid hadronization by focusing on
• net-baryons
• direct photons

9
Testing the PCM Kernel Collisions

• in leading order pQCD, the hard cross section
  sQCD is given by

• number of hard collisions Nhard (b) is related
  to sQCD by

• equivalence to PCM implies
• keeping factorization scale Q2 Q02 with as
  evaluated at Q2
• restricting PCM to eikonal mode

10
Testing the PCM Kernel pt distribution

• the minijet cross section is given by

• equivalence to PCM implies
• keeping the factorization scale Q2 Q02 with as
  evaluated at Q2
• restricting PCM to eikonal mode, without initial
  final state radiation
• results shown are for b0 fm

11
Parton Cascade in a Box
T. Renk

• run PCM in a box with periodic boundary
  conditions
• kinetic and chemical equilibration
• relaxation times
• Equation of State

• box mode with 2-2 scattering
• proper thermal and chemical equilibrium obtained
• chemical equilibration time 2500 fm/c!!

12
Parton Rescattering cut-off Dependence

• duration of perturbative (re)scattering phase
  approx. 2-3 fm/c
• decrease in pt cut-off strongly enhances parton
  rescattering

13
Collision Rates Numbers
b0 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?

14
SPS vs. RHIC a study in contrast

• perturbative processes at SPS are negligible for
  overall reaction dynamics
• sizable contribution at RHIC, factor 14 increase
  compared to SPS

15
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
• Intensity interferometry of direct photons in
  AuAu collisions- S.A. Bass, B. Mueller and D.K.
  Srivastava, Phys. Rev. Lett. 93 (2004) 162301
• Dynamics of the LPM effect in AuAu Collisions at
  200 AGeV- T. Renk, S.A. Bass and D.K.
  Srivastava, Phys. Lett. B632 (2006) 632

16
Photon Production in the PCM

• relevant processes
• Compton q g ?q ?
• annihilation q qbar ? g ?
• bremsstrahlung q ?q ?

• photon yield very sensitive to parton-parton
  rescattering

17
What can we learn from photons?

• primary-primary collision contribution to yield
  is lt 10
• emission duration of pre-equilibrium phase 0.5
  fm/c

• photon yield directly proportional to the of
  hard collisions
• photon yield scales with Npart4/3

18
Photons pre-equilibrium vs. thermal

• pre-equilibrium contributions are easier
  identified at large pt
• window of opportunity above pt2 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 t00.3 fm/c allows
  for a smooth continuation of emission rate
• caveat medium not equilibrated at t0

19
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 h/pi
• results are given in terms of outward, sideward
  longitudinal correlators

20
Photons HBT Interferometry

• pt2 GeV pre-thermal photons dominate, small
  radii
• pt1 GeV superposition of pre- thermal
  photons increase in radii

21
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 its daughters does not take place
• likewise for parton f with respect to e

22
LPM Reaction Dynamics
gluon pt distribution

• high pt harder slope, enhanced particle
  production
• low pt suppression of particle production

23
Photon Production LPM comparison to data

• PCM without LPM
• overprediction of photon yield
• PCM with LPM
• photon yield for pt lt 6 GeV strongly reduced
• strong pt dependence of LPM suppression
• decent agreement with data

24

• 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 (2005)
25
Photon sources

• Hard direct photons
• EM bremsstrahlung
• Thermal photons from hot medium
• Jet-photon conversion

Turbide, Gale Rapp, PRC 69 014903 (2004)
26
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 aEM 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?

27
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 gt 1 GeV/c.
• photon carries momentum of the hard parton
• Jet-Photon Conversion

28
Jet-Photon Conversion Rates

• annihilation and compton rates
• thermal medium

29
FMS Results Comparison to Data
calibrate pQCD calculation of direct and
Bremsstrahlung photons via pp data

• for ptlt6 GeV, FMS photons give significant
  contribution to photon spectrum 50 _at_ 4 GeV

Fries, Mueller Srivastava, PRC 72 (2005) 041902
30
Application Monitoring Jet Quenching

• full jet reconstruction not possible at RHIC
• Measure suppression of single inclusive hadron
  spectra (compare to pp baseline)
• better photon-tagged jets (Wang Sarcevic)
  
• qg ? 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

31
Summary

• Parton Cascade Model
• promising tool to study the dynamics of hard
  probes
• pQCD processes cannot create sQGP medium
• 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 hydro
• Photon Production via Jet-Medium Interactions
• jet-photon conversion may contribute up to 50 _at_
  4 GeV to photon yield
• results compatible with PHENIX data (centrality
  dependence, RAA)
• analogous process for virtual photons
  contribution to dilepton production

32
FMS Centrality Dependence and Jet-Quenching

• centrality dependence well described
• effect of energy-loss on jets before conversion
  20

(Turbide, Gale, Jeon Moore hep-ph/0502248)