RHIC Physics with the Parton Cascade Model

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Net baryon density in AuAu collisions at the
Relativistic Heavy Ion Collider
Steffen A. Bass, Berndt Mueller, Dinesh K.
Srivastava
Duke University RIKEN BNL Research Center VECC
Calcutta

• Motivation
• The PCM Fundamentals Implementation
• Tests comparison to pQCD minijet calculations
• Application Reaction Dynamics Stopping _at_ RHIC
• Outlook Plans for the Future

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Why is stopping important?

• the amount of stopping / baryon-transport is a
  direct measure of the violence of the collision
• Thermodynamics net-baryon density relates to µB
• validation of simplified scenarios e.g. Bjorken
  scenario
• tests the validity of novel physics concepts
  e.g. Baryon Junctions

• Initial theoretical expectations
• TDHF and mean field calculations complete
  transparency
• 1F Hydrodynamics complete stopping
• String models incomplete (weak) stopping
• Microscopic transport with rescattering
  incomplete (strong) stopping

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Complication pair production of B B

• at RHIC, pair production dominates over baryon
  transport!

(ISR)
STAR preliminary
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BRAHMS Net protons vs Rapidity!
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Basic Principles of the PCM

• 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 behaviour
• guiding scales initialization scale Q0, pT
  cut-off p0 / Debye-mass µD,
  intrinsic kT, virtuality gt µ0

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Initial State Parton Momenta

• flavor 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

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Parton-Parton Scattering Cross-Sections

• a common factor of pas2(Q2)/s2 etc.
• further decomposition according to color flow

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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?

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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
• direct photons
• net-baryons

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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

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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

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Debye Screening in the PCM

• the Debye screening mass µD can be calculated in
  the one-loop approximation Biro, Mueller Wang
  PLB 283 (1992) 171
• PCM input are the (time-dependent) parton
  phase-space distributions F(p)
• Note ideally a local and time-dependent µD
  should be used to self-consistently calculate the
  parton scattering cross sections
• currently beyond the scope of the numerical
  implementation of the PCM

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Choice of pTmin Screening Mass as Indicator

• screening mass µD is calculated in one-loop
  approximation
• time-evolution of µD reflects dynamics of
  collision varies by factor of 2!
• model self-consistency demands pTmingt µD
• lower boundary for pTmin approx. 0.8 GeV

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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
• are time-scales and collision rates sufficient
  for thermalization?

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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?

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Stopping at RHIC Initial or Final State Effect?

• net-baryon contribution from initial state
  (structure functions) is non-zero, even at
  mid-rapidity!
• initial state alone accounts for
  dNnet-baryon/dy?5
• is the PCM capable of filling up mid-rapidity
  region?
• is the baryon number transported or released at
  similar x?

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Stopping at RHIC PCM Results

• primary-primary scattering releases baryon-number
  at corresponding y
• multiple rescattering fragmentation fill up
  mid-rapidity domain
• initial state parton cascading can fully
  account for data!

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Stopping Dynamics Parameters

• net-baryon density at mid-rapidity depends on
  initialization scale and cut-off Q0
• collision numbers peak strongly at mid-rapidity

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pt dependence of net-quark dynamics

• slope of net-quark pt distribution shows rapidity
  dependence
• qbar/q ratio sensitive to rescattering
• forward/backward rapidities sensitive to
  different physics than yCM

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Time evolution of net-quark dynamics

• net-quark distributions freeze out earlier in the
  fragmentation regions than at yCM
• larger sensitivity to initial state?

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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

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Limitations of the PCM Approach

• Fundamental Limitations
• lack of coherence of initial state
• range of validity of the Boltzmann Equation
• interference effects are included only
  schematically
• hadronization has to be modeled in an ad-hoc
  fashion
• restriction to perturbative physics!
• Limitations of present implementation (as of Oct
  2003)
• lack of detailed balance (no N ? 2 processes)
• lack of selfconsistent medium corrections
  (screening)
• heavy quarks?

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PCM status and the next steps

• results of the last year
• Parton Rescattering and Screening in AuAu at
  RHIC -
  Phys. Lett. B551 (2003) 277
• Light from cascading partons in relativistic
  heavy-ion collisions
  - Phys. Rev. Lett. 90 (2003) 082301
• Semi-hard scattering of partons at SPS and RHIC
  a study in contrast - Phys.
  Rev. C66 (2002) 061902 Rapid Communication
• Net baryon density in AuAu collisions at the
  Relativistic Heavy Ion Collider
• Phys. Rev. Lett. 91 (2003) 052302
• Transverse momentum distribution of net baryon
  number at RHIC
• Journal of Physics G29 (2003) L51-L58
• the next steps
• inclusion of gluon-fusion processes analysis of
  thermalization
• investigation of the microscopic dynamics of
  jet-quenching
• heavy quark production predictions for charm
  and bottom
• hadronization develop concepts and
  implementation

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stay tuned for a lot more!