# Presentation: 948462

## RHIC Physics with the Parton Cascade Model

- Duke University
- RIKEN BNL Research Center
- VECC Calcutta

-  The PCM: fundamentals & implementation
-  Applications: stopping @ RHIC and direct photons
-  Outlook & plans for the future

**RHIC Physics with the Parton Cascade Model**

## The PCM Model: current status

- results since QM’02:
*Parton Rescattering and Screening in Au+Au 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 Au+Au 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

## 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 *d**min** *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 > μ0

## 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 Dec 2003)**
-  lack of detailed balance: (no N  2 processes)
-  lack of selfconsistent medium corrections (screening)
-  heavy quarks?

## Initial State: Parton Momenta

-  virtualities are determined by:

-  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

## 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 color flow

## Initial and final state radiation

**space-like branchings:**

**time-like branchings:**

- Probability for a branching is given in terms of the Sudakov form factors:

-  Altarelli-Parisi splitting functions included: Pqqg , Pggg , Pgqqbar & Pqqγ

## 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

## Model Parameters

- momentum cut-off p0

## 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

## 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 pTmin> μD :
- lower boundary  for pTmin : approx. 0.8 GeV

## Baryon stopping at RHIC

- influence of initial state
- parton rescattering
- temporal evolution

## Baryon 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?

## Baryon 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!

## pt dependence of net-quark dynamics

-  slope of net-quark pt distribution shows rapidity dependence
-  net-quark distributions freeze out earlier in the fragmentation regions than at yCM
-  forward/backward rapidities sensitive to initial state / CGC?

## Direct Photons

- spectra and mass dependence
- production times & dynamics
- comparision: RHIC vs. SPS

## 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

## What can we learn from photons?

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

- primary-primary collision contribution to yield is < 10%
- emission duration of pre-equilibrium phase: ~ 0.5 fm/c

## Photon Production at SPS

- at SPS, effects of parton rescattering can be observed via direct photons
- including intrinsic kT, the PCM can account for measured photon yield

## SPS vs. RHIC: a study in contrast

|  | SPS | RHIC |
| --- | --- | --- |
| cut-off ptmin (GeV) | 0.7 | 1.0 |
| # of hard collisions | 255.0 | 3618.0 |
| # of fragmentations | 17.0 | 2229.0 |
| av. Q2 (GeV2) | 0.8 | 1.7 |
| av.         (GeV)  | 2.6 | 4.7 |

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

## Summary and Outlook

- Baryon Stopping:
-  initial state + PCM are compatible with the measured net-baryon density
-  no need for exotic and/or non-perturbative mechanisms
-  initial state contributes 30%, parton scattering 70% to dN/dy
-  forward/backward rapidities may be sensitive to initial parton distribution
- Direct Photons:
-  strong sensitivity to parton rescattering
-  short emission duration in pre-equilibrium phase
- Outlook:
-  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

## The End