1. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #1 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 @ RHIC Outlook & Plans for the Future Net baryon density in Au+Au collisions at the Relativistic Heavy Ion Collider

2. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #2 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 μ B 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

3. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #3 Complication: pair production of B & B STAR preliminary (ISR)  at RHIC, pair production dominates over baryon transport!

4. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #4 BRAHMS: Net protons vs Rapidity!

5. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #5 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 Q 0, p T cut-off p 0 / Debye-mass μ D, intrinsic k T, virtuality > μ 0

6. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #6 Initial State: Parton Momenta virtualities are determined by: flavor and x are sampled from PDFs at an initial scale Q 0 and low x cut-off x min initial k t is sampled from a Gaussian of width Q 0 in case of no initial state radiation

7. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #7 Parton-Parton Scattering Cross-Sections g g  g gq q’  q q’ q g  q gq qbar  q’ qbar’ g g  q qbarq g  q γ q q  q qq qbar  g γ q qbar  q qbarq qbar  γ γ q qbar  g g a common factor of πα s 2 (Q 2 )/s 2 etc. further decomposition according to color flow

8. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #8 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: P q  qg, P g  gg, P g  qqbar & P q  qγ

9. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #9 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

10. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #10 Testing the PCM Kernel: Collisions in leading order pQCD, the hard cross section σ QCD is given by: number of hard collisions N hard (b) is related to σ QCD by: equivalence to PCM implies:  keeping factorization scale Q 2 = Q 0 2 with α s evaluated at Q 2  restricting PCM to eikonal mode

11. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #11 Testing the PCM Kernel: p t distribution the minijet cross section is given by: equivalence to PCM implies:  keeping the factorization scale Q 2 = Q 0 2 with α s evaluated at Q 2  restricting PCM to eikonal mode, without initial & final state radiation results shown are for b=0 fm

12. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #12 Debye Screening in the PCM the Debye screening mass μ D 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 μ D should be used to self- consistently calculate the parton scattering cross sections  currently beyond the scope of the numerical implementation of the PCM

13. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #13 Choice of p T min : Screening Mass as Indicator screening mass μ D is calculated in one-loop approximation time-evolution of μ D reflects dynamics of collision: varies by factor of 2! model self-consistency demands p T min > μ D :  lower boundary for p T min : approx. 0.8 GeV

14. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #14 Parton Rescattering: cut-off Dependence duration of perturbative (re)scattering phase: approx. 2-3 fm/c decrease in p t cut-off strongly enhances parton rescattering are time-scales and collision rates sufficient for thermalization?

15. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #15 Collision Rates & Numbers 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? b=0 fm # of collisions lofull q + q70.6274 q + qbar1.338.52 q + g428.32422.6 g + g514.44025.6

16. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #16 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 dN net-baryon /dy  5 is the PCM capable of filling up mid-rapidity region? is the baryon number transported or released at similar x?

17. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #17 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!

18. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #18 Stopping: Dynamics & Parameters net-baryon density at mid-rapidity depends on initialization scale and cut-off Q 0 collision numbers peak strongly at mid-rapidity

19. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #19 p t dependence of net-quark dynamics slope of net-quark p t distribution shows rapidity dependence qbar/q ratio sensitive to rescattering forward/backward rapidities sensitive to different physics than y CM

20. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #20 Time evolution of net-quark dynamics net-quark distributions freeze out earlier in the fragmentation regions than at y CM  larger sensitivity to initial state?

21. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #21 SPS vs. RHIC: a study in contrast SPSRHIC cut-off p t min (GeV)0.71.0 # of hard collisions255.03618.0 # of fragmentations17.02229.0 av. Q 2 (GeV 2 )0.81.7 av. (GeV)2.64.7 perturbative processes at SPS are negligible for overall reaction dynamics sizable contribution at RHIC, factor 14 increase compared to SPS

22. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #22 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?

23. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #23 PCM: status and the next steps … results of the last year: 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 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

24. Bass, Mueller, SrivastavaRHIC Physics with the Parton Cascade Model #24 stay tuned for a lot more!