Net baryon density in Au+Au collisions at the Relativistic Heavy Ion Collider

1. Net baryon density in Au+Au 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 @ RHIC Outlook & Plans for the Future Bass, Mueller, Srivastava

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 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 Bass, Mueller, Srivastava

3. Complication: pair production of B & B • at RHIC, pair production dominates over baryon transport! (ISR) STAR preliminary Bass, Mueller, Srivastava

4. BRAHMS: Net protons vs Rapidity! Bass, Mueller, Srivastava

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 dminof 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 Bass, Mueller, Srivastava

6. 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: Bass, Mueller, Srivastava

7. Parton-Parton Scattering Cross-Sections a common factor of παs2(Q2)/s2 etc. further decomposition according to color flow Bass, Mueller, Srivastava

8. 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 Bass, Mueller, Srivastava

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 Bass, Mueller, Srivastava

10. Testing the PCM Kernel: Collisions in leading order pQCD, the hard cross section σQCD is given by: number of hard collisions Nhard (b) is related to σQCD by: • equivalence to PCM implies: • keeping factorization scale Q2 = Q02 with αs evaluated at Q2 • restricting PCM to eikonal mode Bass, Mueller, Srivastava

11. Testing the PCM Kernel: pt distribution the minijet cross section is given by: • equivalence to PCM implies: • keeping the factorization scale Q2 = Q02 with αs evaluated at Q2 • restricting PCM to eikonal mode, without initial & final state radiation • results shown are for b=0 fm Bass, Mueller, Srivastava

12. 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 Bass, Mueller, Srivastava

13. 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 Bass, Mueller, Srivastava

14. 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? Bass, Mueller, Srivastava

15. Collision Rates & Numbers b=0 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? Bass, Mueller, Srivastava

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 dNnet-baryon/dy5 • is the PCM capable of filling up mid-rapidity region? • is the baryon number transported or released at similar x? Bass, Mueller, Srivastava

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! Bass, Mueller, Srivastava

18. Stopping: Dynamics & Parameters net-baryon density at mid-rapidity depends on initialization scale and cut-off Q0 collision numbers peak strongly at mid-rapidity Bass, Mueller, Srivastava

19. 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 Bass, Mueller, Srivastava

20. Time evolution of net-quark dynamics • net-quark distributions freeze out earlier in the fragmentation regions than at yCM • larger sensitivity to initial state? Bass, Mueller, Srivastava

21. 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 Bass, Mueller, Srivastava

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? Bass, Mueller, Srivastava

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 Bass, Mueller, Srivastava

24. stay tuned for a lot more! Bass, Mueller, Srivastava