Relativistic nuclear collision in pQCD and corresponding dynamic simulation

1. Relativistic nuclear collision in pQCD and corresponding dynamic simulation Ben-Hao Sa China Institute of Atomic Energy CIAE

2. INTRODUCTION • HADRON-HADRON COLLI. IN pQCD • DYNAMIC SIMULATION FOR hh COLLI. (PYTHIA MODEL) • NUCLEUS-NUCLEUS COLLI. IN pQCD • DYNAMIC SIMULATION FOR NUCLEUS-NUCLEUS COLLI. (PACIAE MODEL) • LONGITUDINAL SCALING CIAE

3. INTRODUCTION CIAE

4. RHIC, hottest physical frontier in particle and nuclear physics • Primary goal ofRHIC: Study properties of extremely high energy and high density matter • Explore phase transition from HM to QGM, QGP transition • Evidences for sQGP, existed, however, it is still debated CIAE

5. The ways studying RHIC: • Perturbative QCD (pQCD) • Phenomenologic model (eg. NJL) • Hydrodynamic • Dynamical simulation: • Hadron cascade model: PYTHIA,RQMD,HIJING,VENUS, QGSM, HSD, LUCIAE (JPCIAE), AMPT, uRQMD, etc. CIAE

6. Parton and hadron cascade model: PCM (VNI), AMPT (string melting), PACIAE Zhe Xu & C. Greiner • Better parton and hadron cascade model, required by presentRHICexperiments CIAE

7. HADRON-HADRON COLLI. INpQCD CIAE

8. 1. Cross section of hadron production in hadron-hadron ( + ) colli. hh colli. = superposition of parton-parton colli. CIAE

9. : cross section of sub-process : parton ( ) distribution function in hadron ( ) : momentum fraction taking by from : scale of scattering : fragmentation function of to CIAE

10. 2. cross section of partonic sub-process CIAE

11. Subprocess cross section expresses as (after average and sum over initial and final states) LO pQCD cross section of seven contributed processes and two processes with photon are: CIAE

12. CIAE

13. Mandelstum variables: p1 p3 p2 p4 CIAE

14. 3. Parton distribution function (PDF) and fragmentation (decay) function (PFF) • Can’t calculate from first principle • There are a lot of parameterizations based on the experimental data of lepton-hadron deep inelastic scatterings (for PDF) and/or of the annihilations (for PFF) CIAE

15. Most simplest PDF (without depen.) at large x region is something like • Most simple PFF is some thing like • Total fractional momentum carried by : CIAE

16. Approximately 3/5 of parton momentum goes to pions and the rest to kaon and baryon pair. • As gluon is a flavor isosinglet its momentum equally distributes among CIAE

17. DYNAMIC SIMULATION FOR HADRON-HADRON COLLI. (PYTHIA MODEL) CIAE

18. Sketch for pp simulation inPYTHIA Remnant Initial state radiation p Rescattering ? … h Parton distribution function Decay p Final state radiation Hadronization Remnant CIAE

19. Differences from pQCD are: • Monte Carlo simulation instead of analytic calculation • There is additions of initial and final states QCD radiations • String fragmentation instead of rule played by fragmentation function in pQCD CIAE

20. Semihard interactions between other partons of two incoming hadrons (multiple interaction) • Addition of soft QCD process such as diffractive, elastic, and non-diffractive (minimum-bias event) • Remnant may have a net color charge to relate to the rest of final state • Multiple string fragmentation CIAE

21. Multiple String Fragmentation … • Hadron rescattering (?) and decay CIAE

22. We have expended PYTHIA 6.4 including parton scattering and then hadronization (both string fragmentation and coalecense) and hadron rescattering. We are please if you are interested to use it CIAE

23. NUCLEUS-NUCLEUS COLLI. • IN pQCD CIAE

24. A) Hadron production cross section in nucleus-nucleus (A+B) collision is calculated under assumptions of • Nucleus-nucleus collision is a superposition of nucleon-nucleon collision • A+B reaction system is assumed to be a continuous medium B) Convolution method CIAE

25. ``Skecth of AB collision projected to transverse plane” (beam, i. e. z axis, is perpendicular to page) A bA oA b-bB+bA b bB oB B CIAE

26. The cross section can be expressed as • : normalized thickness function of • nucleus • Phenomenological considerations for: CIAE

27. Nuclear shadowing • Multiple scattering (ela. diffractive,…) • Jet quenching (energy lose) CIAE

28. C) Glauber method (Glauber theory with nn inelastic cross replaced by pQCD nn cross section) • : probability having a nn colli. • within transverse area when nucleon • passes at impact parameter • : thickness • function of nn • collision nucleon a c CIAE

29. : probability finding a nucleon in volume in nucleus A at , which is normalized as • Probability for occurring an inela. nn colli. when nucleusA passes Bat an impact parameter is CIAE

30. Probability for occurring n inela. colli. is as there can be up to collisions • Total probability for occurring an event Probability having an inela. Colli. combinations CIAE

31. of nucleus-nucleus inela. colli. at impact parameter is • Total cross section of above event is • If one use pQCD p+p cross section instead of in above equations one has pQCD inela. cross section for (A+B) colli. CIAE

32. DYNAMIC SIMULATION OF NUCLEUS-NUCLEUS COLLI. (PACIAE MODEL) CIAE

33. Overview for PACIAE model: • In PACIAE model • Nucleus-nucleus colli. is decomposed into nucleon-nucleon (nn) colli. • nn colli. is described by PYTHIA, where nn colli. is decomposed into parton-parton colli. described by pQCD • The PACIAE constructs a huge building usingblock of PYTHIA &plays a role like convolution in nucleus-nucleus cooli. in pQCD CIAE

34. ThePACIAE model is composed of (1) Parton initialization (2) Parton evolution (3) Hadronization (4) Hadron evolution four parts CIAE

35. (1) Parton initialization • Nucleon in colliding nucleus is distributed due to Woods-Saxon ( ) and 4 (solid angel) distributions • Nucleon is given beam momentum • Nucleon moves along straight line • nn collision happens if their least approaching distence CIAE

36. their collision time is then calculated • Particle (nucleon) list order # of particle four momenta . . . . . . and nn collision time list CIAE

37. order # of colliding pair collis. time . . . . . . . . . are constructed CIAE

38. A nn collision with least colli. time, selected in colli. time list, executed by PYTHIA with fragmentation switched off • Consequence of nn collision is a configuration of and g ( if diquark (anti-diquark) is forced splitting into randomly) • Nucleon propagate along straight line in time interval equal to difference between last and current colli. times CIAE

39. Update particle list, i. e. move out colliding particles and put in produced particles • Update colli. (time) list: • Move out colli. pairs which constituent involves colliding particle • Add colli. pairs with components one from colliding nucleon and another from particle list • Next nn colli. is selected in updated colli. list, processes above are repeated until nn colli. list is empty CIAE

40. (2) Parton evolution (scattering) • Only 2→2 process, considered for parton scattering and LO pQCD cross section,employed. • If LO pQCD differential cross section denotes as CIAE

41. For process of , for instance • That has to be regularized as by introducing color screening mass CIAE

42. Total cross section of sub-process (4) at high energy • Using above cross sections parton scattering can be simulated by MC CIAE

43. (3) Hadronization • Partons begin to hadronize when their interactions have ceased (freeze-out). • Hadronized by: — Fragmentation model : • Field-Feynman model (IF) • Lund siring fragmentation model — Coalescence model CIAE

44. Ingredients of coalescence model: • Field-Feynman parton generation mechanism is applied to deexcite energetic parton and increase parton multiplicity like multiple fragmentation of string in Lund model • The gluons are forcibly splitting into pair randomly • There is a hadron table composed of CIAE

45. Field-Feynman parton generation mechanism … Original quark jet Created quark pairs from vacuum (if mother with enough energy) 1 3 5 7 9 11 … CIAE

46. mesons & baryons, made of u, d, s, & c quarks Meson: pseudoscalar and vector mesons, and Baryon: SU(4) multiplets of baryons and • Two partons, coalesce into a meson, three partons into a baryon (anti-baryon), due to theirflavor, momentum, and spatial coordinate and accordingtovalencequark CIAE

47. structureof hadron • If coalescing partons can form either a pseudoscalar or a vector meson, such as can form either a or a , a principle of less discrepancy between invariant mass of coalescing partons and mass of coalesced hadron invoked to select one from them The same for baryon. • Three momentum conservation is required CIAE

48. Phase space requirement CIAE

49. (4) Hadron evolution (rescattering) • Consider only rescattering among • FOR simplicity, is assumed at high energ • Assume • Usual tow-body collision model, employed CIAE

50. LOGITUDINAL SCALING CIAE