An Introduction to Particle Production in High Energy Nuclear Collisions

1. An Introduction to Particle Production in High Energy Nuclear Collisions Jamal Jalilian-Marian Institute for Nuclear Theory University of Washington

2. Outline • Perturbative QCD (pQCD) • Proton-proton collisions • Collinear factorization • Distribution functions • QCD at high energy/large A • Color Glass Condensate (CGC) • Proton (deuteron)-nucleus collisions • Particle production • Signatures of CGC at RHIC • Outlook

3. Quantum ChromoDynamics (QCD) Theory of strong interactions between quarks and gluons (partons) Gluons: bosons (spin 1) Flavor: blind Color: 8 Quarks: fermions (spin 1/2) Flavor: up, down, strange, charm, bottom, top Color: 3 (upupup) gs gs the coupling constant:

4. running of the coupling constant perturbative QCD: expansion in the coupling constant

5. pQCD in pp Collisions Collinear factorization: separation of long and short distances fragmentation function distribution functions hard scattering

6. Fraction of hadron momentum carried by a parton = xF Parton model • Bjorken: but xBj=Q2/S fixed distribution functions depend only on xBj • Feynman: Parton constituents of proton are “quasi-free” on interaction time scale 1/Q << 1/L (interaction time scale between partons)

7. evolution of distribution functions Bj scaling Dokshitzer-Gribov-Lipatov-Altarelli-Parisi

8. Resolving the hadron -DGLAP evolution increasing But… the phase space density decreases -the proton becomes more dilute

9. How about scattering of nuclei? RHIC, LHC I) modification of initial state: “nuclear shadowing” II) modification of hard scattering: multiple scattering III) modification of fragmentation functions

10. modification of the nuclear structure functions

11. QCD in the Regge-Gribov limit Regge Gribov

12. DIS in the Regge-Gribov limit: evolution with x Balitsky-Fadin-Kuraev-Lipatov

13. Resolving the nucleus/hadron:Regge-Gribov limit Radiated gluons have the same size (1/Q2) - the number of partons increase due to the increased longitudinal phase space Physics of strong fields in QCD, multi-particle production- possibly discover novel universal properties of theory in this limit

14. Particle production in the Regge-Gribov limit kt factorization: Incoming partons have kt Un-integrated distributions: are they universal? Factorization theorems are proven to Leading Order+ in as

15. Road map of the strong interactions Energy (rapidity) L2QCD Momentum Resolution Q2

16. Non-linear evolution: Gluon recombination Gribov,Levin,Ryskin QCD Bremsstrahlung Nucleus

17. Mechanism for parton saturation Competition between “attractive” bremsstrahlung and “repulsive” recombination effects Maximal phase space density => saturated for

18. Bosons with large occupation # ~ - form a condensate • Typical momentum of gluons is Nucleus/Hadron at high energy is a Color Glass Condensate • Gluons are colored • Random sources evolving on time scales much larger than natural time scales-very similar to spin glasses

19. The nuclear “oomph” factor d ~ 0.3

20. Scale separating sources and fields The effective action Generating functional: Gauge invariant weight functional describing distribution of the sources where To lowest order, McLerran,Venugopalan; Jalilian-Marian,Kovner,Leonidov,Weigert; Fukushima

21. The classical field of the nucleus at high energies Saddle point of effective action-> Yang-Mills equations Solutions are non-Abelian Weizsäcker-Williams fields Careful solution requires smearing in

22. Random Electric & Magnetic fields in the plane of the fast moving nucleus z

23. Integrate out small fluctuations => Increase color charge of sources QCD at High Energy: Wilsonian RG ( as Log 1/x ) Fields Sources

24. Wilson RG at small x Color charge grows due to inclusion of fields into hard source with decreasing x: Because of strong fields All insertions are O(1) obeys a non-linear Wilson renormalization group equation

25. At each step in the evolution, compute 1-point and 2-point functions in the background field The JIMWLK (functional RG) equation Jalilian-Marian,Iancu,McLerran,Weigert,Leonidov,Kovner

26. JIMWLK equations describe evolution of all N-point correlation functions with energy the 2-point function Tr [1 - U+ (xt) U (yt)] (probability for scattering of a quark-anti-quark dipole on a target) Rummukainen,Weigert Can solve JIMWLK in two limits: I) Strong field: exact scaling - f (Q2/Q2s) for Q < Qs II) Weak field: perturbative QCD

27. How does Q_s behave as function of Y? Fixed coupling LO BFKL: LO BFKL+ running coupling: Re-summed NLO BFKL + CGC: Triantafyllopolous Very close to HERA result!

28. How can we probe all this?

29. Signatures of CGC at RHIC • Multiplicities (dominated by pt < Qs): • energy, rapidity, centrality dependence • Single particle production: hadrons, photons, dileptons • rapidity, pt, centrality dependence • Fixed pt: vary rapidity (evolution in x) • Fixed rapidity: vary pt (transition from dense to dilute) • Two particle production: • back to back correlations

30. Kinematics RHIC (S = 200 GeV):  y ~ 5.3 LHC (S = 5.5 TeV):  y ~ 8.6 LHC (S = 14 TeV):  y ~ 9.6  y beam remnants mid rapidity (y = 0,  = 900) forward rapidity  --> 0 y = 0: x1 = x2 = 10-2 y ~ 4: x1~ 0.55, x2~10-4 (RHIC: for pt2= 4 GeV2) Qs2 (y=0) = 2 GeV2 Qs2 (y=4) = 2 e0.3 y = 6.65 GeV2 two orders of magnitude evolution in x

31. CGC: qualitative expectations Classical (multiple elastic scattering): pt >> Qs : enhancement RpA = 1 + (Qs2/pt2) log pt2/L2 + … RpA (pt ~ Qs) ~ log A position and height of enhancement are increasing with centrality Gelis,Jalilian-Marian Quantum evolution in x: essential as we go to forward rapidity can show analytically the peak disappears as energy/rapidity grows and levels off at RpA ~ A-1/6Kharzeev,Kovchegov,Tuchin

32. CGC vs. RHIC enhancement suppression BRAHMS

33. Consider scattering of a quark from the classical field Am if the field is strong, we need to include multiple scattering Weak field: single gluon exchange = strong field similar for gluon scattering

34. Single inclusive hadron production: as corrections + integration over final state momenta: collinear divergence 2 2 2 as Pg/q Log Q2 dsg A --> g X

35. Single Hadron Production in pA NF, NA are dipoles in fundamental and adjoint representation and satisfy the JIMWLK evolution equation Dumitru, Hayashigaki, Jalilian-Marian NPA765 (2006) 464

36. 2 ---> 1 Kinematics for dA at RHIC

37. Application to dA at RHIC • Distribution/fragmentation functions • fq/p, fg/p from HERA, Dh/q,g from e+ e- • Ignore deuteron shadowing • Dipole cross sections: NF , NA • Solution of JIMWLK evolution equations • Parameterizations • IIM (fit to HERA data on protons) • KKT (fit to RHIC data on dA) • DHJ (fit to RHIC data on dA) • pt spectra at y=0, 3.2 and y=4

38. Application to dA at RHIC

39. Predictions for dA at RHIC Dumitru, Hayashigaki,Jalilian-MarianNPA765 (2006) 464 J. Adams for STAR, nucl-ex/0602011 submitted to PRL

40. 2 ---> 1 Kinematics for dA at RHIC

42. KKT

43. IIM vs. DHJ

44. Particle production in dA at RHIC Dumitru, Hayashigaki, Jalilian-Marian hep-ph/0512129

45. Photon + Hadron production Jalilian-Marian, NPA

46. Photon + Hadron: isolation cut Jalilian-Marian, NPA

47. Current and future colliders Parton density LHC eRHIC RHIC HERA SLAC R ~1fm

48. kinematics: forward RHIC ~ mid rapidity LHC

49. From pA to DIS: crossing symmetry + pA: DIS: + + Gelis,Jalilian-Marian PRD67 (2003) 074019 CGCdegrees of freedom: dipoles

50. Deep Inelastic Scattering structure function: F2 HERA eRHIC Dumitru,Hayashigaki,Jalilian-Marian, in progress