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Correlation in Jets at RHIC

This presentation provides an outline of the correlation observed in jets at RHIC, including discussions on hadron production, centrality dependence of correlation, the ridge under the jet peak, the Omega puzzle and its resolution, proton trigger and meson partners, and more.

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Correlation in Jets at RHIC

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  1. Correlation in Jets at RHIC Rudolph C. Hwa University of Oregon Institute of Nuclear Theory University of Washington December 5, 2006

  2. Outline • General comments on hadron production at high pT • d-Au collisions • Au-Au collisions • centrality dependence of correlation • ridge under the jet peak • Omega puzzle and its resolution • proton trigger and meson partners • Transfragmentation region • Mid-F/B rapidity correlation • Away-side correlation • 2-jet recombination -- LHC

  3. pT 0 2 4 6 8 10 soft hard Regions of transverse momentum Traditional classification in terms of scattering pQCD + FF

  4. pT 0 2 4 6 8 10 soft hard A different classification in terms of hadronization pT 0 2 4 6 8 10 (low) (intermediate) (high) shower-shower thermal-thermal thermal-shower Terminology used in recombination Regions of transverse momentum Traditional classification in terms of scattering pQCD + FF

  5. soft TT TS hard SS Phenomenological successes of this picture thermal Pion distribution (log scale) fragmentation Transverse momentum

  6. fragmentation thermal TT TS SS  production in AuAu central collision at 200 GeV Hwa & CB Yang, PRC70, 024905 (2004)

  7. Shower parton distributions are determined from Fragmentation function Basic assumption: Dynamically independent, kinematically constrained. Basic equationfor meson production by recombination

  8. e e p U p U TTS+TSS D Proton production by recombination Proton recombination function determined in the valon model

  9. for pT ~ 3 GeV/c in Au-Au collision at 200 GeV. recombination/coalescence Commonly regarded as “baryon anomaly”. There is no “baryon anomaly”, if fragmentation is not regarded as the standard hadronization process.

  10. Since , the p/ ratio is characteristic of fragmentation. Conventional thinking: Jets  fragmentation of hard partons That’s true in e+e- annihilation, and pp collision, but false in heavy-ion collisions at moderate pT (even with modified fragmentation function). May still be valid for pT>8 GeV/c

  11. correlations between shower partons produced hadrons jets in x colliding system e+e- Au-Au

  12. no correlation  0 x1 x2 Hwa & Tan, PRC 72, 024908 (2005)

  13. fi(k) fi(k) fi(k) fi(k) is small for 0-10%, but smaller for 80-92%

  14. Factorizable terms: k q1 q2 q3 q4 Non-factorizable terms correlated Correlation of pions in jets in HIC Two-particle distribution They do not contribute to C2(1,2)

  15. negative correlation Pion transverse momenta p1 and p2 Hwa & Tan, PRC 72, 024908 (2005)

  16. STAR, PRL 95, 152301 (2005) Trigger 4 < pT < 6 GeV/c Factor of 3 enhancement C2(1,2) treats 1 and 2 on equal footing. Experimental data choose particle 1 as trigger, and studies particle 2 as an associated particle. (background subtraction) Hard for medium modification of fragmentation function to achieve, but not so hard for recombination involving thermal partons.

  17. Au+Au @ 200 GeV 3GeV/c<pTtrigger<6GeV/c STAR preliminary Bielcikova, at Hard Probes (06) Associated particle distributions in the recombination model Hwa & Tan, PRC 72, 057902 (2005)

  18. If initial transverse broadening of parton gives more hadrons at high pT, then • forward has more transverse broadening • backward has no broadening Forward-backward asymmetry in d+Au collisions Expects more forward particles at high pT than backward particles F/B > 1 B/F < 1

  19. Backward-forward ratio at intermediate pT in d+Au collisions (STAR) B/F

  20. STAR preprint nucl-ex/0609021 B/F asymmetry calculated in the Recombination Model (Hwa, Yang, & Fries, PRC 05)

  21. BRAHMS, PRL 93, 242303 (2004) BRAHMS data show that in d+Au collisions there is suppression at larger . Hwa, Yang, Fries, PRC 71, 024902 (2005). No change in physics from =0 to 3.2 Soft parton density decreases, as is increased (faster for more central collisions). Large  TS recombination diminishes at higher . More suppressed in central than in peripheral collisions.

  22. P1 Pedestal Why? P2 Correlation with triggers  and  distributions STAR, PRL 95, 152301 (2005)

  23. Longitudinal Transverse t=0 later

  24. Events with jets Thermal medium enhanced due to energy loss of hard parton in the vicinity of the jet new parameter T’- T = T > 0 Thermal partons Events without jets

  25. enhanced thermal trigger associated particle peak in  &  Pedestal ForSTSTrecombination Sample with trigger particles and with background subtracted

  26. P1 parton distribution 0.15 < p2 < 4 GeV/c, P1 = 0.4 2 < p2 < 4 GeV/c, P2 = 0.04 less reliable P2 T ’ adjusted to fit pedestal find T ’= 0.332 GeV/c cf. T = 0.317 GeV/c T = 15 MeV/c Pedestal in  more reliable

  27. pedestal T=15 MeV Chiu & Hwa, PRC 72, 034903 (2005)

  28. Associated particle distribution in  Chiu & Hwa, PRC 72, 034903 (2005)

  29. pT distribution of  by recombination For   and  production at intermediate pT Strange quark shower is very suppressed.

  30. Hwa & CB Yang, nucl-th/0602024 hard parton scattering recombination s s s s s s fragmentation There are other particles associated with and recombination If it is hard scattering followed by fragmentation, one expects jets of particles. Thermal-parton recombination

  31. Predict: no associated particles giving rise to peaks in , near-side or away-side. A prediction that can be checked now! Since shower partons make insignificant contribution to  production for pT<8 GeV/c, no jets are involved. Select events with  or  in the 3<pT<6 region, and treat them as trigger particles. Thermal partons are uncorrelated, so all associated particles are in the background. STAR did the analysis to check our prediction, and reported their result at QM06.

  32. STAR Ruan (Tuesday, plenary) Barranikova (Wed, plena.) Bielcikova (Sunday, 3.1) Phantom jet At face value the data falsify the prediction and discredits RM. I now explain why the prediction was wrong and how the data above can be understood. Recombination still works, but we need a deeper understanding of what is going on.

  33. (1)  spectrum is exponential up to 6 GeV/c. (2)  triggered events have associated particles. The core issue is the (seemingly) contradictory phenomena: (1) means that there is no contribution from hard scattering, which is power-law behaved; hence, there is no jet. (2) means that there is jet structure. The resolution is to recognize that it is a phantom jet.

  34. 3<pt,trigger<4 GeV pt,assoc.>2 GeV Au+Au 0-10% preliminary Jet+Ridge ()Jet () Jet) preliminary  yield,)    Jet yield is independent of centrality. Npart Calderon showed on Tuesday But p/ ratio depends on centrality. A lot of action is going on in the ridge!

  35. J/R~10-15% Jet+ridge Jet only J. Bielcikova (HP06, QM06) at lower pt(assoc)  trigger even lower! Jet+Ridge on near side J. Putschke, QM-1.3 Unidentified charged hadron

  36. Thus we have a ridge without any significant peak on top. The ridge would not be there without a hard scattering,but it is not a usual jet, because it contain no shower partons, only thermal partons. Phantom Jet When pT(trig) is low, and the trigger is , it is not in the jet, since s quark is suppressed in the shower partons. The s quarks in the ridge form the . One can see the usual peak when pT(assoc) is increased, and the ridge height will decrease.

  37. The ridge has been interpreted as the recombination of enhanced thermal partons due to the energy loss to the medium by the passage of hard parton. Radial expansion does not broaden the ridge under the peak in  Longitudinal expansion results in broad  ridge Chiu & Hwa, PRC 72, 034903 (2005)

  38. The  looks like a peak, but it is all ridge. Resolution of the  puzzle The ridge contains thermalized partons: u, d, s Hence, sss recombine to form the trigger . Other partons can form the associated particles. (1)The pT distribution of  is exponential. (2)There are associated particles. Our earlier prediction that there is no jet is still right, if ‘jet’ is meant to be the usual jet. But we were wrong to conclude that there would be no associated particles, because a phantom jet is associated with the  and it is the ridge that sits above the background.

  39. Since  is among the particles in the ridge and is formed by TTT recombination, everything calculated previously remains valid. Predictions for  triggered events: The ridge should be found in . The ridge has abundant u, d, s. So the associated particles should have the characteristic feature of recombination, i.e., large p/ and /K ratios, ~O(1). Since the ridge arises out of enhanced thermal partons, the associated particles should have exponential pT distribution.

  40. meson trigger from the jet baryon trigger from the ridge J/R < 0.1? J/R > 1? Baryon vs meson triggered events (PHENIX) Meson yield in jet is high. Meson yield in ridge decreases exponentially with pT. Ridge is developed in very central collisions.

  41. PHOBOS, nucl-ex/0509034 Back et al, PRL 91, 052303 (2003) Forward production of hadrons Without knowing pT, it is not possible to determine xF

  42. BRAHMS, nucl-ex/0602018

  43. xF = 0.9 xF = 0.8 TFR

  44. In pB collision the partons that recombine must satisfy p B A B But in AB collision the partons can come from different nucleons Theoretically, can hadrons be produced at xF > 1? (TFR) It seems to violate momentum conservation, pL > √s/2. In the recombination model the produced p and  can have smooth distributions across the xF = 1 boundary.

  45. proton pion • : momentum degradation factor proton-to-pion ratio is very large. Regeneration of soft parton has not been considered. Particles at xF>1 can be produced only by recombination. Hwa & Yang, PRC 73,044913 (2006)

  46. xF = 0.9 xF = 0.8 xF = 1.0 TFR TS ? TTT TT

  47. Hwa & Yang, nucl-th/0605037

  48. Hwa & Yang, nucl-th/0605037 (to be revised)

  49. Hwa & Yang, nucl-th/0605037 Thermal distribution fits well High Rp/ is already known from 200 GeV data, not 62.4 GeV yet.  no shower partons involved  no jets involved  no jet structure This is not a ridge effect, since jets are suppressed at large .  no associated particles

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