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Ridges and Jets at RHIC and LHC
Rudolph C. Hwa University of Oregon Quantifying Hot QCD Matter INT UW June, 2010
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What is common between RHIC and LHC:
Partons have to hadronize at the end when density is low, no matter what the initial state may be. Universal approach: parton recombination at all pT at any initial energy What is different: Which partons recombine? Jet-jet reco at LHC. Key point of this talk: Late-time physics can affect our assumption about the nature of early-time physics Have to understand RHIC data well, before projecting to LHC.
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Introduction Usual domains in pT at RHIC pT Hadronization ReCo Hydro
low ReCo intermediate high pT 2 6 Hydro pQCD GeV/c TT TS SS Hadronization Cooper-Frye Fragmentation kT > pT k1+k2=pT lower ki higher density
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Regions in time (fm/c) Initial state scattering occurs even earlier.
0.6 rapid thermalization hydro (fm/c) 1 8 Initial state scattering occurs even earlier. hadronization An example of late-time physics affecting thinking about early-time physics: Cronin effect: --- initial-state or final-state effect? Cronin effect in pA is larger for proton than for ; it implies final-state effect (in ReCo), not hard-scattering+frag, not hydro. Early-time physics: CGC, P violation, … Pay nearly no attention to hadronization at late times.
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Large structure of Ridge --- PHOBOS
PHOBOS, PRL104,062301(10) ~ 4, pTtrig>2.5GeV/c Referred to as “long-range” correlation on the near side Before understanding that, we should understand single-particle distribution, summed over all charged and integrated over all pT PHOBOS PRL 91, (03) BRAHMS has dN/dy at fixed =0.4 GeV/c Simpler scenario
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y is commonly identified with
BRAHMS PLB 684,22(10) BRAHMS only PHOBOS all charged How is this difference to be understood? How much does it contribute to the distribution? Proton contribution should not be ignored.
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how one goes from initial-state to final state in one step
Dusling, Gelis, Lappi, Venugopalan arXiv: Early-time physics: CGC how one goes from initial-state to final state in one step
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Ridge without detailed input on early-time physics
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First, we need to understand single-particle distribution in
First, we need to understand single-particle distribution in pT, , Npart, and before correlation. Topics to be covered: Hadronization Ridges with or without trigger Jets
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Hadron production at low pT in the recombination model
Pion at y=0 Recombination function q and qbar momenta, k1, k2, add to give pion pT It doesn’t work with transverse rapidity yt TT At low pT same T for partons, , p Proton at y=0 phase space factor in RF for proton formation TTT empirical evidence
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PHENIX, PRC 69, 034909 (04) went on to mT plot
Same T for , K, p in support of recombination. went on to mT plot Proton production from recombination Slight dependence on centrality --- to revisit later
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Ridge formation SS ST TT trigger peak (J) ridge (R) Mesons:
associated particles SS trigger ST peak (J) TT ridge (R) Mesons: Baryons: TTT in the ridge Suarez QM08 B/M in ridge even higher than in inclusive distr.
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Jet and Ridge Yield STAR Preliminary Feng, QM08 s
jet part, near-side ridge part, near-side 20-60% jet part, near-side ridge part, near-side top 5% In-plane Out-of-plane 1 4 3 2 5 6 s 3<pTtrig<4, 1.5<pTassoc<2.0 GeV/c Different s dependencies for different centralities --- important clues on the properties of correlation and geometry
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Hard parton directed at s , loses energy along the way, and enhances thermal partons in the vicinity of the path. s The medium expands during the successive soft emission process, and carries the enhanced thermal partons along the flow. Flow direction normal to the surface Reinforcement of emission effect leads to a cone that forms the ridge around the flow direction . But parton direction s and flow direction are not necessarily the same. s If not, then the effect of soft emission is spread out over a range of surface area, thus the ridge formation is weakened. Correlation between s and
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Correlated emission model (CEM)
Chiu-Hwa, PRC 79, (09) STAR Feng QM08 3<pTtrig <4 1.5 <pTassoc <2 GeV/c s
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Single-particle distribution at low pT (<2 GeV/c)
That was Ridge associated with a trigger Single-particle distribution at low pT (<2 GeV/c) Region where hydro claims relevance --- requires rapid thermalization 0 = 0.6 fm/c Something else happens even more rapidly Semi-hard scattering 1<kT<3 GeV/c Copiously produced, but not reliably calculated in pQCD t < 0.1 fm/c 1. If they occur deep in the interior, they get absorbed and become a part of the bulk. 2. If they occur near the surface, they can get out and they are pervasive.
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? Ridge can be associated with a semihard parton without a trigger.
Ridge, dependent on , hadrons formed by TT reco Base, independent of , not hydro bulk How is this untriggered ridge related to the triggered ridge on the near side of correlation measurement? Correlated part of two-particle distribution on the near side Putschke, Feng (STAR) Wenger (PHOBOS) trigger assoc part JET RIDGE
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Ridge is present whether or not 1 leads to a trigger.
2 Two events: parton 1 is undetected thermal partons 2 lead to detected hadrons with the same 2 Ridge is present whether or not 1 leads to a trigger. Semihard partons drive the azimuthal asymmetry with a dependence that can be calculated from geometry. (next slide) If events are selected by trigger (e.g. Putschke QM06, Feng QM08), the ridge yield is integrated over all associated particles 2. untriggered ridge triggered ridge yield
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Geometrical consideration for untriggered Ridge
Hwa-Zhu, PRC 81, (2010) Geometrical consideration for untriggered Ridge b normalized to RA Top view: segment narrower at higher b Side view: ellipse (larger b) flatter than circle (b=0) around =0. For every hadron normal to the surface there is a limited line segment on the surface around 2 through which the semihard parton 1 can be emitted. 2 elliptical integral of the second kind Ridge due to enhanced thermal partons near the surface R(pT,,b) S(,b) nuclear density D(b)
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Single-particle distribution at low pT with Ridge
After average over , Compare with data that show exponential behavior r(pT,b) can be determined; dependence comes only from S(,b); v2 can be calculated.
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Ridge yield with trigger at 1
Feng QM08 s dependence is calculated Normalization adjusted to fit, since yield depends on exp’tal cuts Normalization is not readjusted. S(,b) correctly describes the dependence of correlation
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RAA(pT, , b) can be calculated with the dependence arising entirely from the ridge.
art Hwa-Zhu, PRC 81, (2010) Summary dependencies in Ridge R(pT,,b) v2(pT,b)=<cos 2 > yield YR() RAA(pT,,b) are all inter-related for pT<2 GeV/c
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Jets Dependence on and Npart pT>2 GeV/c
PHENIX Dependence on and Npart pT>2 GeV/c pT Npart Need some organizational simplification Clearly, and b are related by geometry.
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Geometrical considerations
Nuclear medium that hard parton traverses x0,y0 k Geometrical path length D(x(t),y(t)) density (Glauber) Dynamical path length to be determined Average dynamical path length Probability of hard parton creation at x0,y0
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Define It contains all the information on the relationship between and b. looks universal, except for c=0.05 (no dep at c=0) centrality It suggests that P(,,c) may depend on fewer variables.
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We can plot the exp’tal data
Define KNO scaling For every pair of and c: we can calculate PHENIX data gives We can plot the exp’tal data
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Scaling behavior in 5 centralities and 6 azimuthal angles () in one universal curve for each pT Lines are results of calculation in RM. Hwa-Yang, PRC 81, (2010) Complications to take into account: details in geometry dynamical effect of medium hadronization
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TS+SS recombination Nuclear modification factor
q hadronization geometrical factors due to medium k probability of hard parton creation with momentum k degradation Nuclear modification factor only adjustable parameter
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Result of calculation in terms of
is dimensionless
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Two-jet recombination at LHC
At LHC, the densities of hard partons is high. At kT not too large, adjacent jets can be so close that shower partons from two parallel jets can recombine. Two hard partons
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Recombination of two shower partons from two jets
Overlap of two jet cones - probability for overlap of two shower partons from adjacent jets =10-3: 1-jet (S1S’1) =10-1: 2-jet (S1S2) =10-m, m=1, 2, 3 same jet 1 different jets
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Go back to , b are the same for the two jets, but and ’ are independent ’ For given , b there is only one (,b) KNO scaling implies Inclusive distribution
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Pion production at LHC Scaling badly broken Scaling
Hwa-Yang, PRC 81, (2010) 2 jet Scaling 1 jet >1 ! modest increase at 50-60% for 1-jet for 2 jets scales The admixture of ruins the scaling behavior. Observation of large RAA at pT~10 GeV/c will be a clear signature of 2-jet recombination.
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Recombination (2 jets) vs fragmentation (1 jet)
pT~10 GeV/c k1 k2 (2-j recombination) pT=k’1+k’2 k’i kT~20 GeV/c (1-j fragmentation) gluon more probable pT=k’1+k’2 +k’3 (2-j recombination) k1 k2 k’i p pT~10 GeV/c kT>20 GeV/c (1-j fragmentation) gluon even more probable If pT>20 GeV/c, 2-j requires higher ki, whose density is lower; thus smaller reduces probability of recombination.
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Production rates of p and are separately reduced, as pT is increased, but the p/ ratio is still >1 even up to pT~20 GeV/c 5-20 Hwa-Yang, PRL97, (2006)
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Ridge If 2-jet dominates single-particle inclusive at pT~10 GeV/c, then there are many such hadrons ( and p) at that pT at all . Using trigger at pTtrig ~ 10 GeV/c to find ridge would involve subtraction of a huge background. If higher pTtrig ( > 30 GeV/c), then 1-jet dominates, and ridge is not expected (from RHIC). It probably will be hard to find detectable ridge at LHC. ~ 4 correlation at RHIC
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1/Ntrig dNch/d Jet peak TS reco
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Single-particle distribution
factorizble Longitudinal: TransVerse: similarly for h=p BRAHMS, PRL 94,162301(05) <pT> essentially independent of y
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Two-particle distribution
Chiu-Hwa (preliminary) Two-particle distribution ridge Ridge distribution per trigger correlation in transverse component --- ridge no correlation in
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Where is the long-range correlation that requires early-time physics?
Correlation is in the transverse component, (ridge being TT+TTT reco) with negligible correlation between trigger 1 and associated 2 map 1(2) to dN/d: PHOBOS 1(trig) PHOBOS 1/Ntrig dNch/d Where is the long-range correlation that requires early-time physics?
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Conclusion Hadronization and initial geometry are important to understanding RHIC and LHC physics pT<2GeV/c semihard partons ridge (TT reco) dependence pT>2GeV/c (RHIC): TS+SS reco scaling pT~10GeV/c (LHC): 2j-SS reco scaling broken Probably no ridge at higher pTtrig and pTassoc at LHC. 1 and dN/d are related with no need for long-range correlation between (trig) and (ridge).
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