1. Ridges and Jets at RHIC and LHC
Rudolph C. Hwa
University of Oregon
Quantifying Hot QCD Matter
INT UW
June, 2010

2. 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.

3. 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

4. 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.

5. 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

6. 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.

7. 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

8. Ridge without detailed input on early-time physics

9. 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

10. 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

11. 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

12.   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.

13. 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

14. 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 

15. Correlated emission model (CEM)
Chiu-Hwa, PRC 79, (09)
STAR
Feng QM08
3<pTtrig <4
1.5 <pTassoc <2 GeV/c s 

16. 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.

17. ? 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

18. 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

19. 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)

20. 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.

21. 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

22. 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

23. 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.

24. 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

25. 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.

26.  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

27. 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

28. 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 

29. Result of calculation in terms of 
 is dimensionless

30. 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

31. 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

32. 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

33. 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.

34. 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.

35. 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)

36. 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

37. 1/Ntrig dNch/d
Jet peak TS reco

38. Single-particle distribution
factorizble
Longitudinal:
TransVerse:
similarly for h=p
BRAHMS, PRL 94,162301(05)
<pT> essentially independent of y

39. Two-particle distribution
Chiu-Hwa (preliminary)
Two-particle distribution
ridge
Ridge distribution per trigger
correlation in transverse component --- ridge
no correlation in 

40. 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?

41. 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).