Ridges and Jets at RHIC and LHC

Ridges and Jets at RHIC and LHC

Rudolph C. HwaUniversity 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

Fragmentation

kT > pT

Hadronization

Cooper-Frye

k1+k2=pT

lower ki higher density

TT TS SS

Usual domains in pT at RHIC

pQCDHydro

low high

ReCo

intermediate

2 6pT

GeV/c

4

Regions in time

(fm/c)

1 8

hadronization

0.6rapid thermalization

hydro

Cronin effect: --- initial-state or final-state effect?

Early-time physics: CGC, P violation, …

Pay nearly no attention to hadronization at late times.

Cronin effect in pA is larger for proton than for ; it implies final-state effect (in ReCo), not hard-scattering+frag, not hydro.

An example of late-time physics affecting thinking about early-time physics:

Initial state scattering occurs even earlier.

5

QuickTime™ and a decompressor

are needed to see this picture.

Large structure of Ridge --- PHOBOS

~ 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, 052303 (03)

PHOBOS, PRL104,062301(10)

BRAHMS has dN/dy at fixed =0.4 GeV/cpT

Simpler scenario

6

y is commonly identified with


are needed to see this picture.BRAHMS only

PHOBOS all charged

Proton contribution should not be ignored.





BRAHMS PLB 684,22(10)

How is this difference to be understood?



How much does it contribute to the distribution?

7







Dusling, Gelis, Lappi, Venugopalan

arXiv: 0911.2720



how one goes from initial-state to final state in one step

Early-time physics: CGC

8



Ridge without detailed input on early-time physics

9

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

Recombination function

R (k1,k2 , pT ) k1k2

pT2(

k1 k2

pT

1)

q and qbar momenta, k1, k2, add to give pion pT

It doesn’t work with transverse rapidity yt

TT F(ki ) Cki exp( ki / T )dN

pT dpT

C 2

6exp( pT / T )

TTTdN p

pT dpT

N p

pT2

mT

exp( pT / T ) same T for partons, , p

empirical evidence

At low pT

phase space factor in RF for proton formation

Pion at y=0 p0 dN

dpT

dk1

k1

dk2

k2

Fqq (k1,k2 )R (k1,k2 , pT )

Proton at y=0

p0 dN p

dpT

dk1

k1

dk2

k2

dk3

k3

Fuud (k1,k2 ,k3)Rp (k1,k2 ,k3, pT )

11



p



PHENIX, PRC 69, 034909 (04)

went on to mT plot

dN p

pT dpT

N p

pT2

mT

exp( pT / T )

Proton production from recombination

Same T for , K, p --- in support of recombination.

Slight dependence on centrality --- to revisit later

12

Ridge formation

associated particles

SS

trigger

TT ridge (R)ST

peak (J)

Mesons:Baryons: TTT in the ridge

Suarez QM08

B/M in ridge even higher than in inclusive distr.

13

Jet and Ridge Yield

20-60% top 5%jet part, near-side

ridge part, near-side

jet part, near-side

ridge part, near-side

STAR Preliminary

3<pTtrig<4, 1.5<pT

assoc<2.0 GeV/c

Feng, QM08

In-plane

Out

-of-

plan

e

1

43

2

56s

Different s dependencies for different centralities --- important clues on the properties of correlation and geometry

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The medium expands during the successive soft emission process, and carries the enhanced thermal partons along the flow.

Hard parton directed at s , loses energy along the way, and enhances thermal partons in the vicinity of the path.

s

But parton direction s and flow direction are not necessarily the same.

s

Reinforcement of emission effect leads to a cone that forms the ridge around the flow direction .

If not, then the effect of soft emission is spread out over a range of surface area, thus the ridge formation is weakened.

Flow direction normal to the surface

Correlation between s and

C(x, y,s ) exp (s (x, y))2

2 2

15

QuickTime™ and aTIFF (LZW) decompressor


CEM

s

Correlated emission model (CEM)

Chiu-Hwa, PRC 79, 034901 (09)

; 0.33

STAR

Feng QM08

3<pTtrig <4

1.5 <pTassoc

<2 GeV/c

16

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.

That was Ridge associated with a trigger

17

Base, independent of , not hydro bulk

Ridge, dependent on , hadrons formed by TT reco

Correlated part of two-particle distribution on the near side 2

corr (1,2) 2J (1,2) 2

R (1,2)

Putschke, Feng (STAR) Wenger (PHOBOS)

trigger

assoc part

JET RIDGE

How is this untriggered ridge related to the triggered ridge on the near side of correlation measurement?

Ridge can be associated with a semihard parton without a trigger.

1(pT ,,b) B(pT ,b) R(pT ,,b)

?

18

1

2

1

2

Two events: parton 1 is undetected thermal partons 2 lead to detected hadrons with the same 2

R(2 ) d1 2R (1,2 )

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.

Y R (1) d2 2R (1,2 )

R(2 ) 2R (1,2 ) Y R (1)

untriggered ridge triggered ridge yield

19

Geometrical consideration for untriggered Ridge


are needed to see this picture.QuickTime™ and a

decompressorare needed to see this picture.

Ridge due to enhanced thermal partons near the surface

R(pT,,b) S(,b)nuclear density D(b)

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 S(,b) dl

arc [w2 sin2 h2

cos2 ]1/2 d

h E(,1 w2 / h2 )

tan 1[h

wtan( )]

elliptical integral of the second kind



b normalized to RA

Top view: segment narrower at higher b

Side view: ellipse (larger b) flatter than circle (b=0) around =0.

Hwa-Zhu, PRC 81, 034904 (2010)

20

Single-particle distribution at low pT with Ridge

1(pT ,,b) B(pT ,b) R(pT ,,b) N(b)[e pT /T0 D(b)S(,b)r(pT ,b)]

After average over ,

1(pT ,b) N(b)[e pT /T0 D(b)S (b)r(pT ,b)]

T (b) 0.3(1 0.03b2 ) GeV

Compare with data that show exponential behavior

1(pT ,b) N(b)e pT /T (b)



T0 T (b 2)

r(pT,b) can be determined; dependence comes only from S(,b);



v2 can be calculated.

21

S(1,b)



Ridge yield with trigger at 1



Feng QM08

s 1

Normalization adjusted to fit, since yield depends on exp’tal cuts

Normalization is not readjusted.

s dependence is calculated

S(,b) correctly describes the dependence of correlation

d2 2R (1,2 ) Y R (1)

22

RAA(pT, , b) can be calculated with the dependence arising entirely from the ridge.



art

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

Hwa-Zhu, PRC 81, 034904 (2010)

23

JetsPHENIX 0903.4886

Need some organizational simplification. Clearly, and b are related by geometry.

pT>2 GeV/c

Dependence on and Npart

pT

Npart

24

Nuclear medium that hard parton traverses

x0,y0

k

Dynamical path length

l (x0 , y0 ,,b) to be determined

Geometrical considerations

Average dynamical path length

(,b) dx0dy0 l (x0 , y0 ,,b)Q(x0 , y0 ,b)

Q(x0 , y0 ,b) TA (x0 , y0 , b / 2)TB (x0 , y0 ,b / 2)

d 2rsTA (rs

rb / 2)TB (

rs

rb / 2)

Probability of hard parton creation at x0,y0

Geometrical path length

(x0 , y0 ,,b) dtD[x(t), y(t)]

0

t1 (x0 ,y0 , ,b)

D(x(t),y(t))density (Glauber)

25

Define

(,b) dP( ,,b)

It suggests that P(,,c) may depend on fewer variables.

P(,,b) dx0 dy0Q(x0 , y0 ,b)[ l (x0 , y0 ,,b)]

It contains all the information on the relationship between and b.



(,c) looks universal, except for c=0.05 (no dep at c=0)

centrality

26

Define





KNO scaling

z / dz (z) 1 dzz (z) 1

For every pair of and c:

• we can calculate

• PHENIX data gives

(,c)

RAA (,c)

We can plot the exp’tal data

RAA ( )

(z) (,c)P(,,c)

27

Scaling behavior in

Lines are results of calculation in RM.

Hwa-Yang, PRC 81, 024908 (2010)

5 centralities and 6 azimuthal angles () in one universal curve for each pT





Complications to take into account:

• details in geometry

• dynamical effect of medium

• hadronization

28

1

TSSS (pT ,,b) dq

q Fii (q,,b)H i (q, pT )

b

q

TS+SS recombination

G(k,q,) q (q ke )

degradation

hadronization

dNihard

kdkdyy0

fi (k)

Fi (q,) dkkfi (k)G(k,q,)

k probability of hard parton creation with momentum k

Fi (q,,b) dP( ,,b)Fi (q,)

geometrical factors due to medium

Nuclear modification factor

RAA (pT ,,c)

dNAA / dpT d

NcolldN pp / dpT

only adjustable parameter l (x0 , y0 ,,b)

xDi (x)

dx1

x1

dx2

x2

Sij (x1),Si

j '(x2

1 x1

)

R (x1, x2 , x)x pT / q

dNSS

pT dpT

(pT ,) 1

pT2

dq

qi Fi (q,)SSŽ (q, pT )

TSŽ (q, pT ) dq2

q2 Si

j (q2

q) dq1 Ce q1 /T R (q1,q2 , pT )

dNTS

pT dpT

(pT ,) 1

pT2

dq

qi Fi (q,)TSŽ (q, pT )

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Result of calculation in terms of





exp( 2.6 ) is dimensionless

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Two-jet recombination at LHC

At kT not too large, adjacent jets can be so close that shower partons from two parallel jets can recombine.

H ii '(q,q ', pT ) 1

pT2

dq1

q1

dq2

q2

Sij (

q1

q)Si '

j '(q2

q ')R

(q1,q2 , pT )

At LHC, the densities of hard partons is high.

Two hard partons

dNAA2 j

pT dpT d1

2 j (pT ,,b)

dq

qdq '

q 'Fi (q

ii ' ,,b)Fi '(q ',,b)H ii '(q,q ', pT )

Fi (q,,b) dP( ,,b)Fi (q,)

12 j (pT ,,b) dd 'P(,,b) P( ',,b)1

2 j (pT ,, ')

12 j (pT ,, ')

dq

qdq '

q 'Fi (q

ii ' ,)Fi '(q ', ')H ii '(q,q ', pT )

31

Overlap of two jet cones

Recombination of two shower partons from two jets

H ii '(q,q ', pT ) 1

pT2

dq1

q1

dq2

q2

Sij (

q1

q)Si '

j '(q2

q ')R

(q1,q2 , pT )

- probability for overlap of two shower partons from adjacent jets

R

(q1,q2 , pT ) R (q1,q2 , pT )

=10-3: 1-jet (S1S’1)

=10-1: 2-jet (S1S2)=10-m, m=1, 2, 3

same jet 1

different jets

32

12 j (pT ,,b) dd 'P(,,b) P( ',,b)1

2 j (pT ,, ')

12 j (pT ,, ')

dq

qdq '

q 'Fi (q

ii ' ,)Fi '(q ', ')H ii '(q,q ', pT )

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

12 j (pT ,,b) dzdz ' (z) (z ')1

2 j (pT , z, z ', (,b))

RAA (pT ,,b)

dNAA / pT dpT d(b)

Ncoll (b)dN pp / pT dpT

dNAA

pT dpT d(b) 1

TSSS (pT ,,b) 12 j (pT ,,b)Inclusive distribution

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Scaling

1 jet QuickTime™ and a decompressor


Scaling badly broken

Hwa-Yang, PRC 81, 024908 (2010)

2 jet

Pion production at LHC

Observation of large RAA at pT~10 GeV/c will be a clear signature of 2-jet recombination.

>1 !

RAA (pT ,,b)

dNAA / pT dpT d(b)

Ncoll (b)dN pp / pT dpT 1

2 j (pT ,,b) / Ncoll2 scales

modest increase at 50-60% for 1-jet Ncoll for 2 jets N

coll

2

The admixture of ruins the scaling behavior. 11 j 1

2 j

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Recombination (2 jets) vs fragmentation (1 jet)

pT~10 GeV/c

kT~20 GeV/c (1-j fragmentation)

gluon

p pT~10 GeV/c

kT>20 GeV/c (1-j fragmentation)

gluon

If pT>20 GeV/c, 2-j requires higher ki, whose density is lower; thus smaller reduces probability of recombination.

more probable

even more probable

k1

k2

(2-j recombination)

pT=k’1+k’2k’i

pT=k’1+k’2 +k’3 (2-j recombination)

k1

k2

k’i

35




are needed to see this picture.5-20

Hwa-Yang, PRL97,042301 (2006)

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

36

12 j (pT , (,c))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 .

Ridge

Using trigger at pTtrig ~ 10 GeV/c to find ridge

would involve subtraction of a huge background.If higher pT

trig ( > 30 GeV/c), then 1-jet dominates, and ridge is not expected (from RHIC).

11 j (pT , (,c))

~ 4 correlation at RHIC

It probably will be hard to find detectable ridge at LHC.

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1/N

tri g d

Nch

/d

Jet peak TS reco

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1BR

h (, pT ) dNBR

h

dpT dpT

J h (, pT )

pT2

Lh (, pT )VBRh (pT )

Longitudinal:

TransVerse:

X pT

s / 2cosh

z k1 / pTL (, pT ) dzz(1 z)F(zX)F((1 z)X)

V (pT ) C 2 pT2e pT /T

similarly for h=p



BRAHMS, PRL 94,162301(05)

factorizble

Single-particle distribution

<pT> essentially independent of y

39

2h1h2 (1, pt ;2 , pa ) 1

h1 (1, pt )1h2 (2 , pa )C2

h1h2 (1, pt ;2 , pa )

2h1h2 (1, pt ;2 , pa ) 1

h1 (trig)(1, pt )1BR

h2 (2 , pa )

C2h1h2 (1, pt ;2 , pa ) 1

h1 (trig)(1, pt )J h2 (2 , pa )

pa2

Lh2 (2 , pa )[VBRh2 (pa ) VB

h2 (pa )]

VRh2 (pa )

Ridge distribution per trigger

dNRh2

d(pa )

1

Ntrig

C2h1h2 (1, pt ;2 1 , pa )

1

pa2

J h2 (2 , pa )Lh2 (2 , pa )VRh2 (pa )

dNRch

d dpa

h2

pa

dNRh2

d(pa ) d10

1.5

dN ch

d2 2 1

ridge

no correlation in

correlation in transverse component --- ridge

Chiu-Hwa (preliminary)Two-particle distribution

40

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: dN ch / d10

1.5

1ch ( 1)

PHOBOS


are needed to see this picture.1/

Ntr

i g d

Nch

/d

Where is the long-range correlation that requires early-time physics?



PHOBOS

1(trig)

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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) dependencepT>2GeV/c (RHIC): TS+SS reco scaling

pT~10GeV/c (LHC): 2j-SS reco scaling broken

Probably no ridge at higher pTtrig and pT

assoc at LHC.

1 and dN/d are related with no need for long-range correlation between (trig) and (ridge).

Ridges and Jets at RHIC and LHC

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