High p T Physics in Heavy Ion Collisions Rudolph C. Hwa University of Oregon CIAE, Beijing June 13, 2005

High pT Physics in Heavy Ion Collisions

Rudolph C. HwaUniversity of Oregon

CIAE, Beijing

June 13, 2005

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Well studied for 20 years ---- pQCD

What was a discovery yesterday

is now used for calibration today.

Instead of being concerned with 5% discrepancy in pp collisions, there are problems involving factors of 10 differences to understand in nuclear collisions.

High pT Physics of Nuclear Collisions at High Energy

particle

3

4

Chunbin Yang (HZNU, Wuhan; UO)

Rainer Fries (Univ. of Minnesota)

Zhiquang Tan (HZNU, Wuhan; UO)

Charles Chiu (Univ. of Texas, Austin)

Work done in separate collaborations with

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Outline

Anomalies at high pT according to the

“standard model of hadronization” --- parton fragmentation

The resolution: parton recombination

• Recombination in fragmentation• Shower partons• Inclusive distributions at all pT• Cronin effect• Hadron correlations in jets

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Conventional approach to hadron production at high pT

D(z)

h

qA A

Hard scattering near the surface because of energy loss in medium --- jet quenching.

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If hard parton fragments in vacuum, then the fragmentation

products should be independent of the medium.

h

q

Particle ratio should depend on the FF D(z) only.

The observed data reveal several anomalies according to that picture.

D(z)

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Anomaly #1 Rp/π

1

Not possible in fragmentation model:

Dp/ q <<Dπ /q

Rp/π

Dp/q

Dπ /q

u

9

cm energy cm energy

10

Anomaly #2 in pA or dA collisions

kT broadening by multiple

scattering in the initial state.

Unchallenged for ~30 years.

If the medium effect is before fragmentation, then should be independent of h= or p

Cronin Effect Cronin et al, Phys.Rev.D (1975)

p

q

hdNdpT

(pA→ πX)∝ Aα , α >1

A

RCPp >RCP

πSTAR, PHENIX (2003)

Cronin et al, Phys.Rev.D (1975)

p >

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RHIC data from dAu collisions at 200 GeV per NN pair

Ratio of central to peripheral collisions:

RCP

RCPh (pT ) =

dNh

dpT

1NColl

central( )

dNh

dpT

1NColl

peripheral( )

PHENIX and STAR experiments found (2002)

RCPp (pT )>RCP

π (pT )

Can’t be explained by fragmentation.

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RCPp (pT )>RCP

π (pT )Anomaly # 2

STAR

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Anomaly #3 Azimuthal anisotropy

v2(p) > v2() at pT > 2.5

GeV/c

v2: coeff. of 2nd harmonic of distribution

PHENIX, PRL 91 (2003)

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Anomaly #4 Forward-backward asymmetry at intermed. pT

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

in d+Au collisions (STAR)B

/F

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Forward-backward asymmetry in d+Au collisions

Expects more forward particles at high pT than backward particles

If initial transverse broadening of parton gives hadrons at high pT, then

• backward has no broadening

• forward has more transverse broadening

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Rapidity dependence of RCP in d+Au

collisions BRAHMS PRL 93, 242303(2004)

RCP < 1 at

=3.2

Central more suppressed than peripheral collisions

Interpreted as possible signature of Color Glass Condensate.

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Anomaly #5 Jet structure

Hard parton jet { (p1) + (p2) + (p3) + ···· }

trigger particle associated particles

The distribution of the associated particles should be independent of the medium if fragmentation takes place in vacuum.

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Anomaly #5 Jet structure for Au+Au collisions is different from that for p+p collisions

pp

Fuqiang Wang (STAR) nucl-ex/0404010

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How can recombination solve all those puzzles?

Parton distribution (log scale)

p

p1+p2p q

(recombine) (fragment)

hadron momentum

higher yield heavy penalty

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The black box of fragmentation

q

A QCD process from quark to pion, not calculable in pQCD

z1

Momentum fraction z < 1

Phenomenological fragmentation function

D/q

z1

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Let’s look inside the black box of fragmentation.

q

fragmentation

z1

gluon radiation

quark pair creation

Although not calculable in pQCD (especially when Q2 gets low), gluon radiation and quark-pair creation and subsequent hadronization nevertheless take place to form pions and other hadrons.

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Description of fragmentation by recombination

known from data (e+e-, p, … )

known from recombination model

can be determined

hard partonmeson

fragmentationshower partons recombination

xD(x) =dx1x1

∫dx2

x2Fq,q (x1,x2)Rπ (x1,x2,x)

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Shower parton distributions

Fqq '(i )(x1,x2) =Si

q(x1)Siq ' x2

1−x1

⎛

⎝ ⎜ ⎞

⎠ ⎟

Sij =

K L Ls

L K Ls

L L Ks

G G Gs

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

u

gs

s

d

du

K =KNS+L

Ks =KNS +Ls

Sud,d ,u ,u(sea) =L

valence

sea

L L DSea

KNS L DV

G G DG L

Ls DKSea

G Gs DKG

R

RK

5 SPDs are determined from 5 FFs.

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Shower Parton Distributions

Hwa & CB Yang, PRC 70, 024904 (04)

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BKK fragmentation functions

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Once the shower parton distributions are known, they can be applied to heavy-ion collisions.

The recombination of thermal partons with shower partons becomes conceptually unavoidable.

D(z)

h

qA A

Conventional approach

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Once the shower parton distributions are known, they can be applied to heavy-ion collisions.

The recombination of thermal partons with shower partons becomes conceptually unavoidable.

hNow, a new component

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hard parton (u quark)

d

u

π+

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Inclusive distribution of pions in any direction

r p

pdNπ

dp=

dp1p1

∫dp2

p2Fqq (p1,p2)Rπ (p1, p2,p)

dNπ

pdp=

1p3 dp10

p∫ Fqq (p1,p−p1)

pTPion Distribution

p1p2

pδ(p1 +p2 −p)

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Pion formation: qq distribution

thermal

shower

soft component

soft semi-hard components

usual fragmentation

(by means of recombination)

T

SFqq =TT+TS+SS

Proton formation: uud distribution

Fuud =TTT +TTS +TSS +SSS

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T(p1)=p1dNq

th

dp1=Cp1exp(−p1/T)

Thermal distribution

Fit low-pT data to determine C & T.

Shower distribution in AuAu collisions

S(p2)=ξ∑i ∫dkkfi(k)Sij(p2 /k)

hard parton momentum

distribution of hard parton i in AuAu collisions

SPD of parton j in shower of hard parton i

fraction of hard partons that get out of medium to produce shower

calculable

Contains hydrodynamical properties, not included in our model.

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thermal

fragmentation

soft

hard

TS Pion distribution (log scale)

Transverse momentum

TT

SS

Now, we go to REAL DATA, and real theoretical results.

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production in AuAu central collision at 200 GeV



Hwa & CB Yang, PRC70, 024905 (2004)

TS

fragmentation

thermal

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Proton production in AuAu collisions



TTS+TSS

TSS

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Anomaly #1 Proton/pion ratio

resolved

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are needed to see this picture.All in recombination/ coalescence model

Compilation of Rp/ by R. Seto (UCR)

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d

d

central peripheral

more T more TS

less T less TS

RCPh (pT ) =

dNh

dpT

1NColl

central( )

dNh

dpT

1NColl

peripheral( ) ⇒

more TSless TS

>1

Anomaly #2 d+Au collisions (to study the Cronin Effect)

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d+Au collisions





Pions

Hwa & CB Yang, PRL 93, 082302 (2004)

No pT broadening by multiple scattering in the initial state.Medium effect is due to thermal (soft)-shower

recombination in the final state.

soft-soft

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Proton

Thermal-shower recombination is negligible.

Hwa & Yang, PRC 70, 037901 (2004)

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Nuclear Modification Factor



RCPp >RCP

πAnomaly #2

because 3q p, 2q

This is the most important result that validates parton recombination.

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Molnar and Voloshin, PRL 91, 092301 (2003).

Parton coalescence implies that v2(pT)

scales with the number of constituents

STAR data

Anomaly #3 Azimuthal anisotropy

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More interesting behavior found in large pT and large pL region.

It is natural for parton recombination to result in forward-backward asymmetry

Less soft partons in forward (d) direction than backward (Au) direction.

Less TS recombination in forward than in backward direction.

Anomaly #4 Forward-backward asymmetry

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Hwa, Yang, Fries, PRC 71, 024902 (2005)

Forward production in d+Au collisions

Underlying physics for hadron production is not changed from backward to forward rapidity.

BRAHMS data

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Jet Structure

Since TS recombination is more important in Au+Au than in p+p collisions,

we expect jets in Au+Au to be different from those in

p+p.

Consider dihadron correlation in the same jet on the near side.

Anomaly #5 Jet structure in Au+Au different from that in p+p

collisions

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Correlations

1. Correlation in jets: trigger, associated particle, background subtraction, etc.

2. Two-particle correlation with the two particles treated on equal footing.

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Correlation function

C2(1,2) =ρ2(1,2)−ρ1(1)ρ1(2)

ρ2(1,2)=dNπ1π2

p1dp1p2dp2

ρ1(1) =dNπ1

p1dp1

Normalized correlation function

K2(1,2) =C2(1,2)

ρ1(1)ρ1(2)=r2(1,2)−1 r2(1,2) =

ρ2(1,2)ρ1(1)ρ1(2)

In-between correlation function

G2(1,2)=C2(1,2)

ρ1(1)ρ1(2)[ ]1/ 2

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Correlation of partons in jets

A. Two shower partons in a jet in vacuum

Fixed hard parton momentum k (as in e+e- annihilation)

k

x1

x2

ρ1(1) =Sij(x1)

ρ2(1,2)= Sij(x1),Si

j'(x2

1−x1

)⎧ ⎨ ⎩

⎫ ⎬ ⎭

=12

Sij(x1)Si

j'(x2

1−x1

) +Sij (

x1

1−x2

)Sij'(x2)

⎧ ⎨ ⎩

⎫ ⎬ ⎭

r2(1,2) =ρ2(1,2)

ρ1(1)ρ1(2)

x1 +x2 ≤1

The two shower partons are correlated.

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no correlation

Hwa & Tan, nucl-th/0503052

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B. Two shower partons in a jet in HIC

Hard parton momentum k is not fixed.

ρ1(1) =Sj(q1) =ξ dkkfi∫

i∑ (k)Si

j(q/ k)

ρ2(1,2)=(SS)jj'(q1,q2) =ξ dkkfi∫

i∑ (k) Si

j(q1

k),Si

j'(q2

k−q1

)⎧ ⎨ ⎩

⎫ ⎬ ⎭

r2(1,2) =ρ2(1,2)

ρ1(1)ρ1(2)fi(k)

fi(k) fi(k)

fi(k) is small for 0-10%, smaller for 80-92%

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Correlation of pions in jets

Two-particle distribution

dNππ

p1dp1p2dp2=

1(p1p2)

2

dqi

qii∏

⎡

⎣ ⎢ ⎤

⎦ ⎥ ∫ F4(q1,q2,q3,q4)R(q1,q3,p1)R(q2,q4, p2)

F4 =(TT+ST+SS)13(TT+ST+SS)24

k

q3

q

1

q4

q2

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Correlation function of produced pions in HIC

C2(1,2) =ρ2(1,2)−ρ1(1)ρ1(2)

ρ2(1,2)=dNπ1π2

p1dp1p2dp2

ρ1(1) =dNπ1

p1dp1


Factorizable terms: (TT)13(TT)24 (ST)13(TT)24 (TT)13(ST)24

Do not contribute to C2(1,2)

Non-factorizable terms (ST+SS)13(ST+SS)24

correlated

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C2(1,2) =ρ2(1,2)−ρ1(1)ρ1(2)




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G2(1,2)=C2(1,2)

ρ1(1)ρ1(2)[ ]1/ 2



along the diagonal

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56



Hwa and Tan, nucl-th/0503052

RCPG2 (1,2) =

G2(0−10%)(1,2)

G2(80−92%)(1,2)

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Trigger at 4 < pT < 6 GeV/c

p+p: mainly SS fragmentation Au+Au: mainly TS

Associated particle

p1 (trigger)

p2 (associated)

kq1

q2

q3

q4

ξ∑i ∫dkkfi(k)S(q1)T(q3)R(q1,q3,p1) trigger

S(q2)T(q4)R(q2,q4,p2) associated

Correlation studied with triggers

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Correlation of pions in jets

Two-particle distribution

dNππ

p1dp1p2dp2=

1(p1p2)

2

dqi

qii∏

⎡

⎣ ⎢ ⎤

⎦ ⎥ ∫ F4(q1,q2,q3,q4)R(q1,q3,p1)R(q2,q4, p2)


backgroundassociated particle

2<p2<4 GeV/c

must also involve S

trigger

4<p1<6 GeV/c

must involve S

q4

q2

k

q3

q

1

59

STAR has measured: nucl-ex/0501016

Associated charged hadron distribution in pT

Background subtracted and distributions

Trigger 4 < pT < 6

GeV/c

60

and distributions

P1

P2

pedestal

subtraction point no pedestal

short-range correlation?

long-range correlation?

61

New issues to consider:

• Angular distribution (1D -> 3D)

shower partons in jet cone

• Thermal distribution enhanced due to

energy loss of hard parton

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Longitudinal

Transverse

t=0 later

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z

1

p1

trigger

Assoc p2kq2

z

hard parton

shower parton

ψ =θ −θ1

η−η1 =Δη

tanψ2

=g(η,η1)=e−η −e−η1

1+e−η−η1

=e−η1e−Δη −1

1+e−Δη−2η1

⎡

⎣ ⎢ ⎤

⎦ ⎥

Expt’l cut on trigger: -0.7 < 1 < +0.7k

jet cone exp[−ψ 2 /2σ 2(x)]

64

Events without jets T(q) =Cqe−q/T

Thermal medium enhanced due to energy loss of hard parton

Events with jets

T'(q) =Cqe−q/T 'in the vicinity of the jet

T’- T = T > 0new parameter

Thermal partons

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For STST recombination

enhanced thermal

trigger associated particle

Sample with trigger particles and with background subtracted

Pedestal peak in &

F4

' =ξ dkkfi∫i

∑ (k)T'(q3){S(q1),S(q2)}T'(q4)e−ψ 2 /2σ 2 (q2 / k) |ψ =2tan−1 g(η,η1)

F4tr−bg =∑∫L (ST')13 (T'T' −TT)24 +(ST')13 (ST')24

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Pedestal in

P1,2 = dp2pmin(1,2)

4

∫dN(T'T'−TT)

dp2|trig

0.15 < p2 < 4 GeV/c, P1 = 0.4

2 < p2 < 4 GeV/c, P2 = 0.04

more reliable

P1

P2

less reliableparton dist

T'(q) =Cqe−q/T '

found T ’= 0.332 GeV/c

cf. T = 0.317 GeV/c

T ’ adjusted to fit pedestal

T = 15 MeV/c

67Chiu & Hwa, nucl-th/0505014

68

Chiu & Hwa, nucl-th/0505014

69

We have not put in any (short- or long-range) correlation by hand.

The pedestal arises from the enhanced thermal medium.

The peaks in & arise from the recombination of enhanced thermal partons with the shower partons in jets with angular spread.

Correlation exists among the shower partons, since they belong to the same jet.

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Summary

Traditional classification by scattering

pT0 2 4 6 8 10

hardsoft

pQCD + FF

More meaningful classification by hadronization

pT0 2 4 6 8 10

hardsoft semi-hard

(low) (intermediate)

thermal-thermal thermal-shower

(high)shower-shower

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All anomalies at intermediate pT can be understood in terms of recombination of

thermal and shower partons

Recombination is the hadronization process ---- at all pT.

Parton recombination provides a framework to interpret the data on jet correlations.

There seems to be no evidence for any exotic correlation outside of shower-shower correlation in a jet.

Conclusion

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dNtrig−bg

p1dp1p2dp2=

ξ(p1p2)

3 dkkfi∫i∑ (k) dq1 dq2 ⋅∫∫

×

T'(p1 −q1)Sq1

k⎛ ⎝

⎞ ⎠

T'(q2)T'(p2 −q2)−T(q2)T(p2 −q2)[ ]

+T'(p1 −q1){Sq1

k⎛ ⎝

⎞ ⎠ ,S

q2

k−q1

⎛

⎝ ⎜ ⎞

⎠ ⎟ }T'(p2 −q2)J (ψ ,q2 / k)

⎧

⎨ ⎪

⎩ ⎪

⎫

⎬ ⎪

⎭ ⎪

1Ntrig

dNdΔη

=dη1 dp2p2 dp1p1

dNtrig−bg

p1dp1p2dp24

6

∫passocmin

4

∫−0.7

0.7

∫

dη1−0.7

0.7

∫ dp1p1dNtrig

p1dp14

6

∫

dNtrig

p1dp1=

ξp1

3 dkkfi∫i∑ (k) dq1∫ T'(p1 −q1)S

q1

k⎛ ⎝

⎞ ⎠

next slide

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kq2

z

hard parton

shower partonShower parton

angular distribution in jet cone

J (ψ ,q2 /k)=exp−(2tan−1g(η1 +Δη,η1))

2

2σ 2(q2 /k)

⎡

⎣ ⎢ ⎤

⎦ ⎥

Cone width

σ(x) =σ 0(1−x)

another parameter ~ 0.22

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Correlation without triggers

Correlation function

C2(1,2) =ρ2(1,2)−ρ1(1)ρ1(2)

ρ2(1,2)=dNπ1π2

p1dp1p2dp2

ρ1(1) =dNπ1

p1dp1

Normalized correlation function

G2(1,2)=C2(1,2)

ρ1(1)ρ1(2)[ ]1/ 2

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Physical reasons for the big dip:

(a) central: (ST)(ST) dominates

S-S correlation weakened by separate recombination with uncorrelated (T)(T)

(b) peripheral: (SS)(SS) dominates

SS correlation strengthened by double fragmentation

The dip occurs at low pT because at higher

pT power-law suppression of 1(1) 1(2)

results in C2(1,2) ~ 2(1,2) > 0

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Porter & Trainor, ISMD2004, APPB36, 353 (2005)


are needed to see this picture.Transverse rapidity yt

( pp collisions )

G2

STAR

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Documents

High p T Physics in Heavy Ion Collisions Rudolph C. Hwa University of Oregon CIAE, Beijing June 13, 2005