High-p T Physics at RHIC and Evidences of Recombination

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High-pT Physics at RHIC and Evidences of Recombination

Rudolph C. Hwa

University of Oregon

International Symposium on Multiparticle Dynamics

Sonoma, CA, July 2004

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In collaboration with

Chunbin Yang

Hua-zhong Normal University

Wuhan, China

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Outline

Anomalies at high pT according to the

“standard model”

Alternative to the “standard model” at high

pT • Recombination in fragmentation• Shower partons• Inclusive distributions at all pT•

Dihadron correlations

All anomalies can be understood in terms of parton recombination

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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

7

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

Anomaly #2 in pA or dA collisions

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

p

q

hdNdpT

(pA→ πX)∝ Aα , α >1

A

p >

RHIC expt (2003)

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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

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Anomaly #3 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 #3 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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Azimuthal anisotropy Anomaly #4

Anomaly #5 Forward-backward asymmetry at intermediate pT

Come back later when there is time.

Resolution of the anomalies

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How can recombination solve the 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.

18Hwa & CB Yang, hep-ph/0312271

Shower Parton Distributions

u -> u valence

g -> u

u -> d

u -> s

g -> s

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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)

Fqq =TT+TS+(SS)1+(SS)2

Proton formation: uud distribution

Fuud =TTT+TTS +T(SS)1+(SSS)1+T(SS)2+((SS)1S)2+(SSS)3

T

S

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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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fi (k) =dNi

hard

kdkdyy=0density of hard partons with pT = k

Input: parton distributions CTEQ5L nuclear shadowing EKS98 hard scattering pQCD

Srivastava, Gale, Fries, PRC 67, 034903 (2003)

dNjet

d2 pTdyy=0

=K C(1+pT / B)β

C, B, are tabulated for i=u, d, s, u, d, g K=2.5

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2-shower partons in 1 jet:

×Rπ (p1,p2,p)

Diπ (p/k)

Negligible at RHIC, but can be important at LHC.

(SS)1(p1, p2) =ξ dkk∫i∑ fi(k)Si

j(p1

k)Si

j'(p2

k −p1

)

2-shower partons in 2 jets:

(SS)2(p1,p2) =δyφξ dkk∫i∑ fi(k)Si

j (p1

k)×ξ dk'k' fi'(k' )Si'

j'(p2

k')∫

i'∑

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production in AuAu central collision at 200 GeV

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Hwa & CB Yang, nucl-th/0401001, PRC(2004)

TS

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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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Greco, Ko & Levai, PRL (2003)

Monte Carlo Calculation in Coalescence model

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Production of and in central Au+Au

Hwa & Yang, nucl-th/0406072

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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





Hwa & CB Yang, nucl-th/0403001, PRL(2004)

Pions

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

recombination.

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Proton

Thermal-shower recombination is negligible.

nucl-th/0404066

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Nuclear Modification Factor



RCPp >RCP

πbecause 3q p, 2q

Anomaly #2 resolved

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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 #3 Jet structure in Au+Au different from that in p+p

collisions

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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

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There are other contributions as well.

(TS) + [SS]

(SS) + [TS]

(SS) + [SS] too small for Au+Au

but the only term for p+p

trigger associated

(TS) + [TS]

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Associated particle distribution in p2 with trigger at p1

dNπ

dp2 p1

=

∑ i ∫dkkfi (k)dNππ

dp1dp2

(k)

∑ i ∫dkkfi(k)dNπ

dp1(k)

trigger at p1 integrated over 4 < p1 < 6 GeV/c

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(TS)[TS]

(TS)[SS]+(SS)[TS]

(SS)[SS] for p+p collisions much lower

Central Au+Au collisions

+

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Central Au+Au collisions

Hwa & Yang, nucl-th/0407081

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Centrality dependence of associated-particle dist.

Distributions Ratios

Au+Au centrald+Au peripheral

d+Au centrald+Au peripheral

Jets in Au+Au and in p+p are very different.

Anomaly #3

p+p

resolved

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Azimuthal anisotropy

Anomaly #4

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

GeV/c

v2: coeff. of 2nd harmonic of distribution

PHENIX, PRL 91 (2003)

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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

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Anomaly #5 Forward-backward asymmetry at intermed. pT

backwardforward

in d+Au collisions

STAR preliminary data

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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 in backward (Au) direction.

Less TS recombination in forward than in backward direction.

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Summary

Traditional picture

pT0 2 4 6 8 10

hardsoft

pQCD + FF

More realistic picture

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 pT > 9 GeV/c fragmentation dominates, but it can still be expressed as shower-shower recombination.

Thus we need not consider fragmentation separately any more.

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Backup slides

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Rapidity dependence of RCP in d+Au

collisions BRAHMS nucl-ex/0403005

RCP < 1 at

=3.2

Central more suppressed than peripheral collisions

Interpreted as possible signature of Color Glass Condensate.

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=0 RCP > 1

=3.2 RCP < 1

At forward rapidity, parton x is degraded (stopping) more for central than for peripheral

x distributions at various b accounted for by recombination

central < peripheral

RCP < 1 at large

BRAHMS data

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Forward RCP in d+Au collisions



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Forward pT spectra in d+Au collisions

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At very high pT and very high energy like at LHC, then the density of hard partons produced will be so high as to make jet-jet recombination very important .

The effect should be dramatic.

59near side away side

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PHENIX

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Thermal partons

No prediction from our model (without hydro input) Fit data on spectrum for pT < 2GeV/c

C = 23.2 GeV-1 , T = 0.317 GeV

Shower partons

= 0.07

ξ fraction of hard partons that can get out of the dense medium to produce shower

Au+Au: adjusted to fit the data at intermediate pT.

ξ

d+Au: = 1ξ

High-p T Physics at RHIC and Evidences of Recombination

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