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Near-Side Ridge and Early Parton Momentum Distribution

Cheuk-Yin Wong Oak Ridge National Laboratory

Dubna July 19, 2008

• Introduction ► the jet, near-side jet, away-side jet, and the ridge

► how does the ridge arise • The relation between the early parton momentum distributio

n & the ridge distribution • Use the experimental ridge distribution to extract the early p

arton momentum distribution• Conclusions

C.Y.Wong, Phy.Rev.C76,054908(’07)C.Y.Wong, arXiv:0712.3282(‘07)C.Y.Wong, arXiv:0804.4017(’08)C.Y.Wong, arXiv:0806.2154(’08)

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Why study the early parton momentum distribution?

• Early parton momentum distribution is an important quantity

• It provides information in early collision dynamics

• It provides initial value data for subsequent evolution to quark-gluon plasma

• Not much is known experimentally about early parton momentum distribution

• We propose to use the ridge distribution to extract early parton momentum distribution

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Jet production

Jets are particles with high transverse momenta produced by nucleon-nucleon hard-scattering process.

jet

jet

N

N

parton

parton

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Jet properties

►Jets are particles with high transverse momenta.

Incident parton Incident parton

jet

jet

►Jets come as a back-to-back pair

►A jet is nearly degenerate with its fragments

►The jet fragments form a jet conejet fragment

s

cone

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The term “jet” are often used for different objects:• jet parton (the totality of all jet fragments)• trigger particle (one of the jet fragments) • fragments in the jet cone (not including the trigger)

Ambiguity can be removed by judging from the context.

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Near-side and away-side jetsNear-side jet

Away-side jet is subject to strong absorption.Absorption is strongest in the most-central collision

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Δφ Δη

What is the ridge phenomenon?

Find: Δφ- Δη correlationProbability distribution P(Δφ, Δη ) in Δφ- Δη is in the form of (i) a “jet component” (ii) a “ridge component”.

jet

ridge• Occurrence of a near-side “jet” • Associated particles are observed in c

oincidence with the jet • The momentum and angles of these p

articles are measured: pt(particle) Δφ=φ (particle)- φ (jet) Δη=η (particle)- φ (jet)

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Experimental information about the ridge

• (i) Ridge yield correlated with N_participants• (ii) Ridge yield nearly independent of pt, flavor, b

aryon, meson characters of the jet trigger• (iii) Tjet>>Tridge > Tinclusive • (iv) Ridge particles have Δφ ~0• (v) Ridge particles nearly uniform in Δη

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Many Ridge Models

• S.A.Voloshin, Phys. Lett. B632, 490 (`06)• C.Y.Wong, Phy.Rev.C76,054908(’07);arXiv:0712.3282;arxiv:0806.2154(’08)• E. Shuryak, C76, 047901 (`07)• V. S. Pantuev, arxiv:0710.1882• R.C. Hwa, arXiv:0708.1508 • Nestor Armesto, Carlos A. Salgado, Urs Achim Wiedemann, Phys. Re

v. C 76, 054908 (2007) • Adrian Dumitru, Yasushi Nara, Bjoern Schenke, Michael Strickland

, arXiv:0710.1223• A. Majumder, B. Müller, and S. A. Bass, Phys. Rev. Lett. 99, 042

301 (2007) • R. Mizukawa, T. Hirano, M. Isse, Y. Nara, A. Ohnishi, arXiv:0805.

2795 • Sean Gavin, Larry McLerran, George Moschelli, arXiv:0806.4718• A. Dumitru,F. Gelis, L. McLerran, and R. Venugoplan, arxiv:0804.

3858. • •••• many more

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Questions• How does the ridge phenomenon occur?• What is the momentum distribution of the early medium partons?• What is the dominant mechanism of jet momentum loss?

These questions are linked together and can be answered by the momentum kick model:

Ridge particles are medium partons kicked by the jet.

The kicked partons carry direct information on the medium parton momentum distribution and the magnitude of the momentum kick . The momentum kick is related to the jet momentum loss.

11Δφ Δη

Schematic picture of the momentum kick model

jet

ridge

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Ridge particles are medium partons kicked by the jet

• (i) Ridge yield correlated with N_participants• (ii) Ridge yield nearly independent of pt trigger, flavor, baryon, meson characters of the jet• (iii) Tjet>>Tridge > Tinclusive

• (iv) Δφ ~ 0 implies that the ridge particles acquire their azimuthally properties from the jet

• (v) jet-(medium parton) interactions are short-ranged because of non-perturbative screening

The most likely explanation:

~

ridge particles are medium partons kicked by the jet and they acquire a momentum kick q along the jet direction

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Basic idea of the momentum kick model

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Mathematical details

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15

Simplification for Ntrig and RAA

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How to calculate the ridge yield per trigger?

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• Ridge yield per trigger depends on the number of kicked medium particles, <N>.

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Relation between the ridge distribution and the early parton momentum distribution

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•The kicked final partons subsequently materialize as hadrons by parton-hadron duality•The ridge particle distribution depends on the initial parton momentum distribution and the momentum kick q.

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Parametrization of initial parton momentum distribution

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22

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Ridge yield is a maximum at Δφ~0

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The width in Δφ depends on the magnitude of q.

at pt=2 GeV

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initial parton dN/dy ~ (1-x)a

The shape in Δη around Δη=0 depends weakly on a

The shape in Δη around large Δη depends strongly on a

The ridge shape in Δη

at pt=2 GeV

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Experimnetal measurement contains both jet and ridge components

• We need to get a good description of the “jet” component

• The jet component is produced mainly by fragmentation outside the medium. It is the same as in pp collisions for high pt jet.

• We assume that the jet component is an attenuated pp

(jet component in AA)=fJ (jet component in pp)• We need to parameterize pp jet data.

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The observed distribution in the momentum kick model

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32

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We need the pp near-side jet data

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The pp near-side jet data can be described by

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Data fromPRL95,152301(05) & J. Phy. G34, S679 (07)

pp near-side jet data (open blue circles)

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The initial parton momentum distribution

.GeV 1 GeV, 0.5 , 5.0 ,5.232 GeV, 0.1

find we, , Assuming

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/- exp)1(

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AA near-side data (black solid points) described wellby the momentum kick model around Δη~0

Data from STAR CollaborationPRL95,152301(05) & J. Phy. G34, S679 (07)

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AA near-side data (black solid points) described wellby the momentum kick model around |Δη|~3.3

Data from STAR Col.F. Wang et al. arXiv:0707.0815 (‘07)

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Momentum kick model gives the correct prediction

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Parton momentum distribution at the moment of jet-parton collision

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Possible evolution scenario of medium partons

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Conclusions• The ridge particles can be described as medium

partons kicked by the jet, and they carry information on the early parton momentum distribution and the momentum kick.

• The parton momentum distribution at the moment of jet-parton collision is relatively flat in rapidity with a thermal-like transverse momentum distribution and sharp kinematic boundaries.

• The magnitude of the momentum kick gained by the parton is 1 GeV, which is also the momentum loss by the jet in a jet-parton collision.

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Centrality depedence of RAA & ridge yield

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35

Distribution of the number of jet-(medium parton) collisions

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fm 025.0 / ,22.0 eff

The momentum kick model gives a good description of RAA

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Centrality dependence in the momentum kick model

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Energy and mass dependence in the momentum kick model