The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

Quark Coalescenceand Charm Elliptic Flow

Zi-wei LinThe Ohio State University

ZWL & Denes Molnarnucl-th/0304045

Quark coalescence model

effects of quark masses

wavefunction width (momentum spread)

v2(Pt):

effects of different quark masses

effects of wavefunction width

unfold v2(Pt): from hadrons to quarks

Summary & Outlook

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

p+n Deuteron Butler&Pearson, PR129(63); Sato&Yazaki, PLB98 (81); Dover et al, PRC44(91); Scheibl&Heinz,PRC59(99);...

The Coalescence Model(for deuteron productions):

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

Why charm?

New test of quark coalescence

novel quark-mass effect

narrower wavefunction (in momentum)

binding-energy less important

coalescence results more reliable

Information on charm interactions

charm quark energy loss (test pQCD)

J/Ψ destruction and regeneration

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

Hadron multiplicities:Biro,Levai&Zimanyi, PLB347(95); JPG28(02); ...

ALCOR (ALgebraic COalescence Rehadronization) model:

The Quark Coalescence Model (previous applications to heavy ion collisions):

AMPT (A Multi-Phase Transport) model:v2 (Pt: 0-2 GeV): ZWL&Ko, PRC65(02);pion HBT: ZWL,Ko&Pal, PRL89(02)

Flavor ordering of v2 at high Pt: ZWL&Ko, PRL89(02)

Amplification of quark v2 & ordering: Voloshin, nucl-ex/0210014; Molnar&Voloshin, nucl-th/0302014

Enhanced p/pi ratio: Hwa&Yang, PRC65(02); Fries et al, nucl-th/0301087; Greco,Ko&Levai, nucl-th/0301093

see Denes Molnar's talk on 4/28/03

see Che Ming Ko's talk tomorrow (4/30/03)also, Berndt Muller's talk on 4/17/03

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

The Quark Coalescence ModelNear hadronization, gluons may decouple (serve to "dress" quarks),

consider only constituent quarks for hadronization.

hadron wavefunctionquark distributionshadronization

hypersurface

Already ssumed: rare process, small binding energy, factorization of 2-parton distribution functions, slowly-varying quark spatial-distributions, same hypersurface

A convenient starting point:

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

Wavefunction: how much momentum of a fast-moving hadron is carried by each valence quark?

1) Meson in the rest-frame:

2) In LAB frame:

mean value

width(spread)

If and (small binding energy):

Define

-

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

Only consider the quark momentum along the boost direction:

Parametrize hadron wavefunctions as:

same functional form as in the valon model: Hwa&Yang,PRC66(02),67(03)

Assume ,

mean values and this width then give:

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

Examples of meson wavefunctions:

It is a Gaussian for massive mesons (large a & b values):

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

The Quark Coalescence Model onv2

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

X:

impact

paramete

r

Y

Z: beam axis

Elliptic flow (v2):azimuthal asymmetry in transverse momentum

Here, assume v2 as the only anisotropy:

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

Side-notes:a) more particles produced via coalescence vs parton

fragmentation larger mean pt…b) higher baryon/meson ratio

Coalescence in the intermediate region (rare products):

v2

pt

baryons

mesons

quarks

coalescence fragmentation

Low pt quarks High pt quarks

D. Molnar & S. Voloshin,nucl-th/0302014

S. Voloshin @QM'02

The Quark Coalescence Model:amplification of quark v2

(in the limit of zero wavefunction width and identical quark mass)see Denes Molnar's talk on 4/28/03

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

P. Sorensen @SQM'03

Before rescaling:

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

This This parton coalescenceparton coalescence rescaling seems to rescaling seems to work for each of our centrality intervalswork for each of our centrality intervals

# of valence quarksP. Sorensen @SQM'03

After rescaling:

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

Effects of different quark masses(in the limit of zero wavefunction width)

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

Assumed

equal quark mass:

different quark mass:

charm v2 saturates here v2q saturates here at PT=6P0

Example

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

With more realistic v2 profile:

much slower rise of v2(pt) for hadrons with both light and heavy quarks

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

Effects of the wavefunction width

E.g. for a meson:

weight function:

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

Parametrization of parton spectra:

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

Numerical estimate of the wavefunction-spread effects:

Assuming

Concave feature of v2(pt)penalize any momentum spread,reduce elliptic flow

Reduction largest for π & K(also: possible large effects from binding energy, resonance)

Effect negligible (<2%) forΦ, J/Ψ, Ω.(massive hadron w. same quarks)

they better reflect parton v2

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

Examples of weight functions:

peaks at

@high Ptpeaks at

wide wavefunction (large width in z)narrow wavefunction (due to larger mass)

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

~1/Ptn

e

Consider formation of a high Pt meson froma) a leading q and a soft qbar (~Pt+soft)b) q and qbar with equal momentum (Pt/2+Pt/2)

1) For wide wavefunction (large width in z):dominance of a leading parton at high Pt

-aPtFrom momentum distributions:

due to power-law enhancement of high Pt partons

scenario a) dominates

ZWL&Ko, PRL89(02)

2 limits for the weight function

2) For narrow wavefunction:partons with equal share of Pt

Voloshin, nucl-ex/0210014; Molnar&Voloshin, nucl-th/0302014

~ wide for direct pion, K

~ narrow for massive hadrons

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

Unfold quark v2(Pt)from hadron elliptic flow:

For hadrons with narrow wavefunction (e.g., D & Λc):

follow from:

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

Summary

Different quark massesunequal momentum sharingmuch slower rise of v2(pt)for light+heavy hadrons (D ,Λc)

Finite width of hadron wavefunctions reduce v2

large width (~ direct π, K) peaks near z~0,1large reduction of v2

effect is small for massive hadrons (especially Φ, J/Ψ, Ω.)amplification relation works wellunfolding of quark v2(pt)

Test quark coalescence as a hadronization model,and extract info on parton dynamics of dense matter

The First Three Years of Heavy-ion Physics at RHIC INT 4/29/2003 Zi-wei Lin

OutlookFurther tests of current formalism:

experimental data could soon test current predictionsresonance contributions (ρ, K*, ...)region of validity (competition with fragmentation)hadron momentum spectra

Relax assumptions in current formalism:rare process:

needs to transform to linear form at low Pt

space-momentum correlationscould change current results

production of 2 or 3 parton distribution functions:include 2-or-3-parton correlations

small binding energy:tough relativistic bound-state problem

This talk is available at http://nt4.phys.columbia.edu/people/zlin/PUBLICATIONS/lin-int03.pdf