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