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Quark Coalescence at RHIC. Che-Ming Ko Texas A&M University. Introduction Quark coalescence Baryon/meson ratio Hadron elliptic flows and quark number scaling Effect of resonance decays Charm flow Higher-order anisotropic flows - PowerPoint PPT Presentation
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1
Quark Coalescence at RHIC
Che-Ming KoTexas A&M University
Introduction Quark coalescence Baryon/meson ratio Hadron elliptic flows and quark number scaling Effect of resonance decays Charm flow Higher-order anisotropic flows Coalescence in transport model Exotica (pentaquark baryon) Entropy problem Summary
Thanks to: Chen, Greco, Levai, Rapp
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Coalescence model in heavy ion collisions
Extensively used for light clusters production First used for describing hadronization of QGP by Budapest group Currently pursued by Oregon: Hwa, Yang (PRC 66 (02) 025205), ……… Duke-Minnesota: Bass, Nonaka, Meuller, Fries (PRL 90 (03) 202303; PRC 68 (03) 044902 ) Ohio and Wayne States: Molnar, Voloshin (PRL 91 (03) 092301; PRC 68 (03) 044901) Texas A&M: Greco, Levai, Rapp, Chen, Ko (PRL (03) 202302; PRC 68 (03) 034904) Most studies are schematic, based on parametrized QGP parton distributions Study based on parton distributions from transport models has been developed by TAMU group (PRL 89 (2002) 152301; PRC 65 (2002) 034904 ) and is now also pursued by D. Molnar (nucl th/0406066)
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Coalescence model
qq3
3
N)p,x(fE)2(
pddp
36/1gg K Mg
)p,...,p;x,...,(xf )p,x(fE)(2
pddpg=N n1n1niiq,i
n
1=i i3
i3
iin ∫∏π
σ
Quark distribution function
Spin-color statistical factor
e.g. 12/1gg *K
Coalescence probabilityfunction
)p,x(fq
PRL 90, 202102 (2003); PRC 68, 034904 (2003)
Number of hadrons with n quarks and/or antiquarks
54/1gg,108/1gg pp
}]/2Δ)m-(m-)p-exp{[(p×
]/2Δ)x-exp[(x=
)p-p;x-x(f=)p,p;x,(xf
2p
221
221
2x
221
212122121M
px
For baryons, Jacobi coordinates for three-body system are used.
4
Monte-Carlo method
)p,p;x,x(f
)ppp()j(P)i(Pgpd
dN
jijiM
jTiTT)2(
j,iqqM
T2
M
)p,p,p;x,x,x(f
)pppp()k(P)j(P)i(Pgpd
dN
kjikjiB
kTjTiTT)2(
kjiqqqB
T2
B
Introduce quark probabilities Pq(i) according to theirtransverse momentum and spatial distributions
Allow to treat all quarks on same footing
5
5.0≤||,fm5= yτ
• Thermal QGP • Power-law minijets • Choose
GeV2pT GeV2pT
fm8=R
GeV7885.0
y
T
dy
dE
3fm1100⇒ V
Consistent with data (PHENIX)
Parton transverse momentum distributions
149,245 sdu NNN
P. Levai et al., NPA 698 (02) 631
L/
T=170 MeV
quenchedsoft hard
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Other inputs or assumptions
• Minijet fragmentation via KKP fragmentation functions
• Gluons are converted to quark-antiquark pairs with equal probabilities in all flavors.
• Quark-gluon plasma is given a transverse collective flow velocity of β=0.5 c, so partons have an additional velocity v(r)=β(r/R).
• Minijet partons have current quark masses mu,d=10 MeV,
ms=175 MeV, while QGP partons have constituent quark masses
mu,d=300 MeV, ms=475 MeV.
• Use same coalescence radii for all hadrons, i.e., Δx=0.85 fm and
Δp=0.24 GeV.
jet
had
jet2
2jet/had
jet2
had2 p
pz,
z
)Q,z(D
pd
dNdz
pd
dN
7
Au+Au @ 200AGeV (central)
ππρ
Pion and proton spectra
Similar results from other groups
Oregon: parton distributions extracted from pion spectrum
Duke group: no resonances and s+h but use harder parton spectrum
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Baryon/meson ratios
Quark coalescence enhances baryons productionat intermediate transverse momentum
B M
coalescence
fragmentation
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Elliptic flows
Quark v2 extracted from pion and kaon v2 using coalescence model
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Naïve quark coalescence model
Quark transverse momentum distribution
)cos(2)p(v2+1∝)(pf Tq,2Tq φ
Meson elliptic flow
Baryon elliptic flow
)2/p(v2)2/p(v21
)2/p(2v)p(v T2,q
T22,q
T2,qTM2,
)3/p(v3)3/p(v61
)3/p(3v)p(v T2,q
T22,q
T2,qTB2,
Quark number scalingof hadron v2 (except pions):
n)/p(vn
1T2
Only quarks of same momentumcan coalescence, i.e., Δp=0
same for mesons and baryons
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Effects due to wave function and resonance decays
Wave function effectEffect of resonance decays
Wave fun.+ res. decays
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Charm spectra
Charm quark D meson J/ψ
Bands correspond to flow velocities between 0.5 and 0.65
NJ/ψ =2.7 . 10-3
NJ/ψ =0.9 . 10-3
T=0.72 GeVT=0.35-0.50 GeV
13Greco, Rapp, Ko, PLB595 (04) 202
S. Kelly,QM04
Charmed meson elliptic flow
V2 of electrons
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Effect of higher-order parton anisotropic flows
Including 4th order quark flow
)cos(4)p(2v+)cos(2)p(v2+1∝)(pf T4,qTq,2Tq φφ
Meson elliptic flow
Baryon elliptic flow
v
v
3
1+
3
1=
v
v ,
v
v
2
1+
4
1=
v
v ⇒ 2
2,q
4,q2
B2,
B4,22,q
4,q2
M2,
M4,
)v+v(2+1
v+v2= v,
)v+2(v+1
vv2+v2=v 2
4,q22,q
22,q4,q
M4,24,q
22,q
4,q2,q2,q
M2,
)vv+v+6(v+1
v3+vv6+v3+v3= v,
)vv+v+v(6+1
vv6+v3+vv6+v3=v
4,q22,q
24,q
22,q
34,q4,q
22,q
22,q4,q
B4,4,q
22,q
24,q
22,q
24,q2,q
32,q4,q2,q2,q
B2,
Kolb, Chen, Greco, Ko, PRC 69 (2004) 051901
15
22,q4,q2
2
4 2v v 1.2 v
v
Data can be described by a multiphase transport (AMPT) model
22,q4,q v v
Data
Parton cascade
Higher-order anisotropic flows
16
A multiphase transport model
Lin, PaL, Zhang, Li &Ko, PRC 61, 067901 (00); 64, 041901 (01)
• Initial conditions: HIJING• Parton evolution: ZPC• Hadronization: Lund string model for default AMPT Coalescence model for string melting scenario •Hadronic scattering: ART
• Convert hadrons from string fragmentation into quarks and antiquarks• Evolve quarks and antiquarks in ZPC • When stop interacting, combine nearest quark and antiquark to meson, and nearest three quarks to baryon, • Hadron flavors are determined by quarks’ invariant mass
String melting: PRC 65, 034904 (02); PRL 89, 152301 (02)
17
Quark elliptic flows from AMPT
• pT dependence of charm quark v2 is different from that of light quarks• At high pT, charm quark has similar v2 as light quarks• Charm elliptic flow is also sensitive to parton cross sections
18
Pseudorapidity dependence of v1 and v2
• String melting describes data near mid-rapidity (||<1.5)• At large rapidity (||>3), hadronic picture works better
19
Θ+ production in heavy ion collisions
Quark coalescence model
with quark distribution function and Theta+ Wigner function
Chen, Greco, Ko, Lee and Liu, nucl-th/0308006
4
1
4
1
22224
2
4
2
32/32/3
22
5
5
11513
3
/exp8);(
))2/(exp()(),,(
)21(
)4(
5
1
5
4
);(),()2(
i iiiii
qqq
qs
qsdu
iiiq
i
iii
kypxf
Tmpygpyf
TmVm
mNNNg
ppxxfpxfE
pddpgN
Compare to ~ 0.9 (Randrup, PRC 68) and ~ 0.4 (Letessier et al, PRC 68) from statistical model
Take σ=0.86 fm (RΘ~0.9 fm) gives NΘ~0.64, reduced to 0.19 by relativisticcorrection and sensitive to the Θ+ wave function
20
Entropy
For non-relativistic system
thN
Nlog
2
5N
T2
5NS
For g→π assuming mg=mπ
gg
ggg N8.0g
glog-
2
5SS N 5.2S
70% decrease
Coalescence model
4080S 4870S HadQGP 16% decrease
But energy is not conserved ΔE/E~ 18%
Need to take into account binding effect.
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Summary
• Hadronization via parton coalescence seems to work well in understanding observed hadron yields and transverse momentum spectra as well as their elliptic flows.
• Coalescence of minijet partons with partons from QGP
is an alternative mechanism for hadronization of minijet partons.
• Incorporation of parton coalescence in transport models
is useful. For QGP partons, it has already been included in the AMPT model (Lin et al., PRC 65, 034904 (2002); PRL 89, 152301 (2002)). Need to include minijet partons as well.