V. Greco Università di Catania, Italy INFN-LNS Coalescence models for hadronization in uRHIC ? ional Workshop XXXVIII on Gross Properties of Nuclei and Nuclear Exc ional Workshop XXXVIII on Gross Properties of Nuclei and Nuclear Exc Hirschegg, Austria, January 17 - 23, 2010 Hirschegg, Austria, January 17 - 23, 2010
Coalescence models for hadronization in uRHIC. ?. V. Greco Università di Catania, Italy INFN-LNS. International Workshop XXXVIII on Gross Properties of Nuclei and Nuclear Excitations Hirschegg, Austria, January 17 - 23, 2010. Intro to Basic Idea & Relevance for sQGP. - PowerPoint PPT Presentation
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V. GrecoUniversità di Catania, ItalyINFN-LNS
Coalescence models for
hadronization in uRHIC
?
International Workshop XXXVIII on Gross Properties of Nuclei and Nuclear ExcitationsInternational Workshop XXXVIII on Gross Properties of Nuclei and Nuclear ExcitationsHirschegg, Austria, January 17 - 23, 2010Hirschegg, Austria, January 17 - 23, 2010
Relevance for : the Heavy-Quark Sectorthe Heavy-Quark Sector /s of sQGP/s of sQGP A role in the Mach Cones ?A role in the Mach Cones ?
Observation at RHIC hadronization modified RAA-RCP-V2 for baryon and mesons
Ou
tlin
eIntro to Basic Idea & Relevance for sQGP
Basic Theory of coalescence (phase –space) coal. vs fragm. - application to RHIC RAA – v2 and B/M in the coalescence mechanism
Extensions from early realizations Robustness and open issues Formulation from Boltzmann collision integral
Surprises…
In vacuum pp collisions: p/ ~ 0.3
Hadronization has been modifiedHadronization has been modified1< p1< pTT < 5-6GeV !? (> 10 T < 5-6GeV !? (> 10 Tmaxmax))
PHENIX, PRL89(2003)
Baryon/MesonsBaryon/Mesons
Protons appear not suppressed!
QuenchingQuenching
Au+Au
p+p
Jet quenching should affect both
suppression: evidence of jet quenching
before fragmentation
Hadronization in Heavy-Ion CollisionsInitial state: no partons in the vacuum but a thermal ensemble of partonsThe bulk hadronization dynamics much less violent (t ~ 4 fm/c)dense parton systems no need for creation and splitting of partons
Parton spectrum
H
Baryon
Meson
Coal.
Fragmentation
V. Greco et al./ R.J. Fries et al., PRL 90(2003)
Fragmentation: energy needed to create quarks from vacuum hadrons from higher pT
partons are already there $ to be close in phase space $
ph= n pT ,, n = 2 , 3 baryons from lower momenta (denser)
Coalescence:
ReCo pushes out soft ReCo pushes out soft physicsphysicsby factors x2 and x3 !by factors x2 and x3 !
Basic TheoryDiscard details of dynamics -> adiabatic approximation:instantaneous projection of initial state onto final cluster
- Go in the momentum frame- Neglect the transverse momentum- Neglect r,p correlations -> only p-space- direct production (no resonances)
M(r,q) Meson wave function
All fairly good approximationsAt pT > 2 GeV/cxi light-cone momentum fraction
ababMbbbaaba
aM qrprfprfPd
dN,),(),(
,3
Approximation in FMNB (Hwa-Yang)
CM spin-isospin color factor
fragmenting:Ph = z pq, z<1
Recombining :X1Ph+x2Ph=Ph
Fries, QM’04
1
0 21212133,)()(
)2(xxPxfPxfdxdx
PdC
Pd
dNMbaM
M
Fries-Nonaka-Muller-Bass, PRC68(03)
Specific features of Reco in HICSpecific features of Reco in HIC
ReCo for ReCo for power lawpower law jet jet spectraspectra
Tpth Aef /
Bpf jetnn
jet pBC BpFjet
)1(nTp
F
CEven if eventually Fragmentation takes over …
Need of Coalescence + Fragmentation modelNeed of Coalescence + Fragmentation model
Both mesons and baryons have the same distribution at variance with fragmentation
P-> ∞ or m=0
1 ba xx
TPTPxxTPxTPx eeee baba //)(// Meson
ReCo is very effective for ReCo is very effective for thermal thermal spectraspectra::
Fragmentation for Fragmentation for power lawpower law spectra: spectra:
shift small power enhancement Suppressed by a power n=# of quarks
3D-geometry with radial flow space-momentum correlation
ET ~ 740 GeV
T ~ 170 MeV(r)~ 0.5 r/R
GeVfm-3
dS/dy ~ 4800
Experiments
lQCD Tc
like Hydro
L/
T=170 MeV
P. Levai et al., NPA698(02)
quenched
soft hardBulk matter consistent with hydro, experiments,
lQCD
Bulk matter consistent with hydro, experiments,
lQCD
x =p
Meson & Baryon Spectra
V. Greco et al., PRL90 (03)202302 PRC68(03) 034904R. Fries et al., PRL90(03)202303 PRC68(03)44902R. C. Hwa et al., PRC66(02)025205
Au+Au @200AGeV (central)ππρ
Proton suppression hidden by coalescence!
sh
GKL FMNB
ReCo dominates up to 4 (meson)6(baryon) GeV/c; Fragmentation + energy loss takes over above.
Baryon/Meson ratio
TAMU
FMNB Hwa-Yang
Strange particlesfrom a common
quark flow
A Coalescence process carries with it A Coalescence process carries with it another featureanother feature
thanks to non-equilibrium thanks to non-equilibrium
x
yz
px
py
22
22
2 2cosyx
yx
pp
ppv
22
22
xy
xyx
c2s=dP/d
Mass-dependence of v2(pT) suggests common transverse velocity field large At higher pT v2 for Baryon=Mesons in both - hydrodynamics - jet fragmentation
Again surprise Baryon Again surprise Baryon ≠≠ Mesons : vMesons : v22 larger for Baryons larger for Baryons
Elliptic flow at intermediate pT
Coalescence carries another features …Coalescence carries another features …
/3)(p3v)(pv
/2)(p2v)(pv
Tq2,TB2,
Tq2,TM2,
Enhancement of vEnhancement of v22Coalescence scalingCoalescence scaling
n
p
nT
2V1
baryons
mesons
Molnar and Voloshin, PRL91 (2003)
2
22)2()(
T
T
q
T
T
M ppd
dNαp
pd
dN
3
22)3()(
T
T
q
T
T
B ppd
dNp
pd
dN
)2cos(v21φ 2
TT
q
TT
q
dpp
dN
ddpp
dN
Considering only momentum space x - p correlation neglected
narrow wave function collinear approximation
v2 for baryon is larger and saturates at higher pT
v2q fitted from v2
GKL
Quark number scaling!
Again agreement with Again agreement with unexpected observationunexpected observation
No free parameter !No free parameter !
Better scaling vs KET/nq <–> energy conservation
Scaling widely confirmed for all species and centralitiesScaling widely confirmed for all species and centralitiesR. Lacey, PoS CFRNC2006:021,2006. e-Print: nucl-ex/0610029
Is the vIs the v22 (p (pTT) needed by coalescence ) needed by coalescence compatible with a fluid compatible with a fluid /s /s ~ 0.1-0.2~ 0.1-0.2 ? ?
0mmKE TT
But it also means that vBut it also means that v2q2q ~ ~ vv2h2h/2/2
Motivation for a Transport approachMotivation for a Transport approachSolved discretizing the space in x, ycells
It is a 3+1D (viscous hydro 2+1D till now) No gradient expansion, full calculation valid also at intermediate pvalid also at intermediate pTT out of equilibrium out of equilibrium QNS QNS valid at high valid at high /s /s study the effect of the hadronic phasestudy the effect of the hadronic phase include hadronization by coalescence+fragmentationinclude hadronization by coalescence+fragmentation Extension to Bulk viscosity Extension to Bulk viscosity (related also to chiral mass generation)(related also to chiral mass generation)
Simulate a fluid at constant shear viscositySimulate a fluid at constant shear viscosity
sn
pTr trtr /
1
15
1)),(( ,
=cell index in the r-spaceTime-Space dependent cross Time-Space dependent cross
Does mesons & baryons from resonance decay preserve the QNS?
2 ->1->2 can exihibt the scaling!
Dependence on wave function of v2 scaling
p momentum width of w.f.Baryon-to-Meson breaking of the scaling
Wavefunction+ Resonance decays
Breaking :
increasing with p
decreasing with pT
Higher Fock StateCostituent quark picture is a good description of hadron PDFas Q2 < 1 GeV2 (higher Fock state are suppressed)
B. Muller et al., PLB618(05)
...321 qqqqcgqqcqqcM
vv22 scaling scaling is preservedis preserved
Spectra are not affected (at least pT >> m )
pn
n
n
nCp
pn
n
n
nCp
M
M
B
B
vBB
M
M
M
M
vMM
)(
)(
12)(
1
)()(
2
)(
)(
12)(
1
)()(
2
v)(v~
v)(v~
Fock state, n = # partons)5.11(
3
2
2
3
1
sv
s
s
n
n
s = # of sea partons
For narrow w.f. limit
Standard higher twist w.f
Entropy Conservation?Entropy Conservation?Assuming hadronization linear with t during a mixed phase with the spectra of the static GKL model (
SSEE // ZTT
ES log
1
Energy is also not conserved !
15% violation, No factor 2 :- resonances- mass of the particle- degeneracies
Entropy- Energy ConservationEntropy- Energy Conservation
Entropy violation is also related to energy conservation and not to ReCo
Greco, EPJ ST155(2008)35004000 HADQGP SS
Transport approach to Coalescence->Energy Conservation Transport approach to Coalescence->Energy Conservation Miao et al., PRC75(2007)Rapp-Ravagli, PLB655(2007)
Solve energy conservation (except Solve energy conservation (except ))Clarify relation to statistical modelClarify relation to statistical modelKeeps features of coalescence:Keeps features of coalescence:
- show a KET scaling of v- show a KET scaling of v22/n/nqq
Essential property:Essential property:- Product f(pProduct f(p11)* f(p)* f(p22) of 2 distr. funct.) of 2 distr. funct.- suppressed when psuppressed when p11pp22 is too large is too large
r-p from Fokker Planck r-p from Fokker Planck still preservestill preserve
Quark Number ScalingQuark Number Scaling
Ravagli et al. PRC79 (2008)
Good quark number scaling except for too large Q value (<300 MeV) (similar to not too large width
and or non zero quark mass)
KET scaling down to low pT
VV22 quark # Scaling with Energy quark # Scaling with Energy ConservationConservation Scattering for q,Q in QGPScattering for q,Q in QGP
2
2)(
p
fD
p
pf
t
f qqq
Including space-momentum correlation
What happens What happens
to heavy quarks?to heavy quarks?
G.D. Moore and D. Teaney, PRC70 (2005) nucl-th/0412346
Problematic relation of RAA and V2 for heavy quarks
Up-Scaling elastic scattering from pQCD
Too low RAA or
too low v2
Coalescence modifyv2D RAA correlation
datadata
The same problem (even worse!) for radiative energy loss: S. Wicks et al., nucl-th/07010631(QM06), N. Armesto et al., PLB637(2006)362
A() 2()Asakawa
J/
Spectral function in lQCD & ResonancesSpectral function in lQCD & Resonances
VGTVT
qg
Q TS
QQQQQ SSSS 0
q-c “Im T”q-c “Im T” dominated by meson and diquark channel
lQCD
pQCD
Opposite T-dependence of Opposite T-dependence of
Fric
tion
coef
ficie
nt
V(r) - lQCD
Impact of Hadronization for heavy quarksImpact of Hadronization for heavy quarksHQ scattering in QGPHQ scattering in QGP
Langevin simulationin Hydro bulk
HadronizationHadronization
Coalescence + Fragmentation
sQGP2
,2
,, )(
p
fD
p
pf
t
f bcbcbc
BDbcbcMqbcBDBD DfffC
Pd
Nd,,,,,3
,3c,bc,b D,B
, D from resonantscattering according to lQCD V(r)
Van Hees-Mannarelli-Greco-Rapp, PRL100 (2008)
Improved RAA - V2 correlation
• toward a better agreement with data thanks to
a T dependence of the scattering opposite to pQCD
• coalescence can be viewed as coalescence can be viewed as a manifestation of T-matrix interaction a manifestation of T-matrix interaction
in the hadronization processin the hadronization process
Impact of hadronizationImpact of hadronization
Regeneration is revealed in : - pt spectra - elliptic flow
Implication for Quarkonium
Till now we have mainly looked at only J/Y yield, but thanks to coalescence there is a common c-quark collective dynamics with D meson …
Greco, Ko, Rapp PLB595(2004)
Jcoal.
No feed-downNo direct contr.
Suppression only
v2 from v2D :measure of
Ncoal/NINI
Coalecence only
pT- Quarkoniafrom regeneration
are consistent with Open heavy flavor!?
The open issue with the Mach-ConeThe open issue with the Mach-Cone
with G. Torrieri, J. Noronha, M. Gyulassy
A first look at the problem in the coalescence A first look at the problem in the coalescence modelmodel
away
near
Medium Cone Jet
(medium excitation)
High pHigh pTT Parton Parton Lower p Lower pTT “Mach “Mach Cone”?Cone”?
Properties of the cone:Properties of the cone:
angle does not depend on pt
ratio of B/M similar to the bulk one at the same pt
Peaks at the same angle for Baryon and Mesons
Afaniasev, PRL101 (2008)
cSv
cos 1 rad
Range of pRange of pTT is that where is that where
coalescence has manifested coalescence has manifested
its features its features ……
We used the Montecarlo simulations
At such pT coalescence is expected to play a role …Can it affect the peak structure?!
UL=UT=0.3 is the collective velocity in the wave generated by the jet
The double peak is not so easily produced in HydroThe double peak is not so easily produced in HydroHydro simulationHydro simulationLinearized hydro + AdS CFTLinearized hydro + AdS CFT
Quark distribution function before space integrationQuark distribution function before space integration
B.Betz,JPG35
Pure E depos.
Pure p depos.
Results for mesons
Mesons at 2 GeV show a dN/d with 2 peaks even if they come from quarks at 1 GeV that have only 1 peak
The position of the peaks is independent on pT like in experiments
Meson
pd
dN
/
p
Quark
pT
V.G., Torrieri, Noronha,Gyulassy, NPA830(2009)
Meson vs Baryon Meson vs Baryon One may expect a difference between baryon and meson!In the experiment is not observed a difference
But indeed coalescence generates a similar shapefor both angle and width
Why one should expect the same angle? and especiallyThe same depths of the peaks
Angle and depth of the signallook very similar.
Why the peak shows up?Why the peak shows up?The peak is created by the locality od coalescence. The two branches of the wavedoes not talk. Coalescence enhances the peak at each side and then summing up a dip appears.a dip appears.
Meson
Why baryons=mesons?Why baryons=mesons?Correlation should increase, but at pT/3
angular correlations is weaker -> exact compensation and meson/baryon Mach shape are similar.
Why two peaks? Why similar shape for Baryon and Meson?Why two peaks? Why similar shape for Baryon and Meson?
p
quark
meson
)2/()( 2TqTM pfpf
Considering only one side
Considering only one side
)3/()( 3TqTB pfpf
Take home messagesTake home messages (please!)
Hadronization from 2-3 body phase SPACE (pT< 5-6 GeV):
dense medium decrease the role of the vacuum massive quarks close in phase space
hadrons at pt comes from quarks pt/n (shift of soft scale)
Universal elliptic flow (dynamical quarks “visible”): carried by quarks enhanced by coalescence consistent with/s =0.1 ?!
R.J. Fries, V. Greco, P. Sorensen - Ann. Rev. Part. Sci. 58, 177 (2008)
Result are robust against, uncertainty in resonance production,Result are robust against, uncertainty in resonance production,wave function, higher Fock states, energy conservationwave function, higher Fock states, energy conservation
It’s not a question of twiggling parameters to get a better fit to It’s not a question of twiggling parameters to get a better fit to the data, the data,
but there is a physical mechanism that generates relations but there is a physical mechanism that generates relations between between
RRAA AA (R(RCpCp) - v) - v22 for light and for light and heavy quarksheavy quarks + baryon/meson + baryon/meson
branches branches hard hard to get without a coalescence model to get without a coalescence model
More Recent PerspectivesMore Recent Perspectives
Mach-Cone like peaksMach-Cone like peaks: Hard to get but again coalescence can only help …
and this is another consistency
Role inRole in/s determination:/s determination: Transport Theory can entail a consistency between
QNS and /s =0.1-0.2
Heavy Quark interaction in QGP:Heavy Quark interaction in QGP: RAA and v2(pT) explained only if coalescence is present
Consistency between D and J/Y spectra: one underlying c
Open IssuesOpen Issues
Role of Confinement - Vij(r,T) from lQCD (for heavy quarks)
Statistical Model (RR,Miao-Gao…) - Probability of resonance formation (entropy-energy)
Implementation coupled to Transport equations: - role in of correlation in v2 scaling - 2-3 particle jet correlation
Role of finite mass - 3D
Importance of 3D phase-space lowering pT
At low pT scaling can be largely brokenbut dumped by the shape of v2(pT)
Lower mass lead to larger breakingof the scaling due to coalescencebetween quark with large q=p1-p2
2 schematic cases
The observed scaling tells that the coalescingThe observed scaling tells that the coalescingquarks have small relative momentum!quarks have small relative momentum!
realistic shape
Exercise: Entropy of a gas with g d.o.f
Non-RelativisticNo quantistic
thN
NN
TNS log
2
5
2
5
1) g suppose mgm70% decrease
gg NS 5.2g
gg N
g
gNS 3.0log
2
5
3) Coalescence with (PRC68, 034904) - 16 % decrease
Gluon gas at equilibrium Pion gas out-of-equilibrium
Volume expansion needed to compensate the decrease is much larger than in coalecence model
ggg SNNS 7.08.12log2
5
2) Only qq m 28% decrease
N. Armesto et al., PLB637(2006)362S. Wicks et al., nucl-th/07010631(QM06)
lQCD resonant (bound) states persistlQCD resonant (bound) states persistfor QQ and qq -> Qq (D-like) resonant scatteringfor QQ and qq -> Qq (D-like) resonant scattering
lQCD resonant (bound) states persistlQCD resonant (bound) states persistfor QQ and qq -> Qq (D-like) resonant scatteringfor QQ and qq -> Qq (D-like) resonant scattering
RRAA AA , v, v22 of single e – Jet Quenching of single e – Jet Quenching
Radiative energy loss not sufficient
sQGP: non perturbative effect qq
Main Challenge is the in-medium quark interactionMain Challenge is the in-medium quark interaction
Effect of Effect of /s on the hadronic phase/s on the hadronic phase
Does the NJL chiral phase transition affect the elliptic flow of a fluid at fixed /s?
e-Print: arXiv:1001.2736 [hep-ph] - yesterday
Bulk : Charge Fluctuations
kiik
ikii
i
ch
nncnqN
QD 2
2
4
Recombination with all the quark converted into baryon and meson
Correlations cik
Neglecting: Hadronic diffusion Gluons
qqssdduu NNNNNNNQ 45
11
9
1
9
42
Close to the value used in Close to the value used in GKL, PRC68 : NGKL, PRC68 : Nqq ~ 1200 ~ 1200
ALCOR, PLB**: NALCOR, PLB**: Nq q ~~ 1300 1300
Statistical model Nhad at Tc & from recombination Nquark
C. Nonaka et al., nucl-th/0501028
Nhad = 507 (635)Nquark= 1125 (1377)
( ) nonet mesons +octet & decuplet baryons
)350(290
3702
2
COAL
EXP
Q
Q
STAR, PRC68 (2003) 44905
Same Side Correlation at intermediate Same Side Correlation at intermediate pptt
reproduce the relative strength reproduce the relative strength
with baryon and meson triggerwith baryon and meson trigger
Any residual interaction in f(p)
lead correlation in the coalescing hadronsSimilar to effect on v2
to be seen the assumed Cto be seen the assumed Cabab is dynamical reproduceble at is dynamical reproduceble at RHICRHIC-> coupling to transport approach-> coupling to transport approach
Fries et al., PRL94 (2005)
Meson trigger Baryon trigger
2-parton correlation fromjet-bulk interaction
20/1cos
0 jiecCab
c0 and 0 fixed to fit data
pions protons
Miao et al., PRC76(07) - using the Bolzmann Collision approach
Baryon and Mesons spectra
Particles included-> agreement alsoOn yields
)()(
)()()(
xx
xxx
DD
DD
E791 beam: - hard cc production;- c recombine with d valence from - D enhancement
Braaten, Jia, Mehen: Phys. Rev. Lett. 89, 122002 (2002)
Quark-Antiquark Recombination in the Fragmentation Region K.P. Das & R.C. Hwa: Phys. Lett. B68, 459 (1977):
Sea quarks Recombination at XF = 0Rapp and Shuryak, Phys. Rev. D67, 074036 (2003)
Leading Particle EffectReservoir of partons modifies hadronization
Similarly for
at ISR/Fermilab (late ‘70)
In HIC the resorvoir is the thermal bulk!
)(
)(
ucD
dcD
)( ud
=0 from LO fragmentation
beam
A drawback: for themal distrbution there is exact compensation between the shift in pT of coalescence and the enhancement of correlation with pT