qgp formation signals and quark recombination model
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QGP Formation Signals and Quark Recombination Model
Chunbin YangCentral China Normal University
Wuhan
C.B. YangC.B. Yang Recombination ModelRecombination Model 22
OutlineOutlineHeavy ion collisions and QGP formationAnomalies at RHICPhysics ideas in the recombination modelFragmentation in the recombination modelApplications to Au+Au collisions
NCQ scaling of flow v2Violation of the scaling
Particle species dependence of Cronin effectDiscussions
C.B. YangC.B. Yang Recombination ModelRecombination Model 33
PCM & clust. hadronization
NFD
NFD & hadronic TM
PCM & hadronic TM
CYM & LGT
string & hadronic TM
time
Initial conditionsand interactions
Cooling down freezing out
Hot and Dense
QGP formation signalsStrangeness enhancementStrangeness enhancementSuppression of J/Suppression of J/ΨΨDilepton enhancementDilepton enhancementDirect photonDirect photon……
C.B. YangC.B. Yang Recombination ModelRecombination Model 44
Parton degree of QGP?QGP signal from the bulk?
Experimental probes:1) Penetrating probes: “jets” energy loss2) Bulk probes :Elliptic flow, radial flow …
C.B. YangC.B. Yang Recombination ModelRecombination Model 55
Evidence for the formation of QGPSingle hadron
Jet quenchingEnergy loss ofjets in medium
Dihadron
No suppression for p spectrum
C.B. YangC.B. Yang Recombination ModelRecombination Model 66
Hadron production mechanismsHadron production mechanisms
HOW?
Partons are produced in high energy collisions like e++e-, e+p, p+p, p+A,A+A
Partons in the final stage of evolution are converted into hadrons
C.B. YangC.B. Yang Recombination ModelRecombination Model 77
Traditional modelsTraditional models
String formation and break for low p T
Fragmentation for high p T
The string model may not be applicable to heavy ion collisionsFragmentation failed for central Au+Au collisions
C.B. YangC.B. Yang Recombination ModelRecombination Model 88
Anomalies at intermediate pT
• B/M
• v2(pT)
•Jet structure
• Cronin effect
p/ ≈1
v2(baryons) > v2(mesons)
not the same as in pp
RCPp > RCP
Hard to be understood in traditional models
C.B. YangC.B. Yang Recombination ModelRecombination Model 99
Hadronization by recombination
The colliding system generates quarks and gluons in the phase space
The quarks get dressedThe dressed quarks recombine into
hadrons to the detector
C.B. YangC.B. Yang Recombination ModelRecombination Model 1010
Parton distribution (log scale)
(recombine) (fragment)
pp1+p2
p q
meson momentum
higher yield heavy penalty
Why Recombination?
C.B. YangC.B. Yang Recombination ModelRecombination Model 1111
Features
quark momenta add, higher yield for high produced pT hadrons
soft parton density depends on medium more quarks for baryons than for mesons enhanced dependence on centrality for baryons when thermal partons are involved
C.B. YangC.B. Yang Recombination ModelRecombination Model 1212
No anomalies in recombination At intermediate pT, aplenty soft quarks are more important for proton production than for pionsp/1
For baryons, three quarks contribute to the flow, while only two quarks for mesons v2(baryons) > v2(mesons), quark number scaling Soft and semi-soft recombination Cronin effect
Process dependence of soft partons different jet structure in dA and AA
C.B. YangC.B. Yang Recombination ModelRecombination Model 1313
Recombination modelsRecombination models
• Use just the lowest Fock stateUse just the lowest Fock state i.e. valence quarksi.e. valence quarks
qqqqqqB q B q qbarbarMM
• Gluons converted to quarks firstGluons converted to quarks first• The probability for two (three) quarks to form The probability for two (three) quarks to form
a meson (baryon) is given by a process a meson (baryon) is given by a process independent recombination function Rindependent recombination function R
C.B. YangC.B. Yang Recombination ModelRecombination Model 1414
Different implementations
Duke group etc: 6-dimensional phase space using Wigner function from density matrix
Oregon group: one-dimensional momentum space using phenomenological recombination function
C.B. YangC.B. Yang Recombination ModelRecombination Model 1515
Duke approach
Low pLow pTT recombination recombinationhigh phigh pTT fragmentation fragmentation
2 2
23 3 ,
' ' ' 23 3 , ,
( ) / / 2
( , ) ( , (1 ) ) | ( ) |(2 )
( , ) ( , ) ( , (1 ) ) | ( , ) |(2 )
( , ) ( , )
MM
BB
p v T
dN P uE d dxw R xP w R x P xd PdN P uE d dxw R xP w R x P w R x x P x xd P
w p g e e f
C.B. YangC.B. Yang Recombination ModelRecombination Model 1616
Texas/Ohio approachTexas A&M/Budapest (Ko, Greco, Levai,
Chen)Monte Carlo implementation (with spatial
overlap)Soft and hard partonsSoft-hard coalescence allowed
Ohio State (Lin, Molnar)ReCo as a solution to the opacity puzzle
C.B. YangC.B. Yang Recombination ModelRecombination Model 1717
, ,..., ,...3 31 2 1 2
1 2 31 2 3
( , , ) ( , , )p
pdx xdx dx x xdNx F x x x Rdx x x x x x x
Basic formulas in Oregon approachBasic formulas in Oregon approach
C.B. YangC.B. Yang Recombination ModelRecombination Model 1818
Given by the valon distribution of the hadrons
1 2
1 2 3
, ,...1 2 1 2 1 2
, ,...1 2 3 1 2 3 1 2 3
( , ) ( , )
( , , ) ( , , )
KQ Q
p nQ Q Q
R y y y y G y y
R y y y y y y G y y y
1 2
1 2 3
1 2 1 2 1 2
1 2 3 1 2 3 1 2 3
( , ) ( 1)
( , , ) ( 1)
a bQ Q
a b cQ Q Q
G y y y y y y
G y y y y y y y y y
Recombination functions
C.B. YangC.B. Yang Recombination ModelRecombination Model 1919
Determining R
R p was determined from CTEQ From the parton distributions in proton a=b=1.755, c=1.05 at Q2=1GeV2
R was determined from Drell-Yan processes a=b=0 See Phys. Rev. C 66, 025204
C.B. YangC.B. Yang Recombination ModelRecombination Model 2020
Fragmentation? Recombination?
Answer: NO FRAGMENTATION only RECOMBINATION
Fragmentation is not a description of the hadronization process.
It uses phenomenological functions D(z) that give the probability of momentum fraction z of a hadron in a parton jet
C.B. YangC.B. Yang Recombination ModelRecombination Model 2121
D(z)q
A A
Fragmentation
C.B. YangC.B. Yang Recombination ModelRecombination Model 2222
Parton shower
q
Initiating parton (hard)
Parton shower (semi-hard)
h
recombination
fragmentation
C.B. YangC.B. Yang Recombination ModelRecombination Model 2323
Fragmentation function known from fitting e+e- annihilation data S V G S K G K
BKKKKP etc
Recombination function known in the recombination modelHwa, Phys. Rev. D (1980).
Shower parton distributionsSi
j(x1)i u,d,s,u ,d ,s , gj u,d,s,u ,d ,s
K, L, G, Ls, Gs
Recombination for fragmentation
C.B. YangC.B. Yang Recombination ModelRecombination Model 2424
Fitted results
C.B. YangC.B. Yang Recombination ModelRecombination Model 2525
Shower parton distributions
C.B. YangC.B. Yang Recombination ModelRecombination Model 2626
Application to Au+Au collisions
Thermalized low pT (soft) partonsHard partons (semi-hard) shower partonsThree types of recombination for mesons
thermal parton & thermal parton thermal parton & shower parton shower parton & shower parton
Joint parton distribution is not factorizable
C.B. YangC.B. Yang Recombination ModelRecombination Model 2727
Parton sources
Thermal parton distribution is assumed
exp( / )T Tdp C p T
Hard parton distributions fi(k) can be calculated from
pQCD nuclear shadowing nuclear geometry
C.B. YangC.B. Yang Recombination ModelRecombination Model 2828
Parton sources
Single shower parton distribution Single shower parton distribution isis
( ) ( / )ji i
dpdkkf k S p kp
Joint two (three) shower parton distributionJoint two (three) shower parton distribution can also be written downcan also be written down
C.B. YangC.B. Yang Recombination ModelRecombination Model 2929
Spectrum (0-10%)
C.B. YangC.B. Yang Recombination ModelRecombination Model 3030
Nuclear modification RAA
AA
T TAA pp
CT T
dNp dp dydR
dNNp dp dyd
C.B. YangC.B. Yang Recombination ModelRecombination Model 3131
p spectrum
C.B. YangC.B. Yang Recombination ModelRecombination Model 3232
p/
C.B. YangC.B. Yang Recombination ModelRecombination Model 3333
Centrality dependence
C.B. YangC.B. Yang Recombination ModelRecombination Model 3434
New physics
Thermal-thermal recombination makes p/ increase from very small value to about 1 at pT3GeV/c
Thermal-shower recombination plays an important role
This recombination can be equivalently regarded as modification of the fragmentation functions
C.B. YangC.B. Yang Recombination ModelRecombination Model 3535
NCQ scaling
)3(3)(
)2(2)(
22
22
Tquark
Tbaryon
Tquark
Tmeson
pvpv
pvpv
partons moving-co of ecoalescencby formation hadronFor AMPT model results:
Scaling in v2: partonic dof dominant; No scaling in v2 : hadronic dof dominant=>A tool to search for the possible phase boundary!
The beam energydependence of the partonic cross sections will not affect the v2 scaling argument.
=>Important for Beam Energy Scan program.
C.B. YangC.B. Yang Recombination ModelRecombination Model 3636
NCQ scaling violation
Why NCQ scaling ?
C.B. YangC.B. Yang Recombination ModelRecombination Model 3737
φdependence joint distribution collinearAssumptions: F(p1,p2)=F(p1)F(p2)
Validity of the assumptions?
Because of quark interactions, joint Because of quark interactions, joint distributions are not products of quark distributions are not products of quark distributionsdistributions
Recombined quarks not necessarily have Recombined quarks not necessarily have the same momentumthe same momentum
Fluctuations: large n=1,3 terms appears in Fluctuations: large n=1,3 terms appears in quarks distributions. They contribute to vquarks distributions. They contribute to v22
NCQ at RHIC may be coincidentNCQ at RHIC may be coincident
C.B. YangC.B. Yang Recombination ModelRecombination Model 3838
Why NCQ scaling violates?
C.B. YangC.B. Yang Recombination ModelRecombination Model 3939
Application to d+Au collisions
Basic formulas the same as for Au+Au collisions
Soft parton distribution the same form, T not temperature but inverse slope
No jet quenchingNuclear shadowing a little different from
that in Au+Au case
C.B. YangC.B. Yang Recombination ModelRecombination Model 4040
Pion spectrum
C.B. YangC.B. Yang Recombination ModelRecombination Model 4141
Centrality dependence
C.B. YangC.B. Yang Recombination ModelRecombination Model 4242
Cronin effect
Enhancement of hadron spectrum in pAEnhancement of hadron spectrum in pA collisions at high pcollisions at high pTT
Traditional explanation: Traditional explanation: initial interactions Many soft collisions before the last hardMany soft collisions before the last hard one, each gives a one, each gives a kT kick
C.B. YangC.B. Yang Recombination ModelRecombination Model 4343
Cronin effect
)
)
(
(
Central
C T TCP
Peripheral
C T T
dNN p dp dyR dN
N p dp dy
Shadowing effect is cancelled partiallyShadowing effect is cancelled partially
C.B. YangC.B. Yang Recombination ModelRecombination Model 4444
Puzzles
If Cronin effect is really due to initial interactions, dilepton spectrum should show similar effect.
Experimentally, the effect for dilepton is very small, no definite conclusion
Species dependence of the Cronin effect
C.B. YangC.B. Yang Recombination ModelRecombination Model 4545
From recombination
Medium density depends on centralityMedium effects are different in meson
and baryon production
C.B. YangC.B. Yang Recombination ModelRecombination Model 4646
Proton spectrum
T differentT differentfor differentfor differentcentralitiescentralities
C.B. YangC.B. Yang Recombination ModelRecombination Model 4747
RCP for proton
C.B. YangC.B. Yang Recombination ModelRecombination Model 4848
RCP for p &
C.B. YangC.B. Yang Recombination ModelRecombination Model 4949
DiscussionsDiscussions
QGP signal can be found from the bulkHadronization of partons can be described
by ReCo for d+Au and Au+Au collisionsReCo naturally explains species
dependence, such as baryon enhancement, v2 scaling...
Cronin effect can be interpreted as from final state interactions
C.B. YangC.B. Yang Recombination ModelRecombination Model 5050
DiscussionsCombination with other models, such as
hydrodynamics etc, is needed and under development
Recombination formulism from pQCD How to calculate the joint distributions?
C.B. YangC.B. Yang Recombination ModelRecombination Model 5151
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