QGP Formation Signals and Quark Recombination Model

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 v2

Violation of the scalingParticle species dependence of Cronin effectDiscussions


PCM & clust. hadronization

NFD

NFD & hadronic TM

PCM & hadronic TM

CYM & LGT

string & hadronic TM

time

Initial conditions

and interactions

Cooling down

freezing out

Hot and Dense

QGP formation signals

Strangeness enhancementStrangeness enhancementSuppression of J/Suppression of J/ΨΨDilepton enhancementDilepton enhancementDirect photonDirect photon……


Parton degree of QGP?

QGP signal from the bulk?

Experimental probes:

1) Penetrating probes: “jets” energy loss

2) Bulk probes :Elliptic flow, radial flow …


Evidence for the formation of QGPSingle hadron

Jet quenching

Energy loss ofjets in medium

Dihadron

No suppression for p spectrum


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


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


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


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


Parton distribution (log scale)

(recombine) (fragment)

p

p1+p2p q

meson momentum

higher yield heavy penalty

Why Recombination?


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


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


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


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


Duke approach

Low pLow pTT recombination recombination

high 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 x

d P

dN P uE d dxw R xP w R x P w R x x P x x

d P

w p g e e f


Texas/Ohio approach

Texas 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


, ,..., ,...3 31 2 1 2

1 2 31 2 3

( , , ) ( , , )p

pdx xdx dx x xdNx F x x x R

dx x x x x x x

Basic formulas in Oregon approachBasic formulas in Oregon approach


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


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


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


D(z)

qA A

Fragmentation


Parton shower

q

Initiating parton (hard)

Parton shower (semi-hard)

h

recombination

fragmentation


Fragmentation function known from fitting e+e- annihilation data S V G S K G K

BKKKKP etc

Recombination function known in the recombination model

Hwa, Phys. Rev. D (1980).

Shower parton distributions

Sij(x1)

i u,d,s,u ,d ,s , g

j u,d,s,u ,d ,s

K, L, G, Ls, Gs

Recombination for fragmentation


Fitted results


Shower parton distributions


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


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


Parton sources

Single shower parton distribution Single shower parton distribution isis

( ) ( / )ji i

dpdkkf k S p k

p

Joint two (three) shower parton distributionJoint two (three) shower parton distribution

can also be written downcan also be written down


Spectrum (0-10%)


Nuclear modification RAA

AA

T TAA pp

CT T

dNp dp dyd

RdN

Np dp dyd


p spectrum


p/


Centrality dependence


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


NCQ scaling

)3(3)(

)2(2)(

22

22

Tquark

Tbaryon

Tquark

Tmeson

pvpv

pvpv

partons moving-co of ecoalescenc

by 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 energy

dependence of the partonic cross sections will not affect the v2 scaling argument.

=>

Important for Beam Energy Scan program.


NCQ scaling violation

Why NCQ scaling ?


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


Why NCQ scaling violates?


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


Pion spectrum


Centrality dependence


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


Cronin effect

)

)

(

(

Central

C T TCP

Peripheral

C T T

dN

N p dp dyR

dN

N p dp dy

Shadowing effect is cancelled partiallyShadowing effect is cancelled partially


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


From recombination

Medium density depends on centrality

Medium effects are different in mesonand baryon production


Proton spectrum

T differentT different

for differentfor different

centralitiescentralities


RCP for proton


RCP for p &


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


DiscussionsCombination with other models, such as

hydrodynamics etc, is needed and under development

Recombination formulism from pQCD How to calculate the joint distributions?

QGP Formation Signals and Quark Recombination Model

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