Hadronization of Dense Partonic Matter

Hadronization of Dense Partonic Matter

Rainer FriesUniversity of Minnesota

Talk at SQM 2006March 28, 2006

Hadronization 2 Rainer Fries

Hadronization

Formation of bound states is non-perturbative in QCD.

Hadrons look differently, depending on how we probe them

Probe different matrix elements of different operators.

If we were able to solve QCD completely, we could compute all of them. … the resolution

of the process

… which process we use to probe

… the reference frame.

How we see a hadron depends on …

u

ud u

d

u

s

d u

d

g g

g p +


An Example

E.g. measure form factor in p + * p


An Example

E.g. measure form factor in p + * p

Sensitive to matrix elements

= wave functions

* describes uud p: resembles recombination

Pduu βα 0~

uud


Fragmentation

E.g. measure hadrons produced in e+e-

Single parton has to hadronize = fragmentation Radiation of gluons + pair production

Factorization:

Holds for Q2

Probing matrix elements like

All these matrix elements are measured, not calculated.

∑ →⊗=p

D hpph σσ

00~hu βα uhhuD →


Dense Parton Systems

Fragmentation = limit of hadronization for very dilute systems (parton density 0)

What happens in the opposite limit (thermalized phase of partons just above Tc)? No perturbative scale in the problem (T QCD)

Naively: recombine partons


Recombination

Simplest realization: Recombine valence quarks of hadrons

Instantaneous projection of quark states on hadron states

Immediate problems: Energy not conserved Where are the gluons?

qq M→ qqq B→

MMM wwCPd

NdΦ⊗⊗= ∫

Σβα3

3

Product of quark distributions

Meson Wigner function


Baryon/Meson Anomaly @ RHIC

Enhanced baryon yield p/ ~ 1 in Au+Au (for PT ~ 2 …4 GeV/c) p/ ~ 0.3 in p+p, p/ ~ 0.1….0.2 in e++e-

PHENIX



Enhanced baryon yield General baryon/meson pattern: p, , , versus

K, , , K*



Enhanced baryon yield General baryon/meson pattern: p, , , versus K, , , K*

No mass effect: behaves like a pion (m mp , m >> m)

Hadron properties don’t matter in this kinematic region. Only the number of valence

quarks! Do we catch a glimpse at

hadronization?

STAR Preliminary


Recombination & Fragmentation

“Dual” model of hadron production: Recombination + pQCD/fragmentation to describe hadron

production at RHIC for PT > 1…2 GeV/c

Competition between Reco und Fragmentation Fragmentation dominates for

power law and high PT.

Recombination dominates for thermal quarks.

fragmenting parton:ph = z p, z<1

recombining partons:p1+p2=ph

⎪⎩

⎪⎨⎧

=

=⇒

−−−−−−

−−−−

−

TPTPxxTPxTPxB

TPTPxTxPMTp

eeeewwwN

eeewwNew

//)1(//

//)1(/

/

~~

~~~

βαβαγβα

βα



“Dual” model of hadron production: Recombination + pQCD/fragmentation to describe

hadron production at RHIC for PT > 1…2 GeV/c

For RHIC:

T = 175 MeV Radial flow β = 0.55 Constituent quark masses Fit to pion data predictive power for all other hadron

species

With B. Muller, C. Nonaka, S. A. Bass

( ) ( ) ( )2 2/ / 2, ,Tp va agw e fp eσ ησ ρ φΔ− ⋅ −=


Hadron Spectra Recombination of thermal partons dominates up

to 4 GeV/c for mesons, 6 GeV/c for baryons


More Hadron Data

Large baryon/meson ratios sharp drop beyond PT 4 GeV/c

Nuclear modification factors: Baryon enhancement can reverse

suppression by jet quenching

RAA > RCP ~ 1 for baryons,

drop in baryon/meson beyond PT 6 GeV/c


Elliptic Flow Scaling

Assume universal elliptic flow v2p of the partons

before the phase transition Recombination prediction:

Scaling works for all hadrons

Deviations for pions arise mostly from resonance decays (Greco et al.)

( ) ( )2 2 2 2an22 3

d 3p pM tt

B tt

pv p vv

pv p

⎛ ⎞= ⎜ ⎟

⎛ ⎞= ⎜ ⎟

⎝⎠ ⎠⎝


Quark Counting Rule for the QGP

Quark counting rules tell us that there is a quark substructure in hadrons Classic example: Counting valence quarks

RHIC 2003: A new quark counting rule Subhadronic degrees of freedom are explicit! Partons Observable v2 describes a collective effect

Bulk matter Equilibrium reached during the build-up of v2?

Thermalization?? Deconfinement is reached: plasma of constituent (?)

quarks at hadronization QGP phase?

3

2

)(

)(=

NNN

σσ

3

2

)3(

)2(

2

2 =pvpv

B

M


How robust is v2 scaling?

Scaling law uses the most primitive approximations Momentum shared equally between constituents

Expect correction for realistic wave function with finite width.

Numerically: effects are small

( )( ) ( ) ( ) ( )( )[ ]

( ) ( )TMM

Tb

Ta

TMMT

M

Pxkxdx

PxvxPvPxkxdxPv

,

1,2

22

2

2φ

φ

∫∫ −+

=

Momentum shared: fractions x and 1-x


Fate of the Gluons? Are there gluons or sea quarks?

No effect on particle yields for thermal spectra!

Resulting elliptic flow for hadrons does not obey scaling For equally shared momenta:

K+++= jjiiijiii qqqqbaqqbabaM 210 ααα

( ) ( ) ( ) K++= ∑ 4/42/2 2

2

12

2

02 Tp

iiT

pT

M PvPvPv αα

TPTP

ii

i

nTPx

i eeei

i //2

1

/2 −−

=

− ==∑∑ ∏ αακ


Zooming in on v2 Scaling

We proposed a new variable: baryon/meson v2 asymmetry (B-M)/(B+M) for scaled v2.

First results: Size and sign of the

effect predicted correctly.

Gluons could be accommodated.

P. Sorensen, QM 05


A New Scaling?

KET scaling = hydro scaling Quark number and quark mass scaling don’t interfere

with each other!

Chiho Nonaka: 3-D Hydro


Soft/Hard Recombination

Attempt to treat reco + fragmentation consistently Hwa and Yang: jets as cones of parton showers at late

times; fitted to fragmentation functions Majumdar, Wang and Wang: 2- and 3- quark constituent

quark fragmentation + recombination ( Q2 evolution) Recombine all partons:

Partons = soft/thermal + showers from jets Two parton distribution function:

( ) 'SSSSTSTTw qq +++=

pTpa

rton

s Soft (T)

Shower (S)

Partons from 2 jets

Partons from 1 jets

soft-shower

soft-soft


Soft/Hard Recombination

Soft/Hard Reco could be important. Signatures in the p/, /K ratio at large PT. Produces hadron correlations.

Hwa and Yang


Hadron Correlations

How can hadrons at intermediate PT show jet-like structure?


Hadron Correlations


Actually there are clear deviations from “vacuum” jets

STAR preliminary

D. Magestro


Hadron Correlations


Correlations can be introduced by Soft/Hard Recombination

Correlations can arise from correlations between soft partons Hot spots: fully or partially

thermalized jets


Assuming 2-particle correlations Interesting scaling law ~ nAnB

Blending in fragmentation Hadron correlations consistent with data can be

generated.

From Parton to Hadron Correlations

Meson trigger Baryon trigger

4 parton pairs leading to meson correlations

Near side


Hadronization in Other Systems

Déjà vu: strong dependence of enhancement in RdAu on hadron species. Traditional explanation for enhancement: initial state

scattering.

There must be a much more effective mechanism in the final state, favoring baryons!

Recombination?

3/12 ~ APTΔ


Recombination in d+Au?

We don’t need a QGP, just a certain parton density Fragmentation is very ineffective for baryons!

It might just be easier to pick up soft partons instead of creating them, even in cold nuclear matter.

e+e-pppAAA


Recombination in d+Au?

Yields of protons and pions can be explained in a picture containing fragmentation and soft/hard recombination. Hwa and Yang:


Summary

Recombination is a very simple model to describe a very complex process.

And it does a remarkable job! v2 scaling is robust, gluons could be

accommodated. Hadron correlations at intermediate PT are not

inconsistent with recombination. Recombination effects for baryons in d+Au are

very likely.


Backup



“Dual” model of hadron production: Recombination + pQCD/fragmentation to describe hadron

production at RHIC for PT > 1…2 GeV/c

Fragmentation dominates for power law and high PT.

Recombination dominates for thermal quarks.

For RHIC:

T = 175 MeV Radial flow β = 0.55 Fit to pion data predictive power for all other hadron species

Exponential: TpTAew /~ −

DAeDwN TzPT /frag ~ −⊗=

TPTeAwwN /2reco ~ −⊗Φ⊗=

Power law: α−Tpw ~

α−TPN ~frag

α2reco ~ −

TPNfor mesons

( ) ( ) ( )2 2/ / 2, ,Tp va agw e fp eσ ησ ρ φΔ− ⋅ −=


Thermal Recombination

Hadron spectrum by convolution of Wigner functions

For PT >> M, kT: collinear kinematics, small mass corrections

Thermal parton distribution meson ~ baryon

),()2

,2

;2

,2

()2()2( 3

33

,3

3

3qrq

PrRq

PrRW

rqddRd

Pd

dNM

M Φ++−−= ∫∑∫ αββα

2-quark Wigner function Meson Wigner function

2

M

2

M3 3

,

B3 3

, ,B

( , ) ( , (1 ) )

( , ) ( , ' ) ( ,

( )

( ,

(

(1 ') '

2 )

'(2 )

) )

dN P uE d dx

d P

dN P

w R xP w R x P

w R xP w R x Pu

E d dx dxd p

w x P xR x

x

x

α β

α β

α β

α β

σ

σ

φ

φ

+ +

+ +

Σ

Σ

+

⋅=

⋅=

−

− −

∑∫ ∫

∑∫ ∫

⎪⎩

⎪⎨⎧

=

=⇒

−−−−−−

−−−−

−

TPTPxxTPxTPx

TPTPxTxP

Tp

eeeewwwW

eeewwWew

//)1(//

//)1(/

/

~~

~~~

βαβαγβααβγ

βααβ


What is in the Parton Phase? Recombination: low Q, no hard scattering No perturbative plasma at hadronization

Effective degrees of freedom; no gluons Constituent quarks?

We need a field theoretic description including chiral symmetry breaking. cf. dynamical masses from instantons, lattice, DSE

Diakonov & PetrovBowman et al.


Hadrochemistry in “Jet Cones”

The baryon/meson ratio is an indicator for the amount of “thermalization” in a jet Far side produces more baryons than near side

Hadronization of Dense Partonic Matter

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