hadron correlations and parton recombination

Hadron Correlations Hadron Correlations and Parton and Parton

RecombinationRecombination

Rainer FriesUniversity of Minnesota

Hard Probes 2006 Asilomar June 11, 2006

Recombination and Hadron Correlations 2 Rainer Fries

Hard Probes

Hard processes as well controlled probes to measure properties of the QGP.

Hard probes high momentum transfer, high quark mass, high temperature

Careful: which value of our scale is sufficiently high depends strongly on the question we ask.

qq


Hard Probes

Careful: which value of our scale is sufficiently high depends strongly on which question we ask.

Single inclusive pion spectrum in p+p: pQCD works from PT 1 GeV

But: single inclusive spectra in A+A: don’t work up to 5 GeV,

Maybe not even at 10 GeV ??


Why Recombination: B/M

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


Why Recombination: RAA

No jet quenching for baryons? (RAA ~ RCP ~ 1) In the range PT ~ 1.5 … 5 GeV/c. Jet quenching not on the parton level?

PHENIX


Why Recombination: v2 scaling

Different v2 saturation for mesons and baryons


Baryon/Meson Anomaly

General baryon/meson pattern: p, , , versus K, , , K* In the region PT 1.5 … 6 GeV/c



General baryon/meson pattern: p, , , versus K, , , K* In the region PT 1.5 … 6 GeV/c

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

STAR Preliminary



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


v2 of < v2 of proton; behaves like meson



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


Hadron properties do not matter in this kinematic region.

Only the number of valence quarks!

We catch a glimpse of hadronization


Hadron Correlations

Away-side jets vanishes Ridge on the

near side

Away side gone/diffuse

STAR

A+A

p+p

Broadening+pedestal on near side

Wiedemann et al.


Signatures in Correlations

Deviations from jet shapes below PT = 5 GeV/c E.g. broadening of the near-side jet cone

STAR preliminary

Width of the peak in

STAR preliminary


Fragmentation?

Hard processes + vacuum fragmentation are ruled out below 4 … 6 GeV/c because of RHIC results on hadron chemistry elliptic flow v2

Recombination idea: hadrons at intermediate PT from recombination of soft partons


Recombination!

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

Recombination = hadronization in the opposite limit: thermalized phase of partons just above Tc


Recombination revisited

Basic assumptions Recombine valence quarks

Instantaneous projection of quark states on hadron states

For simplicity: factorize 2-parton distribution in 1-parton distributions

No correlations assumed!

qq M qqq B

123

3

WdCPd

NdAAA

A

A

2112 wwW


Recombination revisited

Conspiracy of thermal distributions and large P i. e. P >> M, kT (collinear situation); Boltzmann w

No dependence on shape of ! Baryon ~ meson

Reco Frag competition

TPTPxxTPxTPxB

TPTPxTxPMTp

eeeewwwN

eeewwNew

//)1(//

//)1(/

/

~~

~~~

fragmenting parton:ph = z p, z<1

recombining partons:p1+p2=ph


Recombination & Fragmentation

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

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

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

For RHIC:

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

species

2 2/ / 2, ,Tp va agw e fp e


RJF, Muller, Nonaka, Bass

Spectra & Ratios

Good description of spectra, ratios, RAA for all measured hadron species


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


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

2

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:

jjiiijiii qqqqbaqqbabaM 210

4/42/2 2

2

12

2

02 Tp

iiT

pT

M PvPvPv

TPTP

ii

i

nTPx

i eeei

i //2

1

/2


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


Hadron Correlations

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


Hadron Correlations

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

Naturally through soft-hard recombination Soft-hard hadrons and jet hadrons correlated Rudy Hwa’s talk

Naturally if the recombining partons are correlated


Recombination of mesons A, B from partons 1,2,3,4

New: permit 2-particle correlations

Possible ansatz

2-Particle Correlations

123433

6

123

3

WddCPdPd

Nd

WdCPd

Nd

BABAABBA

AB

AAAA

A

jiijCwwwwW 143211234

222

20

220

//1cos

//1cos000

,,

,,,;,

yyyTjTiji

yyyTjTijijjiiij

jiji

jiji

eeppfrrSc

eeppfrrScprprC


Hot Spots

Strong energy loss (dE/dx up to 14 GeV/fm) a lot of quenched/partially thermalized jets Localized deposition of energy and momentum

Hot Spots?

Hot spot can be correlated with remaining jet

Partons in the hot spot can be correlated with themselves

Add collective effects: Mach cone?


Associated Yield

List of assumptions Only near side; integrate rapidity Small correlations, keep only terms linear in c0 and v2

Narrow wave functions Correlations constant over volume Vc

Associated yield

Here

2/20

2 2/0

eNNQCYN BAABA

)(

)(

)(

1

d

NNd

d

dN

NY BAAB

AAB

V

VcC c

00


Amplification of Correlations

Q: Amplification factor Count 2-parton pairs between

the 2 hadrons; for effects linear in c0, only 1 correlation allowed.

Uncorrelated background (for meson-meson)

4 pairings that lead to meson correlations 2 pairings without correlating the mesons

Q=4 Meson-meson

Q=6 Meson-baryon

Q=9 Baryon-baryon

2cos2212/ 220BA

BA vvCNN


Numerical Example

Using Duke parametrization consistent with spectra and ratios!

Consistency with PHENIX data can be reached.

ABAB YdY94.0

0

cone

Large correlationsfrom Frag-Frag.

Lower associated yield when adding SS-SSwithout correlations(C0=0), especially for baryon triggers.

F-F and SS-SS withC0=0.08x100/Npart

(Vc~const.)

Meson trigger Baryon trigger

RJF, Muller, Bass: Phys. Rev. Lett. 94, 122301 (2005)


Identified Particles


Hadrochemistry in “Jet Cones”

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


Where is Fragmentation?

Below PT = 4 … 6 GeV/c: no go for (hadronic) hard probes

Problems for pQCD + fragmentation even above PT = 6 GeV/c ?? Baryon/meson ratio still too large above 5 GeV/c ??





v2 from jet quenching ??





v2 from jet quenching ??

No difference between quark and gluon jets ??

It may be “soft-hard” recombination. Pick-up of soft quarks by jets


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

pT

part

ons 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


Intermediate PT

Naively expected behavior of observables

What is found at RHIC: Some soft physics extends up to 4-6 GeV/c But above 2 GeV/c not described by ideal hydrodynamics

Soft-hard region of phase space = new phenomena

0 1 2 3 4 5 6 7 8 9 10 11 12 GeV/c

Soft/HydropQCD

0 1 2 3 4 5 6 7 8 9 10 11 12 GeV/c

pQCDReCo/soft-hardHydro


Jets & Medium

Recombination alone is not sufficient to understand the soft-hard region. Uses parameterizations of effects on the parton phase

Need understanding of the mechanisms behind jet-medium interaction

Still much to learn

LHC: will the soft/hard region be larger?

Jets Medium


Summary

Soft-hard regime at intermediate PT; extends up to 6 GeV/c, maybe more.

Recombination describes hadronization in this regime.

Recombination translates parton correlations into hadron correlations: possible origin of jet correlations

Hot spots from jet-medium interactions create such correlations.

Soft-Hard correlations are an additional mechanism


Backup


Recombination & Fragmentation

Competition of hadronization mechanisms

Fragmentation dominates for power law spectra in the limit PT

Recombination dominates for exponential spectra

Note: thermal recombination ~ statistical model for PT

Exponential: TpTAew /~

DAeDwN TzPT /frag ~

TPTeAwwN /2reco ~

Power law: Tpw ~

TPN ~frag

2reco ~

TPNfor mesons


Jets vs Medium

Apparent question: what is a jet, what is the medium? Possible (not unique) definition:

Jets dominate when the hadron chemistry matches expectation for jets in the vacuum

No pure jet scenario when partons from the “medium” contribute to hadron production

We compare vacuum fragmentation with recombination Medium influence on jets effectively

taken into account via energy loss Everthing that does not belong to a

vacuum jet, e.g. additional gluon radiation, is assumed to be part of the medium (thermalized or not)


Correlations from Fragmentation

Simple model for correlations from fragmentation: Dihadron fragmentation (Majumder & Wang) here

factorized in single hadron fragmentation Gaussian azimuthal dependence

Note: Contributions from soft-hard are small in our

parametrization Correlations from soft-hard negligible because of the

small yields Different from other groups.

2

02

1

0

2/

20

//2

1

1)1(2

)(

e

Pz

zPDzDE

z

Pg

zz

dzI

dPdP

YNdAT

BT

BaAa

AT

aa

z

zBT

AT

ABA

u minijet

u thermal

d

d

Fragmentation u ++

-


Identified Particles!

Again: no prediction about the input (correlations) on the parton side.

If predictive power, then for comparison of different hadron species.

Au+Au 200 GeVPHENIX Preliminary


Higher Fock States

Tower of Fock states, th state with n partons:

Probability for ejection of a very fast cluster with n partons from a thermal source at fixed P is independent of n!

Elliptic flow:

scaling violated even for very narrow wave functions (xi 1/n)

TPTPn

i

TPxM eeCeCPd

Ndi //

1

/3

3

i

iii

ii

ih PxvxcxdxPv 2

2

2 1

nPvnCPv

nPvnCPv

TpB

TB

TpM

TM

/

/

22

22


Conical Flow?

Preliminary data suggest double peak away side correlation

Mach cone?

More conservative scenario: flowing hot spots? Defocussing through radial flow Supported by PT,trig dependence?

Has to be ruled out before any more daring conclusion


Summary

“Jets” deviate in shape and hadrochemistry from vacuum for values below 6 GeV/c Exact definition needed.

To study jets and energy loss PT,trigger > 6 GeV/c mandatory, maybe more

hadron correlations and parton recombination

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