pqcd a.) pqcd components in elementary collisions b.) modification in aa collisions

pQCD

A.) pQCD components in elementary collisions

B.) modification in AA collisions

hadrons

hadrons

leading particle

Jet: A localized collection of hadrons which come from a fragmenting parton

Parton Distribution FunctionsHard-scattering cross-sectionFragmentation Function

a

b

c

dParton Distribution FunctionsHard-scattering cross-sectionFragmentation Function

c

chbbaa

abcdba

T

hpp

zDcdab

tddQxfQxfdxdxK

pdydd

0

/222 )(ˆ),(),(

High pT (> 2.0 GeV/c) hadron production in pp collisions for √s > 60 Gev:

~

High pT Particle Production (the factorization theorem)

“Collinear factorization”

Hard scattering in longitudinal plane

Generally, momentum fraction x1x2. (Not in PHENIX –0.35<<0.35)

Hard scattering Hard scattering in transverse plane

Point-like partons elastic scattering , 1 , 2 0 T jet T jetp p

Partons have intrinsic transverse momentum kT , 1 , 2 ,1 ,2T jet T jet T Tp p k k

Jet Fragmentation (width of the jet cone)Partons have to materialize (fragment) in colorless world

jet

Tj

jet fragmentation transverse momentum

jT and kT are 2D vectors. We measure the mean value of its projection into the transverse plane |jTy| and |kTy| .

|jTy| is an important jet parameter. It’s constant value independent on fragment’s pT is characteristic of jet fragmentation (jT-scaling).

|kTy| (intrinsic + NLO radiative corrections) carries the information on the parton interaction with QCD medium.

2TTy

2| k | k

2 2vac IS nucl

2AA

2FS nuclk kk k

p+p p+A A+A

2 | |

T TtriggE

Ttrigg

p px

p

Fragmentation Function (distribution of parton momentum among fragments)

In Principle

i | | | | cos( ) parton i parton ii i

p p p p

i| | cos( ) 1| |i

i iiparton

pz zp

/( ) z zD z e

jetiip

Fragmentation function

In Practice parton momenta are not known

cos( ) = z TE trigg

parton

px zp

Simple relation E triggz x z

0 in pp: well described by NLO

Ingredients (via KKP or Kretzer)Ingredients (via KKP or Kretzer) pQCDpQCD Parton distribution functionsParton distribution functions Fragmentation functionsFragmentation functions

p+p->0 + X

HardScatterin

g

Thermally-shaped Soft Production

hep-ex/0305013 S.S. Adler et al.

“Well Calibrated”

Fate of jets in heavy ion collisions?

p

p

?

Au+Au

idea: p+p collisions @ same sNN = 200 GeV as reference

?: what happens in Au+Au to jets which pass through medium?

Prediction: scattered quarks radiate energy (~ GeV/fm) in the colored medium: decreases their momentum (fewer high pT particles) “kills” jet partner on other side

Intrinsic kT , Cronin Effect

Parton Distribution Functions

Shadowing, EMC Effect

Fragmentation Function leading

particle suppressed

Partonic Energy Loss

c

dhadrons

a

b

Hard-scattering cross-section

c

ccch

c

c

bbBaaA

ba

bBbaAa

baabcd

baT

hAB

zQzD

zzPd

cdabtd

dQxSQxS

ggQxfQxf

dddxdxABKpdyd

dN

),(

)(

)(ˆ

),(),(

)()(),(),(

2*0/

1

0

*

22

2/

2/

222

kk

kk (pQCD context…)

High pT Particle Production in A+A

Jet fragment shape parameters jT, kT

Parton distribution functions (hep-ex/0305109)

RHIC

Do we understand hadron productionin elementary collisions ? (Ingredient I: PDF)

RHIC

Ingredient II: Fragmentation functionsKKP (universality), Bourrely & Soffer (hep-ph/0305070)

Non-valence quark contribution to parton fragmentation into octet baryons at low fractional momentum in pp !!

Quark separation infragmentation models is important. FFs are not universal.

Depend on Q, Einc,and flavorzz

How to measure PID ?

Initial PID: charged hadrons vs. neutral pionsInitial PID: charged hadrons vs. neutral pions Detailed PID:Detailed PID:

dE/dx (0.2-0.8 GeV/c)dE/dx (0.2-0.8 GeV/c)TOF / RICH / TRD (1.5-5 GeV/c)TOF / RICH / TRD (1.5-5 GeV/c) rdE/dx (5-20 GeV/c)rdE/dx (5-20 GeV/c)V0 topology (only statistics limited)V0 topology (only statistics limited)

0 in pp: well described by NLO (& LO)


..or simply PYTHIA…..or simply PYTHIA…

p+p->0 + X

HardScatterin

g




pp at RHICStrangeness formation in QCD

Strangeness production not described by leading order calculation (contrary to pion production).It needs multiple parton scattering (e.g. EPOS) or NLO corrections todescribe strangeness production.Part of it is a mass effect (plus a baryon-meson effect) but in addition there is a strangeness ‘penalty’ factor (e.g. the proton fragmentation function does not describe production). s is not just another light quark

nucl-ex/0607033

How strong are the NLO correctionsin LO calculations (PYTHIA) ?

K.Eskola et al.K.Eskola et al.(NPA 713 (2003)):(NPA 713 (2003)):Large NLO Large NLO corrections notcorrections notunreasonable atunreasonable atRHIC energies.RHIC energies.

Should be negligibleShould be negligibleat LHC (5.5 or 14 TeV).at LHC (5.5 or 14 TeV).

STAR

LHC

New NLO calculation based on STAR data (AKK, hep-ph/0502188, Nucl.Phys.B734 (2006))

K0s

apparent Einc dependence of separated quark contributions.

Non-strange baryon spectra in p+p

Pions agree with LO (PYTHIA)Protons require NLO with AKK-FF parametrization(quark separated FF contributions)

PLB 637 (2006) 161

mt scaling in pp

Breakdown of mT scaling in pp ?

mT slopes from PYTHIA 6.3

Gluon dominance at RHICPYTHIA: Di-quark structures in baryon production cause mt-shiftRecombination: 2 vs 3 quark structure causes mt shift

Baryon/meson ratios – p+p collisions

PLB 637 (2006) 161 Bell shape from fragmentation is visible

Collision Energy dependence of baryon/meson ratio

Ratio vs pT seems very energy dependent (RHIC < < SPS or FNAL), LHC ?

Not described by fragmentation !(PYTHIA ratios at RHIC and FNAL are equal)

Additional increase with system size in AA

Both effects (energy and system size dependence) well described by recombination

Recombination vs. Fragmentation(a different hadronization mechanism in medium than in vacuum ?)

Recombination at moderate PRecombination at moderate PTT

Parton pt shifts to higher Parton pt shifts to higher hadron pt.hadron pt.

Fragmentation at high PFragmentation at high PT:T:

Parton pt shifts to lower Parton pt shifts to lower hadron phadron pTT

recombining partons:p1+p2=ph

fragmenting parton:ph = z p, z<1

Recomb.

Frag.

Baryon production mechanism through strange particle correlations …

Test phenomenological fragmentation models

OPAL ALEPH and DELPHI measurements:Yields and cos distribution between correlated pairs distinguishes between isotropic cluster (HERWIG) and non-isotropic string decay (JETSET) for production mechanism.

Clustering favors baryon productionJETSET is clearly favored by the data.

Correlated bar pairs are produced predominantly in the same jet, i.e. short range compensation of quantum numbers.

jetsqqZee 0

Flavor dependence of yield scaling

• participant scaling for light quark hadrons (soft production)• binary scaling for heavy flavor quark hadrons (hard production)• strangeness is not well understood (canonical suppression in pp)

PHENIX D-mesons

up, down strange charm

Charm cross-section measurements in pp collisions in STAR

CharmCharm quarks are believed to be produced at quarks are believed to be produced at early stage by initial gluon fusionsearly stage by initial gluon fusions

Charm cross-section should follow Charm cross-section should follow number of number of binary collisions (Nbinary collisions (Nbinbin) scaling) scaling

MeasurementsMeasurements direct Ddirect D00

(event mixing)(event mixing)

c→c→+X+X(dE/dx, ToF)(dE/dx, ToF)

c→e+X c→e+X (ToF)(ToF)

c→e+Xc→e+X(EMC)(EMC)

ppT T (GeV/c)(GeV/c) 0.10.13.03.0 0.170.170.250.25 0.90.94.04.0 1.51.5

constraintconstraint , , dd/dp/dpTT , , dd/dp/dpTT dd/dp/dpTT

LO / NLO / FONLL?A A LOLO calculation gives you a calculation gives you a rough estimate rough estimate of the cross sectionof the cross sectionA A NLONLO calculation gives you a calculation gives you a better estimate better estimate of the cross section and a of the cross section and a rough estimate rough estimate of of the uncertaintythe uncertaintyFixed-Order plus Next-to-Leading-Log Fixed-Order plus Next-to-Leading-Log (FONLL)(FONLL) Designed to cure large logs in NLO for pDesigned to cure large logs in NLO for pTT >> m >> mcc where mass is not relevant where mass is not relevant Calculations depend on Calculations depend on quark mass mquark mass mc, c, factorization scale factorization scale FF (typically (typically F F = m= mcc

or 2 mor 2 mcc), renormalization scale ), renormalization scale RR (typically (typically R R = = FF), parton density functions ), parton density functions (PDF) (PDF)

Hard to obtain large Hard to obtain large with with R R = = F F (which is used in PDF fits)(which is used in PDF fits)

b

bb

FONLLbb

NLOcc

FONLLcc

99.067.0

381134

400146

87.1

244 ;256

FONLL RHIC (from hep-ph/0502203 ):

LO:

NLO: CDF Run II c to D data (PRL 91,241804 (2003):CDF Run II c to D data (PRL 91,241804 (2003): The non-perturbative charm fragmentation The non-perturbative charm fragmentation

needed to be tweaked in FONLL to describe needed to be tweaked in FONLL to describe charm. FFcharm. FFFONLLFONLL is much harder than used is much harder than used before in ‘plain’ NLO before in ‘plain’ NLO FF FFFONLLFONLL ≠ ≠ FFFFNLONLO

RHIC: FONLL versus Data

Matteo Cacciari Matteo Cacciari (FONLL):(FONLL):

factor 2factor 2 is is notnot a problem a problem factor 5factor 5 is !!! is !!!

)FONLL() from STAR( 0

cc

TOFcc eD

Spectra in pp Spectra in pp seemseem to require a bottom contribution to require a bottom contribution High precision heavy quark measurements are tough at RHIC energies. Need direct High precision heavy quark measurements are tough at RHIC energies. Need direct

reconstruction instead of semi-leptonic decays. Easy at LHC.reconstruction instead of semi-leptonic decays. Easy at LHC. Reach up to 14 GeV/c D-mesons (reconstructed) in pp in first ALICE year.Reach up to 14 GeV/c D-mesons (reconstructed) in pp in first ALICE year.

hep-ex/0609010

nucl-ex/0607012

Conclusions for RHIC pp data We are mapping out fragmentation and hadronization in vacuum as a We are mapping out fragmentation and hadronization in vacuum as a

function of flavor.function of flavor. What we have learnedWhat we have learned::

Strong NLO contribution to fragmentation even for light quarks at RHIC Strong NLO contribution to fragmentation even for light quarks at RHIC energiesenergies

Quark separation in fragmentation function very important. Significant non-Quark separation in fragmentation function very important. Significant non-valence quarks contribution in particular to baryon production.valence quarks contribution in particular to baryon production.

Gluon dominance at RHIC energies measured through breakdown of mt-scaling Gluon dominance at RHIC energies measured through breakdown of mt-scaling and baryon/meson ratio. Unexpected small effect on baryon/antibaryon ratioand baryon/meson ratio. Unexpected small effect on baryon/antibaryon ratio

Is there a way to distinguish between fragmentation and recombination ? Does it Is there a way to distinguish between fragmentation and recombination ? Does it matter ? matter ?

What will happen at the LHC ? What has happened in AA collisions What will happen at the LHC ? What has happened in AA collisions (hadronization in matter) ?(hadronization in matter) ?

0 in pp: well described by NLO


p+p->0 + X

HardScatterin

g




hadrons

hadrons

leading particle

Jet: A localized collection of hadrons which come from a fragmenting parton

Parton Distribution FunctionsHard-scattering cross-sectionFragmentation Function

a

b

c

dParton Distribution FunctionsHard-scattering cross-sectionFragmentation Function

c

chbbaa

abcdba

T

hpp

zDcdab

tddQxfQxfdxdxK

pdydd

0

/222 )(ˆ),(),(

High pT (> 2.0 GeV/c) hadron production in pp collisions:

~

Hadronization in QCD (the factorization theorem)

“Collinear factorization”

Modification of fragmentation functions (hep-ph/0005044)

STAR, nucl-ex/0305015

energyloss

pQCD + Shadowing + Cronin

pQCD + Shadowing + Cronin + Energy Loss

RAA and high-pT suppression

Deduced initial gluon density at = 0.2 fm/c dNglue/dy ≈ 800-1200

≈ 15 GeV/fm3, eloss = 15*cold nuclear matter (compared to HERMES eA) (e.g. X.N. Wang nucl-th/0307036)

Is the fragmentation function modification universal ?

Octet baryon fragmentation function from statistical approach based on measured inclusive cross sections of baryons in e+e- annihilation:

Induced Gluon Radiation ~collinear gluons in cone “Softened” fragmentation

in je

i j t

t

n e

: increases

z : decreaseschn

Modification according toGyulassy et al. (nucl-th/0302077)

Quite generic (universal) but attributable to radiative rather than collisional energy loss

z z

Jet quenching I: hadrons are suppressed, photons are not

FA - QM`04 Strangeness Report 37

nucl-ex/0504001

Energy dependence of RAA

RAA at 4 GeV: smooth evolution with √sNN

Agrees with energy loss models

Radiative energy loss in QCD

CS

coherent

LPM Nqdzd

dIldzd

dI ˆHeitlerBethe

2ˆ~ˆ~ LqLqdzd

dIddzE SCSLPM

L

med

C

cformation Lt

BDMPS approximation: multiple soft collisions in a medium of static color charges

E independent of parton energy (finite kinematics E~log(E))E L2 due to interference effects (expanding medium E~L)

Medium-induced gluon radiation spectrum:

Total medium-induced energy loss:

2

222ˆ

qd

dqqdq mediumTransport coefficient:

Baier, Schiff and Zakharov, AnnRevNuclPartSci 50, 37 (2000)

High-energy parton loses energy byrescattering in dense, hot medium.

qq

“Jet quenching” = parton energy loss

Described in QCD as medium effect on parton fragmentation:

Medium modifies perturbative fragmentation before final hadronization in vacuo. Roughly equivalent to an effective shift in z:

2 (med) 2 2

1 /( , ) ( , ) ,p h p h p h E E

zD z Q D z Q D Q

Important for controlled theoretical treatment in pQCD:

Medium effect on fragmentation process must be in perturbative q2 domain.

MechanismsHigh energy limit: energy loss by gluon radiation. Two limits:

(a) Thin medium: virtuality q2 controlled by initial hard scattering (LQS, GLV)

(b) Thick medium: virtuality q2 controlled by rescattering in medium (BDMPS)

Trigger on leading hadron (e.g. in RAA) favors case (a).

Low to medium jet energies: Collisional energy loss is competitive!

Especially when the parent parton is a heavy quark (c or b).

qq

L

q qg

L

Extracting qhat from hadron suppression data

RAA: qhat~5-15 GeV2/fm

What does qhat measure?q̂

LqxxGN

Nq mediumC

CS ˆ,1

4ˆ2

2

Equilibrated gluon gas:number density ~T3

energy density ~T4

43

ˆ cq

qhat+modelling energy density

• pQCD result: c~2 (S? quark dof? …)• sQGP (multiplicities+hydro): c~10

R. Baier, Nucl Phys A715, 209c

Hadronic matter

QGP

~RHIC data

Model uncertainties

q-hat at RHIC

Pion gas

QGP

Cold nuclear matter

sQGP? ?

RHIC data

EASW BDMPS sCR

4ˆ q L2

ˆ q 2L2 d

0

L

ˆ q ()2ˆ q 00

L

/log14

92

3

ELdy

dNR

C

Eg

Rs

GLV

BDMPS(ASW) vs. GLVBaier, Dokshitzer, Mueller, Peigne, Schiff, Armesto, Salgado, Wiedemann, Gyulassy, Levai, Vitev

1800dy

dN g

ˆ q 10 GeV 2

fm

Rough correspondence: (Wiedemann, HP2006) 900

dydN g

fmGeVq

2

5ˆ

BDMPS

GLV

Medium-induced radiation spectrum

Salgado and Wiedemann PRD68 (2003) 014008

2ˆLqC

30-50 x cold matter density

What do we learn from RAA?

~15 GeV

E=15 GeV

Energy loss distributions very different for BDMPS and GLV formalisms

But RAA similar!

Renk, Eskola, hep-ph/0610059

Wicks et al, nucl-th/0512076v2

BDMPS formalismGLV formalism

Need more differential probes

RAA for 0: medium density I

C. Loizideshep-ph/0608133v2

I. Vitev

W. HorowitzUse RAA to extract medium density:

I. Vitev: 1000 < dNg/dy < 2000

W. Horowitz: 600 < dNg/dy < 1600

C. Loizides: 6 < < 24 GeV2/fmq̂

Statistical analysis to make optimal use of dataCaveat: RAA folds geometry, energy loss and fragmentation

Different partons lose different amounts of energy

1.) heavy quark dead cone effect :Heavy quarks in the vacuum and in

the medium (Dokshitzer and Kharzeev (PLB 519 (2001) 199)) the

radiation at small angles is suppressed

2.) gluon vs. quark energy loss: Gluons should lose more energy

and have higher particle multiplicities due to the color factor

effect.

Yu.Dokshitzer

…but everything looks the same at high pt….

up,down strange charm ?

Particle dependencies: RAA of strangenessA remarkable differencebetween RAA and RCP

that seems unique tostrange baryons.Ordering with strangenesscontent.‘Canonical suppression’is unique to strange hadrons

This effect must occur ‘between’ pp and peripheral AA collisions

Strange enhancement vs. charm suppression ?

But is it a flavor effect ?Kaon behaves like D-meson,we need to measure c

Do strange particles hadronizedifferent than charm particles ?

An important detail: the medium is not totally opaqueThere are specific differences to the flavor of the probeplus: heavy quarks also show effects of collisional e-loss

Theory: there are two types of e-loss:radiative and collisional, plus dead-cone effect for heavy quarksFlavor dependencies map out the process of in-medium modification

Experiment: there arebaryon/meson differences

BUT: heavy quarks show same e-loss than light quarks

RRAA AA of electrons from heavy flavor decayof electrons from heavy flavor decay

Describing the suppression is difficult for modelsDescribing the suppression is difficult for models radiative energy loss with typical gluon densities radiative energy loss with typical gluon densities

is not enough is not enough (Djordjevic et al., PLB 632(2006)81)(Djordjevic et al., PLB 632(2006)81)

models involving a very opaque medium agree models involving a very opaque medium agree better (qhat very high !!) better (qhat very high !!) (Armesto et al., PLB 637(2006)362)(Armesto et al., PLB 637(2006)362)

collisional energy loss / resonant elastic collisional energy loss / resonant elastic scattering scattering (Wicks et al., nucl-th/0512076, (Wicks et al., nucl-th/0512076, van Hees & Rapp, PRC 73(2006)034913) van Hees & Rapp, PRC 73(2006)034913)

heavy quark fragmentation and dissociation in heavy quark fragmentation and dissociation in the medium → strong suppression for charm the medium → strong suppression for charm and bottom (Adil & and bottom (Adil & Vitev, hep-ph/0611109)Vitev, hep-ph/0611109)

Constraining medium viscosity /s Simultaneous description of Simultaneous description of

STAR R(AA) and PHENIX v2STAR R(AA) and PHENIX v2for charm. for charm. (Rapp & Van Hees, PRC 71, 2005)(Rapp & Van Hees, PRC 71, 2005)

Ads/CFT == Ads/CFT == /s ~ 1/4/s ~ 1/4 ~ 0.08 ~ 0.08 Perturbative calculation of D (2Perturbative calculation of D (2t) ~6t) ~6

(Teaney & Moore, PRC 71, 2005) (Teaney & Moore, PRC 71, 2005) == == /s~1/s~1

transport models requiretransport models require small heavy quark small heavy quark

relaxation timerelaxation time small diffusion coefficient small diffusion coefficient

DDHQHQ x (2 x (2T) ~ 4-6T) ~ 4-6 this value constrains the this value constrains the

ratio viscosity/entropyratio viscosity/entropy /s ~ (1.3 – 2) / 4/s ~ (1.3 – 2) / 4 within a factor 2 of within a factor 2 of conjectured lower conjectured lower quantum boundquantum bound consistent with light hadron consistent with light hadron

vv22 analysis analysis electron Relectron RAAAA ~ ~ 00 R RAAAA at high p at high pTT - - is bottom suppressed as well?is bottom suppressed as well?

Energy density of matter

high energy density: > 1011 J/m3

P > 1 MbarI > 3 X 1015W/cm2 Fields > 500 Tesla

QGP energy density > 1 GeV/fm3

i.e. > 1030 J/cm3

pqcd a.) pqcd components in elementary collisions b.) modification in aa collisions

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