Pqcd a pqcd components in elementary collisions b modification in aa collisions
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pQCD A.) pQCD components in elementary collisions B.) modification in AA collisions. High p T Particle Production (the factorization theorem). hadrons. Parton Distribution Functions. hadrons. Hard-scattering cross-section. leading particle. Fragmentation Function.

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pQCD A.) pQCD components in elementary collisions B.) modification in AA collisions

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pQCDA.) pQCD components in elementary collisionsB.) modification in AA collisions


High pT Particle Production (the factorization theorem)

hadrons

Parton Distribution Functions

hadrons

Hard-scattering cross-section

leading particle

Fragmentation Function

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

~

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

c

a

Parton Distribution Functions

Hard-scattering cross-section

Fragmentation Function

b

d

“Collinear factorization”


Hard scattering in longitudinal plane

Hard scattering in transverse plane

Generally, momentum fraction x1x2. (Not in PHENIX –0.35<<0.35)

Point-like partons  elastic scattering

Partons have intrinsic transverse momentum kT

Hard scattering


jet fragmentation transverse momentum

jet

p+p

p+A

A+A

Jet Fragmentation (width of the jet cone)

Partons have to materialize (fragment) in colorless world

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.


In Practice

parton momenta are not known

 Simple relation

Fragmentation Function (distribution of parton momentum among fragments)

jet

In Principle

Fragmentation function


Thermally-shaped Soft Production

“Well Calibrated”

Hard

Scattering

p0 in pp: well described by NLO

p+p->p0 + X

  • Ingredients (via KKP or Kretzer)

    • pQCD

    • Parton distribution functions

    • Fragmentation functions

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


Fate of jets in heavy ion collisions?

idea: p+p collisions @ same

sNN = 200 GeV as reference

p

p

?: 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

?

Au+Au


High pT Particle Production in A+A

Parton Distribution Functions

Intrinsic kT , Cronin Effect

Shadowing, EMC Effect

Hard-scattering cross-section

c

a

Partonic Energy Loss

b

d

hadrons

FragmentationFunction

leading particle suppressed

(pQCD context…)


Jet fragment shape parameters jT, kT


Parton distribution functions(hep-ex/0305109)

RHIC


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

RHIC


z

z

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 in

fragmentation models

is important. FFs are

not universal.

Depend on Q, Einc,

and flavor


How to measure PID ?

  • Initial PID: charged hadrons vs. neutral pions

  • Detailed PID:

    • dE/dx (0.2-0.8 GeV/c)

    • TOF / RICH / TRD (1.5-5 GeV/c)

    • rdE/dx (5-20 GeV/c)

    • V0 topology (only statistics limited)


Thermally-shaped Soft Production

“Well Calibrated”

Hard

Scattering

p0 in pp: well described by NLO (& LO)

p+p->p0 + X

  • Ingredients (via KKP or Kretzer)

    • pQCD

    • Parton distribution functions

    • Fragmentation functions

  • ..or simply PYTHIA…

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


pp at RHIC:Strangeness formation in QCD

nucl-ex/0607033

Strangeness production not described by leading order calculation

(contrary to pion production).

It needs multiple parton scattering (e.g. EPOS) or NLO corrections to

describe 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 L production). s is not just another light quark


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

  • K.Eskola et al.

    (NPA 713 (2003)):

    Large NLO

    corrections not

    unreasonable at

    RHIC energies.

    Should be negligible

    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 RHIC

PYTHIA: Di-quark structures in baryon production cause mt-shift

Recombination: 2 vs 3 quark structure causes mt shift


Baryon/meson ratios – p+p collisions

Bell shape from fragmentation is visible

PLB637 (2006) 161


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 PT

Parton pt shifts to higher

hadron pt.

Fragmentation at high PT:

Parton pt shifts to lower

hadron pT

Recomb.

fragmenting parton:

ph = z p, z<1

recombining partons:

p1+p2=ph

Frag.


Baryon production mechanism through strange particle correlations …

  • Test phenomenological fragmentation models

OPAL ALEPH and DELPHI measurements:

Yields and cosQ distribution between

correlated pairs distinguishes between

isotropic cluster (HERWIG) and

non-isotropic string decay (JETSET)

for production mechanism.

Clustering favors baryon production

JETSET is clearly favored by the data.

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


Flavor dependence of yield scaling

up, down strange charm

PHENIX D-mesons

  • 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)


Charm cross-section measurements in pp collisions in STAR

  • Charmquarks are believed to be produced at early stage by initial gluon fusions

  • Charm cross-section should follow number of binary collisions (Nbin) scaling


FONLL RHIC (from hep-ph/0502203 ):

LO:

NLO:

LO / NLO / FONLL?

  • A LOcalculation gives you a rough estimate of the cross section

  • A NLOcalculation gives you a better estimate of the cross section and a rough estimate of the uncertainty

  • Fixed-Order plus Next-to-Leading-Log (FONLL)

    • Designed to cure large logs in NLO for pT >> mc where mass is not relevant

    • Calculations depend on quark mass mc, factorization scale mF (typically mF = mc or 2 mc), renormalization scale mR (typically mR = mF), parton density functions (PDF)

    • Hard to obtain large s with mR = mF (which is used in PDF fits)

CDF Run II c to D data (PRL 91,241804 (2003):

  • The non-perturbative charm fragmentation needed to be tweaked in FONLL to describe charm. FFFONLL is much harder than used before in ‘plain’ NLO  FFFONLL≠ FFNLO


hep-ex/0609010

RHIC: FONLL versus Data

  • Matteo Cacciari (FONLL):

  • factor 2 is not a problem

  • factor 5 is !!!

nucl-ex/0607012

  • Spectra in pp seem to require a bottom contribution

  • High precision heavy quark measurements are tough at RHIC energies. Need direct reconstruction instead of semi-leptonic decays. Easy at LHC.

  • Reach up to 14 GeV/c D-mesons (reconstructed) in pp in first ALICE year.


Conclusions for RHIC pp data

  • We are mapping out fragmentation and hadronization in vacuum as a function of flavor.

  • What we have learned:

    • Strong NLO contribution to fragmentation even for light quarks at RHIC energies

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

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

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

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


Thermally-shaped Soft Production

“Well Calibrated”

Hard

Scattering

p0 in pp: well described by NLO

p+p->p0 + X

  • Ingredients (via KKP or Kretzer)

    • pQCD

    • Parton distribution functions

    • Fragmentation functions

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


Hadronization in QCD (the factorization theorem)

hadrons

Parton Distribution Functions

hadrons

Hard-scattering cross-section

leading particle

Fragmentation Function

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

~

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

c

a

Parton Distribution Functions

Hard-scattering cross-section

Fragmentation Function

b

d

“Collinear factorization”


Modification of fragmentation functions(hep-ph/0005044)


RAA and high-pT suppression

STAR, nucl-ex/0305015

pQCD + Shadowing + Cronin

energy

loss

pQCD + Shadowing + Cronin + Energy Loss

Deduced initial gluon density at t0 = 0.2 fm/c dNglue/dy ≈ 800-1200

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


Induced Gluon Radiation

  • ~collinear gluons in cone

  • “Softened” fragmentation

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:

Modification according to

Gyulassy 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


Energy dependence of RAA

p 0

nucl-ex/0504001

RAA at 4 GeV: smooth evolution with √sNN

Agrees with energy loss models


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

Radiative energy loss in QCD

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

Transport coefficient:

Medium-induced gluon radiation

spectrum:

Total medium-induced energy loss:

DE independent of parton energy (finite kinematics DE~log(E))

DE  L2 due to interference effects (expanding medium DE~L)


High-energy parton loses energy by

rescattering in dense, hot medium.

q

q

“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:

Important for controlled theoretical treatment in pQCD:

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


L

q

q

g

L

q

q

Mechanisms

High 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).


Extracting qhat from hadron suppression data

RAA: qhat~5-15 GeV2/fm


~RHIC data

QGP

Hadronic

matter

R. Baier, Nucl Phys A715, 209c

What does qhat measure?

  • Equilibrated gluon gas:

    • number density ~T3

    • energy density e~T4

qhat+modelling  energy density

Model uncertainties

  • pQCD result: c~2 (aS? quark dof? …)

  • sQGP (multiplicities+hydro): c~10


RHIC data

sQGP?

?

QGP

Pion gas

Cold nuclear matter

q-hat at RHIC


Salgado and Wiedemann PRD68 (2003) 014008

Medium-induced radiation spectrum

GLV

BDMPS

Baier, Dokshitzer, Mueller, Peigne, Schiff, Armesto, Salgado, Wiedemann, Gyulassy, Levai, Vitev

BDMPS(ASW) vs. GLV

Rough correspondence:

(Wiedemann, HP2006)

 30-50 x cold matter density


What do we learn from RAA?

GLV formalism

BDMPS formalism

~15 GeV

Wicks et al, nucl-th/0512076v2

Renk, Eskola, hep-ph/0610059

DE=15 GeV

Energy loss distributions very different for BDMPS and GLV formalisms

But RAA similar!

Need more differential probes


RAA for p0: medium density I

I. Vitev

C. Loizides

hep-ph/0608133v2

W. Horowitz

Use RAA to extract medium density:

I. Vitev: 1000 < dNg/dy < 2000

W. Horowitz: 600 < dNg/dy < 1600

C. Loizides: 6 < < 24 GeV2/fm

Statistical analysis to make optimal use of data

Caveat: RAA folds geometry, energy loss and fragmentation


Yu.Dokshitzer

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.

Different partons lose different amounts of energy


…but everything looks the same at high pt….

up,down strange charm ?


Particle dependencies: RAA of strangeness

A remarkable difference

between RAA and RCP

that seems unique to

strange baryons.

Ordering with strangeness

content.

‘Canonical suppression’

is unique to strange hadrons

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


Strange enhancement vs. charm suppression ?

Do strange particles hadronize

different than charm particles ?

But is it a flavor effect ?

Kaon behaves like D-meson,

we need to measure Lc


Experiment: there are

baryon/meson differences

Theory: there are two types of e-loss:

radiative and collisional, plus

dead-cone effect for heavy quarks

Flavor dependencies map out the process of in-medium modification

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


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

Describing the suppression is difficult for models

  • radiative energy loss with typical gluon densities is not enough

    (Djordjevic et al., PLB 632(2006)81)

  • models involving a very opaque medium agree better (qhat very high !!)

    (Armesto et al., PLB 637(2006)362)

  • collisional energy loss / resonant elastic scattering

    (Wicks et al., nucl-th/0512076, van Hees & Rapp, PRC 73(2006)034913)

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

  • RAA of electrons from heavy flavor decay


Constraining medium viscosity h/s

  • Simultaneous description of

    STAR R(AA) and PHENIX v2

    for charm.

    (Rapp & Van Hees, PRC 71, 2005)

  • Ads/CFT == h/s ~ 1/4p ~ 0.08

  • Perturbative calculation of D (2pt) ~6

    (Teaney & Moore, PRC 71, 2005)

    == h/s~1

  • transport models require

    • small heavy quark

      relaxation time

    • small diffusion coefficient

      DHQ x (2pT) ~ 4-6

    • this value constrains the

      ratio viscosity/entropy

      • h/s ~ (1.3 – 2) / 4p

      • within a factor 2 of

        conjectured lower

        quantum bound

      • consistent with light hadron

        v2 analysis

      • electron RAA ~ p0 RAA at high pT - is bottom suppressed as well?


  • QGP energy density

  • > 1 GeV/fm3

    i.e. > 1030 J/cm3

Energy density of matter

high energy density:

e > 1011 J/m3

P > 1 Mbar

I > 3 X 1015W/cm2

Fields > 500 Tesla


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