Selected Topics in the Theory of Heavy Ion Collisions

Urs Achim Wiedemann, Physics Department, CERN, Theory Division Summary of Lecture 3

Identical two-particle Correlations measure the space-time extension of collision region at freeze-out

High-Q^2 processes in dense matter Parton propagation in matter results in - pt-broadening in initial and final state - energy loss of leading parent parton

Observable Consequences of “jet quenching” - suppressed leading hadron spectra - exp. test that this suppression is a final state effect - dependence on in-medium pathlength/centrality

More consequences of “jet quenching”

Lecture 4 The medium-modified Final State Parton Shower

Medium characterized by transport coefficient:

¢ 2 ¤ ¡

q £ n density

¥ How much energy is lost ? Characteristic 2 2 ¦

k § © t ¨ q L c z gluon energy ¦ ¦ Phase accumulated in medium: ¦ 2 2

t  

coh 2

Number of coherent scatterings: N coh , k t q t coh t coh 2 2k t q dI dI     Gluon energy distribution:  med 1 1 q    s d dz N coh d dz  

 c dI

      1 Average energy loss E d med q L 2 d  s c s 2 Lecture 4: Hard Processes Escaping the Bulk

a. Leading Hadroproduction - Medium-modified Fragmentation Function - Trigger Bias - “Fragility” of the probe b. Jets and Jet-like particle correlations - Jet shapes and jet multiplicites at the LHC - Jet-like particle correlations at RHIC c. Fragmentation and Hadronization at intermediate pt Hadronization versus Thermalization of Jets

in vacuum h h

h 

 const E  C 

 s R 2 L hadr E E q L Q hadr Q hadr 4 therm

Dynamics of Dynamics of Partonic equilibration processes 100 fm the bulk hadronization Jet Onset of thermalization absorption “DIS on QGP”

L medium

L therm E q ! Q hadr 1GeV 

 2 L hadr E Q hadr 2

" GeV 1 fm q 1 inter- fm soft mediate hard E 1GeV 10 GeV 100 GeV Nuclear Modification Factor % d N AA dp d # #

$ t

R AA pt , % NN # n coll d N dpt d Glauber model & T AA b NN & AA b

' Yield of leading hadrons in Au+Au ( suppressed by factor 5 PHENIX in 0-10 % most central collisions

( unsuppressed in very peripheral (80-92 %) collisions

PHENIX Particle Species Dependence of Nuclear Modification

, Determines pt-range up above which hadronization occurs outside the medium - , High p T L hadr L therm ) ) hadr + parton * * p T 6 7 GeV pT 8 10 GeV “parton thermalization” (hadronization occurs outside medium) , . . Intermediate p T L hadr L therm L med

/ hadr / 0 2 GeV pT 6 7 GeV “dynamics of hadronization” (hadronization interferes with the medium) Hard Processes Escaping the Bulk Parton Energy Loss and kt-Broadening are Connected > > energy loss of leading parton shows kt-broadening of parton shower determined A C characteristic L 2 and 1 B dependence by Brownian motion L 5 4 4 6 c 32

q L 7

c 8 10 7 3 1

2 2 q L 2 4 c c 6 3.2 4 5 4 4 6 1 2 c k 9

2 2 t q L >

integrated spectrum infrared safe > k t -

= kt-broadening determines where 3 2 @

? 3 k 2 : q : R q L 2 the energy lost by the parent parton ;

t < 1

: is distributed to in phase space : 2 : 2 < 1 c R Probability Distribution of Parton Energy Loss Baier, Dokshitzer, Mueller, Schiff, JHEP 0109:033 (2001) D Multiple independent gluon emission used to define the probability that leading parton loses fraction Z of its initial energy H n I E J

F 1 dI G P G d n 0 i 0 i J n ! d i P

Q dI Q O K K S L L L N d R M e p p i i 0

D Probability distribution of energy loss: Average: V W

T E T T T U U d P E Typical: Y X X max Nuclear Modification Factor in Au+AuWORK at RHIC IN Eskola, Honkanen, Salgado, Wiedemann, in preparation PROGRESS \ f e i Calculation of quenched i d d

AA f X g h h f high-pt hadronic spectra d vac f i A x1 f j A x 2 ij e f k ijk nuclear modified pdfs ` ` _ _ c b b ^ ^

AA h X a AA h X vac d med d vac P E , L , q D f _ h z f quenching weight fragementation

\ surface emission limits sensitivity to density ] q 2

[ GeV q 0 fm

2

[ GeV q 1 fm 2

[ GeV q 5 fm Medium-Modified Fragmentation Functions (one element of the calculation on the previous slide)

o Basic assumption: parton energy loss occurs prior to fragmentation

l 1 m m

med 2 k 1 z 2 D j z ,Q d P D j ,Q h q m h q m 0 1 n 1 n p Trigger bias: Salgado, Wiedemann Phys. Rev. Lett. 89, 092303 (2002) The fragmentation and e-loss of partons show a wide probability distributions. Hadronic pt-spectrum is dominated by the tails of the distribution for which the parton has - a very hard fragmentation (large z) - a very small energy loss

Quantitatively, this depends on steepness of partonic pt-spectrum n

q z med 2 j n D h q z ,Q hadron pT Summary Slide on Trigger Bias Triggering on a high-pt hadron, one selects: s a bias favouring hard fragmentation, determined by steepness of spectrum n

r z med 2 j n D h q z ,Q hadron pT s a bias favouring small in-medium pathlength (surface emission)

s a bias favouring small energy loss for fixed in-medium pathlength Average: Typical: v w y x x

t E t t t u u d P E max

s a bias favouring initial-state pt-broadening in the direction of the trigger Leading Hadroproduction- Centrality Dependence

suppression of leading hadrons governed by q L 2 Centrality dependence tests interplay of density and geometry suppression used to deduce X.N. Wang, nucl-th/0307036 { z z € X.N. Wang, nucl-th/0307036  GeV  ~ | } 15 0.2fm c fm 3 Bjorken 0 „

scaling ƒ ƒ  life ‚ QGP 4 2 ? fm c

Uncertainties: - modelling of dynamics and geometry - finite energy constraints Sensitivity of Leading Hadron Spectra

A. Drees, H. Feng, J. Jia, nucl-th/0310044 E-loss models:

2 L , 1-dim expansion L , 1-dim expansion

2 L , static nucl. mod. factor elliptic flow back-to-back correlation

Are there more direct tests of the energy loss mechanism ? Going beyond Leading Hadron Spectra How does the medium-induced radiation evolve towards thermal and chemical equilibrium ? Where does this associated radiation go to ?

Associated radiation:

† How to distinguish from a high-multiplicity background ? † What is the angular distribution of the radiated energy ? † What is its spectrum ? Exponential or powerlaw ? † Does it induce high-pt hadronic correlations ?

† What is its chemical composition ? Jets in Heavy Ion Collisions at the LHC

A. Accardi et al., hep-ph/0310274 CERN TH Yellow Report

E t ‡ ‰ ‡ ˆ

Š Experiments at LHC will detect jets above background

Š How can we quantify their medium modifications above background ? What do we learn from them ? Medium-modified Jet Shapes

 How much energy is radiated outside the “vacuum” jet cone due to medium effects ? ’ ’ • ” “ ‘ 2 2 Energy fraction deposited E t R in fixed jet cone R decreases

Salgado, Wiedemann, hep-ph/0310079

E R  ‹

Œ 1 R t vacuum vac jets Œ Sensitive to kt-broadening N jets E t R 1 medium use Fermilab D0 parametrization Ž Ž

E R  E ‹ ‹ ‹

Œ t  1 

med vac Œ vac E t R 1 E   Broadening of jet shape is small Jet Cross sections expected to scale difficult to measure above background with number of binary collisions Medium-modified Jet Multiplicities

Jet Heating Salgado, Wiedemann, hep-ph/0310079 † Multiplicity within small jet opening cone

. kt

† At large kt, unaffected by soft high multiplicity background

† Kt-broadening sensitive to q L Theory predicts Experimental Tests – Characteristic L- dependence leading hadron spectra — ˜ ™ ™ š as function of centrality and › 1 2 E q L s c s 2 orientation w.r.t. reaction plane jets and jet-like correlations  – Dependence on the identity charmed (beauty) hadrons ž of the parent parton  p p - ratio at high pt

– Relation between energy loss

and pt-broadening 

— hadroproduction associated to E œ q L 2 , p 2 œ q L T high-pt trigger particles  – Dependence on other properties jet shapes and jet multiplicity of the medium distributions (see seminar talk next month) Some Recent Results from RHIC on “jet-like” particle correlations Shapes of “Jet” Fragmentation: p+p and d+Au parton1 Ÿ

For jets: ¡ jet k T k T pT sin ¢

¡ hadr jT j T pT sin jet £ hadr

hadron For leading di-hadrons: Ÿ

p hadr parton2 § T ¨ 2 ¨ 2 J. Rak, M. Miller k © T z Far Near

Qualitative Expectation: ¥ ¤ ¦ ¡ hadr jt-broadening –> final state effect jT pT sin Near kt-broadening --> initial state effect no significant kt-broadening in d+Au

p+p In Au+Au, away-side “Jet” broadens « ª trig ª ª assoc ª 2.5 pT 4.0 1.0 pT 2.5

J. Rak PHENIX prelim

p+p

p+p

Significant interaction of away-side “jet” confirmed by broadening.

Away-side associated particle in general not leading particle of the away-side parent parton. pt-Distribution Associated to High-pt Particle ­

¬ trig ¬ All associated pt ­ ¬ Near: 4 pT 6 GeV c ¬ assoc ® ® ¯ ° °

± 0.15 p 4 GeV c 1.1, 1.4 T

syst. error STAR prelim ® ® ¯ ° ° ± ³ Away: ² 1.1, 1.1 Near: more multiplicity at all pt, consequence of larger initial Near Away parton energy for same trigger pt ? (implies some near-side e-loss)

Away: energy of initial parton converted to lower pt particles, (implies larger parton e-loss in medium but why does pt-shape differ Fuqiang Wang qualitatively from near-side ?) Intermediate pt

Fragmentation inside the medium: what happens now ? Breakdown of Independent (pert.) Fragmentation ¶ ´ µ µ Parton energy loss does not affect ratio D q p D q · in contrast to intermediate pt data ¹ ¸ ¸ Du p Du º

S. Bass

´ How does the bleaching of colour proceed dynamically – medium dependence tests models

dressed quark Recombination or a color string String Fragmentation or bare colored diquark 'bleached' hadron parton or Diquark Dressing ...

2 pQCD: Da » h z,Q Fragmentation versus Recombination ½

start from quark spectrum: w ¼ P z à Fragmentation: ¿

dN 1 Á

h ¾ dz  E w À P z D À z d 3 P 0 z 2 h à Recombination Model Ç

Æ 2 dN È

M Ä 2 3

E C w Å P 2 d q q d 3 P M M

dN Ë B É 3 E C B w Ê P 3 d 3 P Range of applicability: intermediate pt fragmentation

Exp. spectrum: recombination dominates Í p Ì z p , z 1 Powerlaw tail: fragmentation dominates h q upper bound on pt recombination Ï p Î p p This is one of the models discussed h 1 2 currently to account for intermediate pt Successes and Suggestive Features of Recombination Ð Ñ

h Ò 1 Ó v P nv P Elliptic Flow is significantly larger for 2 T 2 n T baryons than for mesons at intermediate pt - if rescaled by number of valence quarks, values are consistent - sign of a common underlying partonic flow Ô of size v 2 p t n ?

Ó In pt-spectra, baryon excess at intermediate Castillo(STAR)@HIC03 transverse momentum can be accounted for, assuming recombination of valence quarks.

Ó Recombination Models do not address - what happens to gluonic degrees of freedom ? - dynamics of the recombination - ... Summary of Lecture 4

Õ Leading Hadroproduction - sensitive to in-medium pathlength and density of matter - sensitivity reduced by trigger bias which prefers small pathlength, small energy loss and hard fragmentation

Õ Jet Shapes and Jet Multiplicities × × Ú Ù Ø

Ö 2 2 - no trigger bias E t R - sensitive to e-loss and pt-broadening - jet-like correlations seen at RHIC

Õ Hadroproduction at intermediate pt - neither “thermal” nor “perturbative” - medium interferes with hadronization process - characteristic changes of particle ratios This was a narrow selection of topics

which did not touch many topics of active research

- charmonium, bottonium in A+A - low-mass dileptons - photons - small-x physics in A+A and p+A - EbyE-physics, fluctuations - ...