Introduction to Heavy Ion Physics

Introduction to Heavy Ion 

Physics 

P.Hristov 

Bachinovo’12

8-th Summer School on Nuclear Physics, 3-12/07/12 2 

Outline 

• Motivation: two puzzles in 

QCD 

• Quark Gluon Plasma and Big 

Bang 

• Nucleus-Nucleus Collisions 

• Geometry of AA collision 

• Bulk observables: 

multiplicity and volume 

• Strangeness enhancement 

• Chemical equilibrium 

• Particle correlations 

• High PT suppression 

• Quark number scaling 

• Identified particles 

• Quarkonia 

• Jets 

• Heavy flavors 

Based on the lectures of 

Federico Antinori, Frascati, 

May 2012 

Peter Jacobs, Primorsko, 

June 2012 

Yves Schutz, CERN, June 2012

Two puzzles in QCD

8-th Summer School on Nuclear Physics, 3-12/07/12 

4 

The Standard Model and QCD 

• strong interaction: 

• binds quarks into hadrons 

• binds nucleons into nuclei 

beauty 

• described by QCD: 

• interaction between particles 

carrying colour charge (quarks, 

gluons) 

• mediated by strong force carriers 

(gluons) 

• very successful theory


5 

• e.g.: pQCD vs production of high energy jets


6 

The Standard Model and QCD 

• strong interaction: 

• binds quarks into hadrons 

• binds nucleons into nuclei 

beauty 

• described by QCD: 

• interaction between particles 

carrying colour charge (quarks, 

gluons) 

• mediated by strong force carriers 

(gluons) 

• very successful theory 

• jet production 

• particle production at high p T 

• heavy flavour production 

• … 

• … but with outstanding puzzles


7 

Two puzzles in QCD: i) hadron masses 

• A proton is thought to be made of 

two u and one d quarks 

• The sum of their masses is around 

12 MeV 

beauty 

• ... but the proton mass is 938 MeV! 

• how is the extra mass generated?


8 

Two puzzles in QCD: ii) confinement 

• Nobody ever succeeded in 

detecting an isolated quark 

beauty 

• Quarks seem to be permanently 

confined within protons, 

neutrons, pions and other 

hadrons. 

• It looks like one half of the 

fundamental fermions are not 

directly observable… 

why?

Lattice QCD 

• rigorous way of doing calculations in non-perturbative regime of QCD 

• discretization on a space-time lattice 

ultraviolet (large momentum scale) divergencies can be avoided 

• zero baryon density, 3 

flavours 

• e changes rapidly around T c 

• T c = 170 MeV: 

3 flavours; (q-q)=0 

e c = 0.6 GeV/fm 3 

• at T~1.2 T c e settles at about 

80% of the Stefan-Boltzmann 

value for an ideal gas of q,q g 

(e SB ) 


9

The QCD Phase diagram 

Temperature 

Early universe 

T c 

critical point ? 

Deconfinement 

Chiral symmetry restoration 

quark gluon plasma 

nucleon gas 

hadron gas 

nuclei 

colour 

superconductor 

CGC 

vacuum 

r 0 

baryon density 

Neutron stars


11 

Restoration of bare masses 

• Confined quarks acquire an additional mass (~ 350 MeV) dynamically, 

through the confining effect of strong interactions 

• M(proton) 938 MeV; m(u)+m(u)+m(d) = 1015 MeV 

• Deconfinement is expected to be accompanied by a restoration of the 

masses to the “bare” values they have in the Lagrangian 

• As quarks become deconfined, the masses go back to the bare values; 

e.g.: 

• m(u,d): ~ 350 MeV a few MeV 

• m(s): ~ 500 MeV ~ 150 MeV 

• (This effect is usually referred to as “Partial Restoration of Chiral 

Symmetry”. Chiral Symmetry: fermions and antifermions have opposite 

helicity. The symmetry is exact only for massless particles, therefore its 

restoration here is only partial)

Nucleus – Nucleus collisions

Measurements with 

telescopes 

Evolution of the 

Early Universe: Big 

Bang and 

deconfinement 

Measurements 

with colliders 

Evolution of a 

Heavy Ion 

Collision 


13


14


15 

Collisions of Heavy Nuclei at SPS and RHIC 

• Super Proton Synchrotron (SPS) at CERN (Geneva): 

• Pb-Pb fixed target, p = 158 A GeV s NN = 17.3 GeV 

• 1994 - 2003 

• 9 experiments: 

• WA97 (silicon pixel telescope spectrometer: production of strange and multiply strange particles) 

• WA98 (photon and hadron spectrometer: photon and hadronn production) 

• NA44 (single arm spectrometer: particle spectra, interferometry, particle correlations) 

• NA45 (e + e - spectrometer: low mass lepton pairs) 

• NA49 (large acceptance TPC: particle spectra, strangeness production, interferometry, event-by-event , …) 

• NA50 (dimuon spectrometer: high mass lepton pairs, J/y production) 

• NA52 (focussing spectrometer: strangelet search, particle production) 

• NA57 (silicon pixel telescope spectrometer: production of strange and multiply strange particles) 

• NA60 (dimuon spectrometer + pixels: dileptons and charm) 

• Relativistic Heavy Ion Collider (RHIC) at BNL (Long Island) 

• Au-Au collider, s NN = 200 GeV 

• 2000 - … 

• 4 experiments: 

• STAR (multi-purpose experiment: focus on hadrons) 

• PHENIX (multi-purpose experiment: focus on leptons, photons) 

• BRAHMS (two-arm spectrometer: particle spectra, forward rapidity) 

• PHOBOS (silicon array: particle spectra)

Nucleus-Nucleus collisions at the LHC! 

SPS RHIC LHC 

s NN [GeV] 17.3 200 5500 

dN ch /dy 450 800 1600 

ε [GeV/fm 3 ] 3 5.5 ~ 10 

• large ε deeper in deconfinement region 

closer to “ideal” behaviour? 

• large cross section for “hard probes” ! 

a new set of tools to probe the medium properties 

e.g.: 

Pb Pb 

b 

b 

b 


b 

16

A Pb-Pb collision at the LHC 


17

Geometry of a Pb-Pb collision 

b 

• central collisions 

• small impact parameter b 

• high number of participants high 

multiplicity 

• peripheral collisions 

• large impact parameter b 

• low number of participants low multiplicity 

for example: sum of the amplitudes 

in the ALICE V0 scintillators 

reproduced by simple model (red): 

• random relative position of nuclei in 

transverse plane 

• Woods-Saxon distribution inside 

nucleus 

• deviation at very low amplitude 

expected due to non-nuclear 

(electromagnetic) processes 

peripheral 

central 


18

Nuclear geometry and hard processes: 

Glauber theory 

Glauber scaling for hard processes with large momentum transfer 

• short coherence length successive NN collisions independent 

• p+A is incoherent superposition of N+N collisions 

Normalized nuclear density r(b,z): 

dzdbr(b,z) 1 

Nuclear thickness function 

T A 

(b) dzr(b,z) 

Inelastic cross section 

for 

p+A collisions: 

 

 

inel 

pA db(1[1T A 

(b) inel NN 

] A ) 


19

Glauber Theory for A+B Collisions 

Nuclear overlap function: 

Average number of binary NN collisions 

for B nucleon at coordinate s B : 

Average number of binary NN collisions for A+B 

collision with impact parameter b: 


20

Glauber test at LHC: 

Scaling of direct photon, Z, W yields in Pb+Pb vs p+p 

R AA 

 

d hard AA 

/dp T 

T AA 

d hard pp 

/dp T 

 

EW boson yields all scale with N bin : Glauber OK for hard processes 


21

Bulk observables: 

multiplicity and volume

Particle multiplicity 

most central collisions at LHC: ~ 1600 charged particles per unit of η 

ALICE: PRL105 (2010) 252301 

• log extrapolation: 

• OK at lower energies 

• finally fails at the LHC 

√s NN =2.76 TeV Pb+Pb, 0-5% central, |η|

Initial Energy Density 

– Bjorken’s estimation 

Bjorken 1983 

Boost invariant hydrodynamics: 

pR 2 

t : proper time 

y : rapidity 

h : pseudo-rapidity 

E T : transverse energy 

N ch : Number of charged particles 

m T : transverse mass 

R: effective transverse radius 


24

Bjorken’s formula 

• To evaluate the energy density reached in the collision: 

e 

1 

Sct 

0 

dET 

dy 

y0 

S transverse dimension of nucleus 

t 

0 

"formation time"~ 1fm/ c 

dET 

• for central collisions at LHC: 1800 GeV 

dy 

• Initial time t 0 normally taken to be ~ 1 fm/c 

• i.e. equal to the “formation time”: the time it takes for the energy initially 

stored in the field to materialize into particles 

2 

1/3 

• Transverse dimension: S 160 fm ( R 1.2A 

fm) 

yo 

A 

 

e ~ (1800/160) GeV/fm 

3 

~10 GeV/fm 

3 

More than enough 

for deconfinement! 


25

Hanbury Brown - Twiss interferometry 

• quantum phenomenon: enhancement 

of correlation function for identical 

bosons 

• from Heisenberg’s uncertainty 

principle: 

• Δp · Δx ~ ħ (Planck’s constant) 

 

 

(width of enhancement) · (source size) ~ ħ 

extract source size from correlation 

function 

• first used with photons in the 1950s by 

astronomers Hanbury Brown and Twiss 

• measured size of star Sirius by aiming at it two 

photomultipliers separated by a few metres 

• e.g.: three components of correlation 

function C(q = momentum difference) 

for pairs of pions for eight intervals 

of pair transverse momentum (k T ) 

C(p 

P(p 

,p 

~ (q 

1 2 

2 

1 ,p2) 

1 

r ) 

P(p1)P(p2 

) 


) 

F.T. of pion source 

26

HBT interferometry 

R out 

from RHIC to LHC: 

• increase of size in the 3 dimensions 

• out, long, and (finally!) side 

• “homogeneity” volume ~ x 2 

R side 

R long 

ALICE: Phys Lett B 696 (2011) 328 


27

Strangeness enhancement

Historic QGP predictions 

• restoration of c symmetry + Pauli principle -> increased 

production of s 

• mass of strange quark in QGP expected to go back to current value 

• m S ~ 150 MeV ~ Tc 

copious production of ss pairs, mostly by gg fusion 

[Rafelski: Phys. Rep. 88 (1982) 331] 

d s 

d 

[Rafelski-Müller: P. R. Lett. 48 (1982) 1066] 

u 

u 

u u d d u 

d u d 

p 

s d d u 

- 

s s d u d d 

u d 

u d d d 

p u 

for multi-strange 

+ s 

d u u u u d 

s 

u s u u 

• can be built recombining s quarks 

s d 

p 

d s d 

W u 

strangeness enhancement increasing 

+ s s u d 

u 

u s s s 

with strangeness content 

u d u 

u 

d 

s d s 

[Koch, Müller & Rafelski: Phys. Rep. 142 (1986) 167] 

L 

• deconfinement stronger effect 


K + 

X - 29

• The QGP strangeness abundance is enhanced 

• As the QGP cools down, eventually the quarks recombine into hadrons 

(“hadronization”) 

• The abundance of strange hadrons should also be enhanced 

• The enhancement should be larger for particles of higher strangeness 

content, e.g.: 

E(W ) > E(X ) > E(L) 

(sss) (ssd) (sud) 

|s| = 3 |s| = 2 |s| = 1 


30

Strangeness enhancement at the SPS 

• Enhancement in Pb-Pb relative to p-Be (WA97/NA57) 

Enhancement is larger for 

particles of higher 

strangeness content 

(QGP prediction!) 

up to a factor ~ 20 for W 

So far, no hadronic model 

has reproduced these 

observations (try harder!) 

Actually, the most reliable 

hadronic models predicted 

an opposite behaviour of 

enhancement vs 

strangeness 


31

Strangeness enhancement: SPS. RHIC. LHC 

• enhancement decreases with increasing √s 

strange/non-strange increases with √s in pp 


32

Chemical Equilibrium 

Thermal Fits 

Chemical Freeze-out

Chemical equilibrium 

• The relative particle abundances measured in Pb-Pb collisions are close to the 

thermodynamical (chemical) equilibrium values (maximum entropy) 

corresponding to a temperature of ~ 170 MeV (“chemical freeze-out 

temperature”). Two parameters: T and μ in the fit. 

this would be a natural 

outcome of statistical 

hadronization of 

uncorrelated quarks 

[P.Braun-Munzinger, I.Heppe, J.Stachel, Phys. Lett. B465 (1999), 15] 

“chemical freeze out”: 

the moment when 

inelastic interactions 

cease 


34

Chemical equilibrium @ RHIC 

• Thermal fits again doing well 

200 GeV 

62.4 GeV 

Jun Takahashi (STAR), SQM`07 


35

• remarkable regularity in freeze-out systematics 

Jean Cleymans, SQM`07 


36

Particle correlations

Flow 

Out-of-plane 

Elliptic Flow 

• Non-central collisions are azimuthally asymmetric 

Y 

Reaction 

plane 

Flow 

In-plane 

X 

 

The transfer of this asymmetry to momentum space provides a 

measure of the strength of collective phenomena 

• Large mean free path 

• particles stream out isotropically, no memory of the asymmetry 

• extreme: ideal gas (infinite mean free path) 

• Small mean free path 

• larger density gradient -> larger pressure gradient -> larger momentum 

• extreme: ideal liquid (zero mean free path, hydrodynamic limit) 


38


39 

dN 

 

dp dyd 

Azimuthal Asymmetry 

• Fourier expansion of azimuthal distribution: 

p 

T 

T 

1 

2p 

p 

T 

dN 

dp 

T 

dy 

 

1 

2v1 cos( ) 

2v2 

cos(2 

) 

... 

v1 cos 

"directed 

flow" 

v2 cos 2 

"elliptic flow" 

@RHIC: 

• at low p T : azimuthal asymmetry 

almost as large as expected at 

hydro limit! 

• “perfect liquid”? 

• very far from “ideal gas” 

picture of plasma

v 2 at the LHC 

• v 2 still large at the LHC 

• v 2 (p T ) very similar at LHC and RHIC 

 

system still behaves very 

close to ideal liquid (low 

viscosity) 

similar hydrodynamical behaviour? 

ALICE: PRL 105 (2010) 252302 


40


41 

Structures in (Δη,Δφ) 

long range structure 

in η on near side 

aka “the ridge” 

near side jet peak 

two shoulders 

on away side 

(at 120 and 240 ) 

aka “the Mach cone”


42 

Mach cone? 

• double-hump structure on awayside, 

at 120 and 240 

• a proposed explanation: 

• shock wave (sonic boom) : 

propagation through medium 

of recoiling parton 

[Casalderrey-Solana, et al.: hep-ph/0411315]

Fluctuations v 3 

Matt Luzum (QM 2011) 

• “ideal” shape of participants’ overlap 

is ~ elliptic 

• in particular: no odd harmonics expected 

• participants’ plane coincides with event 

plane 

• but fluctuations in initial conditions: 

• participants plane event plane 

v 3 (“triangular”) harmonic appears 

[B Alver & G Roland, PRC81 (2010) 

054905] 

• and indeed, v3 0 ! 

• v 3 has weaker centrality dependence 

than v 2 

• when calculated wrt participants 

plane, v 3 vanishes 

• as expected, if due to fluctuations… 

ALICE: PRL 107 (2011) 032301 

v 2 

v 3 

43 

8-th Summer School on Nuclear Physics, 3-12/07/12

Long-η-range correlations 

• “ultra-central” events: dramatic 

shape evolution in a very narrow 

centrality range 

• double hump structure on awayside 

appears on 1% most central 

• visible without any need for v 2 

subtraction! 

• first five harmonics describe 

shape at 10 -3 level 

“ridge” and “Mach cone” 

• explanations based on medium 

response to propagating partons were 

proposed at RHIC 

• Fourier analysis of new data suggests 

very natural alternative explanation in 

terms of hydrodynamic response to 

initial state fluctuations 

ALICE: Andrew Phys. Adare Lett. – B ALICE 708 (2012) (QM2011) 249 


44


45 

Correlations: outlook 

• is there any residual room for medium response 

effects? 

look at the “small print” on the away side 

• quantitative comparisons with full hydrodynamic 

calculations

High-p T suppression

Participants Scaling vs Binary Scaling 

e.g.: 

N part (or N wound ) = 7 “participants” 

N bin (or N coll ) = 12 “binary collisions” 

• “Soft”, large cross-section processes expected to scale like N part 

• “Hard”, low cross-section processes expected to scale like N bin 


47

The nuclear modification factor 

• quantify departure from binary scaling in AA 

ratio of yield in AA versus reference collisions 

• e.g.: reference is pp R AA 

R 

AA 

 

Yield 

Yield 

AA 

pp 

 

1 

Nbin 

AA 

• …or peripheral AA Rcp (“central to peripheral”) 

R 

cp 

 

Yield 

Yield 

AA, central 

AA, periph 

 

Nbin 

Nbin 

AA,periph 

AA, central 


48

High p T suppression: R AA at RHIC 

• High p T particle production 

expected to scale with 

number of binary NN 

collisions if no medium 

effects 

• Clearly does not work for 

more central collisions 

• Interpreted as due to loss 

of energy of partons 

propagating through medium 


49

R AA at the LHC 

• Suppression even larger than 

@ RHIC 

R 

AA 

( p 

T 

) 

 

Yield 

AA( 

p 

Nbin Yield 

AA 

T 

pp 

) 

( p 

T 

) 

• R AA (p T ) for charged particles 

produced in 0-5% centrality 

range 

• minimum (~ 0.14) for p T ~ 6-7 

GeV/c 

• then slow increase at high p T 

• still significant suppression 

at p T ~ 100 GeV/c ! 

• essential quantitative 

constraint for parton energy 

loss models! 


compiled in: CMS: EPJC 72 (2012) 1945 

50

Suppression vs event plane 

• significant effect, even at 20 GeV! 

• further constraints to energy loss models 

Alexandru Dobrin – ALICE (QM2011) 

path-length dependence of energy loss (L 2 , L 3 , …) 


51

Quark number scaling

Baryon puzzle @ RHIC 

• Central Au-Au: as many p - (K - ) 

as p (L) at p T ~ 1.5 2.5 GeV 

• e + e - jet (SLD) 

• very few baryons 

from fragmentation! 

p 

K 

p 


H.Huang @ SQM 2004 53


54 

Rcp 

R 

cp 

 

Yield 

Yield 

AA, central 

AA, periph 

 

Ncoll 

Ncoll 

AA,periph 

AA, central 

• at higher p T, Rcp of baryons 

also comes down! 

• if loss is partonic, shouldn’t it 

affect p and p in the same way?


55 

Quark Recombination(Coalescence)? 

• if hadrons are formed by recombination, features of the parton 

spectrum are shifted to higher p T in the hadron spectrum, 

in a different way for mesons and baryons 

quark number scaling 

K + 

d s 

d 

u 

u 

u u d 

X - 

d u 

d u d 

p 

u s d d u 

- 

s s d d d 

u d d d 

u d 

p + u s 

d u u u u d 

s 

u s u u 

s d 

p 

d s d 

W + s s u u d 

u 

u s s s 

u d u 

u 

d 

s d s 

L 

S.Bass @ SQM`04


Hadronization 

baryon/meson 

anomaly 

• Radial flow 

• Parton fragmentation 

• Coalescence (?) 

56


57 

Quark number scaling and v 2 

• Recombination also offers an explanation for v 2 baryon puzzle... 

dN 

 

p dp dyd 

T 

T 

1 

2p 

dN 

1 

2v1 cos( ) 

2v2 

cos(2 

) ... 

 

p dp dy 

T 

T 

v1 cos 

"direct flow" 

v2 cos 2 

"elliptic flow" 

scaled with n(quarks) 

STAR Preliminary

Identified particles


59 

p T spectra vs hydrodynamics 

• comparison of identified particle spectra with hydro predictions 

• (calculations by C Shen et al.: arXiv:1105.3226 [nucl-th]) 

Michele Floris – ALICE (QM2011) 

 

OK for π and K, but p seem to “misbehave” (less yield, flatter spectrum)


60 

v 2 vs hydrodynamics 

• comparison of identified particles v 2 (p T ) with hydro prediction 

Raimond Snellings 

ALICE (QM2011) 

• (calculation by C Shen et al.: arXiv:1105.3226 [nucl-th]) 

 

again, protons are off… what’s going on with protons? 

to be continued…

Quarkonia


62 

Charmonium suppression 

• QGP signature proposed by Matsui and Satz, 1986 

• In the plasma phase the interaction potential is expected to be 

screened beyond the Debye length l D (analogous to e.m. Debye 

screening): 

• Charmonium (cc) and bottonium (bb) states with r > l D will not bind; 

their production will be suppressed

dN/dp 


1. Ordinary matter 

B 

J/ cc 

Mass 


63

dN/dp 


2. Quark matter 

B 

J/ cc 

Mass 


64


65 

J/y suppression pattern at the SPS 

NA50 

• measured/expected J/y 

suppression vs estimated energy 

density 

• anomalous suppression sets in at 

e ~ 2.3 GeV/fm 3 (b ~ 8 fm) 

• effect seems to accelerate at 

e ~ 3 GeV/fm 3 (b ~ 3.6 fm) 

• this pattern has been 

interpreted as successive 

melting of the c c and of the J/y

J/ψ suppression at RHIC 

• J/ψ ~ as suppressed as 

at SPS (NA50) 

[Hugo Pereira (PHENIX), QM05] 


66

J/ψ @ LHC: high p T 

• LHC: |y| < 2.4, p T > 6.5 GeV/c (CMS) 

prompt J/ψ 

• LHC |y| < 2.5, pT > 3 GeV/c (ATLAS) 

 

more suppressed than 

RHIC: |y| < 1. pT > 5 GeV/c (STAR) 

inclusive J/ ψ 

CMS: arXiv:1201.5069 

ATLAS: PLB 697 (2011) 294 


67


68 

J/ψ @ LHC: low p T 

• LHC: 2.5 < y < 4, p T > 0 (ALICE) 

 

less suppression than 

RHIC: 1.2 < y < 2.2, p T > 0 (PHENIX) 

 

~ as suppressed as 

RHIC: |y| < 0.35. pT > 0 (PHENIX) 

• very flat as a function of N part 

recombination at low p T ?


69 

Υ(1S) suppression 

CMS: arXiv:1201.5069


70 

Υ(2S+3S) suppression! 

CMS: arXiv: 1105.4894 

• additional suppression for Υ(2S+3S) w.r.t. Υ(1S) ?


71 

Quarkonia: outlook 

• the future runs should allow us to establish 

quantitatively the complete quarkonium 

suppression(/recombination?) pattern 

• high statistic measurements 

• open flavour baseline / contamination 

• pA baseline

Jets

High p T Probes of the Matter: Jet Study 

How Jets are produced? 

Event Topology 

p 

isotropic emission 

Hadron Jet 

N 

q 

Fragmentation 

Function 

q 

N 

Jet: A localized collection 

of hadrons which come 

from a fragmenting parton 

N 

K 

p 

r 

N 

Jet event 

Hadron Jet 

N 

K 

r 

N 


73

dN/d 

dN/dp 

Jets 

1. Ordinary matter 

Fragmentation 

function 

-180 O 18O 

Relative angle 


Transverse momentum 

74

dN/d 

dN/dp 

Jets 

2. Quark matter 

Fragmentation 

function 

-18O O 18O 

Relative angle 


Transverse momentum 

75

Jets: Azimuthal Correlation 

• Identify jets on a statistical basis 

• Given a trigger particle with p T > p T 

(trigger), associate particles with p T 

> p T (associated) 

1 1 

C2( 

, 

h) 

 

N( 

, 

h) 

N Efficiency 

TRIGGER 

4 

2 

• Away-side correlation suppression in 

central Au+Au, but not in d+Au. 

• d+Au looks like p+p 

• Medium density up to 100 times normal 

nuclear matter ! 

“Classical” RHIC result 


76


77 

Di-jet imbalance 

• Pb-Pb events with large di-jet imbalance observed at the LHC 

recoiling jet strongly quenched! CMS: arXiv:1102.1957

A J 

• with increasing centrality: 

• imbalance quantified by the di-jet asymmetry variable A J : 

R 0.4 

h 

2.8 

 

enhancement of asymmetric di-jets 

with respect to pp 

• & HIJING + PYTHIA simulation 

ATLAS: PRL105 (2010) 252303 


78


79 

Di-jet Δφ 

• no visible angular decorrelation in Δφ wrt pp collisions! 

CMS: arXiv:1102.1957 

large imbalance effect on jet energy, but very little effect on jet 

direction!

Jet nuclear modification factor 

R 

CP 

 

 

Nbin 

Nbin 

Central 

Peripheral 

Yield 

Yield 

Central 

Peripheral 

 

substantial suppression of jet 

production 

• in central Pb-Pb wrt binary-scaled 

peripheral 

 

out to very large jet energies! 

Brian Cole – ATLAS (QM2011) 


80

Jet fragmentation function 

• distribution of the momenta of the fragments along the jet axis 

z 

 

p 

hadron 

T 

cos(R) 

E 

jet 

T 

central 

peripheral 

Brian Cole – ATLAS (QM2011) 


• distribution is very 

similar in central and 

peripheral events 

• although quenching is 

very different… 

apparently no effect 

from quenching inside 

the jet cone… 

another puzzle ? 

81

What next? 

• understand theoretically what is going on 

• strong di-jet asymmetry 

• no visible effects in fragmentation function, dijet angular 

correlations… 

• g/Z-jet fragmentation functions 

• measure fragmentation function of jets recoiling against 

vector bosons low-bias estimate of jet energy before 

quenching 

• explore the surroundings of away-side jets 

• broadening? softening? re-heating? 

• in-medium fragmentation vs reaction plane 

• path length dependence! 

• b-tagged jets (quark vs gluon jets) 

• extreme suppression? 

• “mono-jet” events? what do they look like? 


82

Heavy flavors


84 

Charm and beauty: ideal probes 

• study medium with probes of known colour charge 

and mass 

e.g.: energy loss by gluon radiation expected to be: 

• parton-specific: stronger for gluons than quarks (colour charge) 

• flavour-specific: stronger for lighter than for heavier quarks 

(dead-cone effect) 

• study effect of medium on fragmentation (no extra 

production of c, b at hadronization) 

independent string fragmentation vs recombination 

• e.g.: D + s/D + 

• + measurement important for quarkonium physics 

• open QQ production natural normalization for quarkonium studies 

• B meson decays non negligible source of non-prompt J/y


85 

Theoretically... 

E 

s 

C 

R 

2 

qˆ L 

average energy loss 

Casimir coupling factor 

R.Baier et al., Nucl. Phys. B483 (1997) 291 (“BDMPS”) 

transport coefficient of the medium 

distance travelled in the medium 

Energy loss for heavy flavours is expected to be reduced: 

i) Casimir factor 

• light hadrons originate from a mixture of gluon and quark jets, 

heavy flavoured hadrons originate from quark jets 

• C R is 4/3 for quarks, 3 for gluons 

ii) dead-cone effect 

• gluon radiation expected to be suppressed for q < M Q /E Q 

[Dokshitzer & Karzeev, Phys. Lett. B519 (2001) 199] 

[Armesto et al., Phys. Rev. D69 (2004) 114003]


86 

Experimentally: at RHIC 

• HF electrons ~ as 

suppressed as light 

hadrons 

• use of high density (qhat), 

introduction of elastic (in 

addition to radiative) 

energy loss... not enough 

• high qhat and no beauty 

electrons does better 

[B.I. Abelev et al (STAR): nucl-ex/0607012]

How much beauty? 

[M. Cacciari et al.: PRL 95 (2005) 122001] 

• high p T region expected 

to be beauty-dominated 

• but how “high”? 

[A. Suaide QM06] 


• not easy to disentangle c/b 

contributions to RHIC HF e 

samples (no heavy flavour vertex 

detectors in RHIC experiments) 

87


88 

Vertex Detectors! 

• need less indirect measurement 

full reconstruction of charm decays! 

• get rid of b/c ambiguities 

• study relative abundances in charm sector 

• Silicon Pixels in ALICE, ATLAS, CMS 

• + Silicon Vertex upgrades in STAR, PHENIX


89 

Track Impact Parameter 

• track impact parameter (d 0 ): separation of secondary tracks from HF 

decays from primary vertex 

• e.g.: d 0 resolution in ALICE

Reconstructed D decays 

strong suppression observed in central 

Pb-Pb (0-20%) with respect to scaled pp 

reference 


90


91 

Comparison: D and π suppression 

0-20% 40-80% 

• charm is substantially suppressed: 

• in central collisions: ~ a factor 4-5 for p T > 5 GeV/c 

• D meson R AA ~ compatible with π R AA


92 

How about the colour factor? 

• quarks (C R = 4/3) expected to 

couple weaker than gluons (C R = 3) 

at p T ~ 8 GeV, factor ~ 2 less 

suppression expected for D than 

for light hadrons in gluon radiation 

energy loss prediction 

… to be continued with higher 

statistics… 

N Armesto et al., Phys. Rev. D71 (2005) 054027


93 

c and b quenching @ LHC 

substantial suppression of 

heavy flavour production 

– beauty, too! 

with larger statistics: study parton mass and colour charge 

dependence of interaction with medium!


94 

Heavy Flavour: outlook 

• high statistics D measurements 

are D really as suppressed as light hadrons? 

• charm thermalisation? 

measure D mesons v2 

• subtract D background pure B electron spectrum 

• beauty energy loss in wide p T range 

• in-medium fragmentation of b-tagged jets !

Conclusions 

• Pre-SPS and SPS studies: strangeness enhancement, charmonium 

suppression => indications of QGP 

• RHIC studies: jet quenching, flow => QGP becomes hot dense matter 

(ideal liquid) 

• in November 2010, the field of ultrarelativistic nuclear collisions has 

entered a new era with the start of heavy ion collisions at the LHC 

• abundance of hard probes 

• exciting results already from 2010 data sample 

• flow + fluctuations => death of ridge and Mach cone? 

• anomalies in proton yields & momentum distributions 

• pattern of jet and heavy flavour suppression => challenge to Eloss models 

• and the future looks bright! 

• ~ 150/µb delivered by LHC in 2011 

• p-Pb run scheduled for 2012 

 

 

precision measurements + handle on cold nuclear matter effects 

close in on dynamic and coupling properties of medium 

and … look out for surprises!!! 

8-th Summer School on Nuclear Physics, 3-12/07/12 95

Thank you!

Backup slides 


97

Rapidity and Pseudorapidity 

rapidity 

pseudorapidity 

y 

 

1 

2 

 

log 

 

 

E 

E 

 

 

p 

p 

z 

z 

 

 

 

h 1 2 log p p z 

 

p p z 

 

1 

2 log(tan(q 2 )) 

• in the ultrarelativistic limit: p ~ E h ~ y 

• for the transverse variables: 

 

rapidity 

pseudorapidity 

p 

E 

z 

m 

m 

T 

T 

sinh( y) 

cosh( y) 

p 

p 

z 

 

 

p 

p 

T 

T 

sinh( h) 

cosh( h) 


98

Transverse variables 

• Transverse momentum: 

2 2 

pT 

px 

py 

pT 

( px, 

py 

) 

• Transverse mass: 

m 

 

m 

 

2 2 

T 

p T 

E 

 

m 

2 

 

p 

2 

 

2 2 

m T 

p z 

p z 

mT 

sinh(y) E m cosh(y) 

T 

• Transverse energy: 

E 

 

T 

E i 

i 

sinq 

i 

q i = angle w.r.t. beam direction 


99

Invariant cross-section 

• A + B a 1 + a 2 + … + a n 

• we may be interested only in the production of a specific type of 

particle e.g.: 

Pb + Pb W + X 

• Differential cross section: 

• but d 3 p is not Lorentz invariant; is used instead: 

3 

d p 

E 

dp 

x 

dp 

y 

dy 

 

d 

d 

3 

 

3 

p W 

d 3 

p 

E 

Lorentz-invariant for a boost along z 


100

• Invariant cross-section: 

E 

3 

d 

 

3 

dp 

3 

d 

dp dp dy 

x 

y 

• in terms of p T : 

E 

3 

d 

 

3 

dp 

p 

T 

3 

d 

dp ddy 

T 

• integrating over : 

1 

2pp 

T 

2 

d 

dp dy 

T 

2 

1 d 

 

2 

p d( 

p ) dy 

T 

2 

1 d 

 

2 

p d( 

m ) dy 

T 

 

1 

2pm 

T 

2 

d 

dm dy 

T 


101

Introduction to Heavy Ion Physics

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