Heavy Ion Physics at the LHC
Scottish Universities' Summer
School 57
St. Andrews
•
•
•
•
•
•
August 18 – 29, 2003
QCD at high temperature: the quark-gluon plasma
Probes of ultradense matter
Structure of nuclei at small x
Matter formation and breakup
Insights from the first 3 years of RHIC
The LHC heavy ion programme
Part I
QCD at high temperature:
The quark-gluon plasma (QGP)
Matter under extreme conditions
1.
2.
Squeeze slowly Cold, dense matter
Squeeze fast Hot, “dense” matter
(1) is much more difficult to do than (2): Beyond nuclear
matter density (? B > ? 0 = 0.15 fm-3) only in the core of
collapsed (neutron) stars.
(2) Happened once: t < 20 s after it all began.
Can also be achieved by colliding nuclei at high energy.
20 years of history: Bevalac, AGS, SPS, RHIC LHC.
Goal: energy density e » MN ? 0 = 0.14 GeV/fm3.
The Big Bang “experiment”
Thermal history of the universe
The “Little Bang” experiment
Au+Au Collision at RHIC
The “Little Bang”
Quantum chromodynamics
Ga Ga
1
4
LQCD
a
Aa t a
g
f
a
mf
f
Degrees of freedom
• At extreme (energy) density, particle masses can
be neglected relative to the kinetic energy:
d3 p
E
( 2 )3 e E / T 1
2
30
aT
4
with a
with
E
p2
m2
7 / 8(fermions)
1 (bosons)
Quarks:
2 2 NC N F
Gluons:
2 ( N C2 1) 16
12 N F
Hadrons or quarks & gluons?
If QCD had NF light quark flavors, there would be
(NF2-1) nearly massless Goldstone bosons (“pions”):
N
2
F
1
For large NF the pions win out over quarks, but for
NF=2-3 the quarks and gluons win out:
at high T matter is composed of a colored
plasma of quarks and gluons, not of hadrons!
From hadrons to QGP
2
30
T
4
QGP = quark-gluon plasma
0
QCD equation
of state from
lattice QCD
Hadron gas
0
Is there a phase transition?
Most likely:
NOT
Crossover of phases
Susceptibilities peak at Tc, but do not diverge. Vacuum
properties change smoothly, but rapidly “crossover”
A phase transition at high baryon density
Tc (
B
)
First order phase
transition line
Controls baryon density
Color screening
2
a
g
a
G
( b) g
a
Q
( b)
Induced color density
a
with
Tr t
2
G
a
d3 p
e
3
(2 )
2
( gT ) ,
2
Q
Static color charge (heavy quark) generates potential
( E g bt b ) / T
1
2
1
NF
( gT ) 2
6
a
ta
s
r
e
r
a
Color screening (lattice)
Screened potential
Perturbative screening
r in units of 0.45 fm
Linear confining potential disappears above Tc
160 MeV
The perturbative QGP
At T > 2Tc the QGP looks perturbative (neglect mq):
15
1
4
s
16 2 4
T
30
1
2
s
50
1
21
3
2
2
q
q
Expansion in s does not
converge, rather one must
include interactions into the
particle modes (“quasiparticles”)
as basis for the expansion.
(
2
s
T2
21 2
N FT 4
30
1
2
2
q
)
Quasiparticles in the QGP
Physical excitation modes at high T are not elementary
quarks and gluons, but “dressed” quarks and gluons:
T
Compton scattering
on a thermal gluon!
(k , )
Propagator of transversely polarized gluons
D(k , )
1
2
k2
1
1
( gT ) 2 1
2
2 k
mG*
k
0
mG*
k
0
Effective mass of gluon:
k
ln
1
gT
3
1
gT
2
k
k
QCD phase diagram
initial
LHC
state
RHIC
LHC
Color superconducting
quark matter
Part II
Probes of ultra-dense matter
Signatures of a QCD phase change
•
•
•
•
•
•
•
•
•
•
Effects of “latent heat” in (E,T) relation
Effects of large CV on thermal fluctuations
Net charge and baryon number fluctuations
Enhancement of s-quark production
Thermal l+l- and radiation
Disappearance of light hadrons (?0)
Dissolution of ? , Y bound states
Large energy loss of fast partons (jet quenching)
Bulk hadronization
Collective vacuum excitations (DCC)
Thermodynamics near Tc
2
30
g DOFT
4
T
E
Additional energy is
used up to liberate
new degrees of
freedom (color!) in
transition region
Hadrons at the boiling point ?
RHIC
SPS
AGS
Plateau is an indicator of latent heat of phase transformation.
Elliptic Flow
Anisotropic or “elliptic” flow is defined for b > 0 collisions.
•
Reaction plane analysis
dN/d
Force
P
•
Elliptic flow “measures” the
transverse pressure at very
early times ( < 3 fm/ c).
•
lab-
plane)
Two-particle correlations
dN/d( 1-
More flow in collision plane
than perpendicular to it.
1 + 2v2cos2(
2)
1 + 2v22cos(2[ 1-
2])
Four-particle correlations
exp[i2( 1+
2-
3-
4
)]
=
-v
4
2
Strangeness enhancement…
…probes chiral symmetry restoration and deconfinement
Mass (MeV)
NA57 data
1000000
Q CD mass
100000
Higgs mass
(sss)
10000
(qss)
1000
100
(qqs)
10
1
u
d
s
Flavor
c
b
t
Charmonium suppression…
VQQ(r) is screened at distance scales r > (gT)-1
heavy quark bound states dissolve above some Td:
J/ suppression.
Karsch et al.
But: J/ may survive
above Td as a narrow
resonance, as recent
lattice calculations of
the spectral function
suggest.
Or charmonium enhancement?
If more than one c-quark pair is formed within y 1,
and if the c-quarks are thermalized, J/ may be formed
by recombination:
This could easily result in a large
enhancement of J/ production
under LHC conditions. Depends
critically on the stopping power for
c-quarks (less than for light quarks)
J/
J/
suppression
Energy/Momentum
Data are consistent with:
Hadronic comover breakup w/o QGP
Limiting suppression via surface emission
Dissociation + thermal regeneration
Jet Quenching
High-energy parton loses energy by
rescattering in dense, hot medium.
q
q
Radiative energy loss:
L kT 2
dE / dx
L
Scattering centers = color charges
q
q
g
Can be described as medium effect on
parton fragmentation:
Dp
2
(
z
,
Q
)
h
Dp
2
(
z
,
Q
)
h
Dp
z
h
1
E/E
, Q2
Energy loss in QCD
Gluon radiation is suppressed due to multiple scattering by LPM
effect. LPM suppression differs from QED due to rescattering of
the radiated gluon. Critical frequency:
c
1
2
2
ˆ
qL
d
q dq
dq 2
2
qˆ
with
Energy loss spectrum for a fast parton is (
2
D( )
s
C2 / ) :
2
c
2
2
2
exp
c
2
Radiative energy loss is suppressed like ( c/E)1/2 overall, and
more strongly at small (Landau-Pomeranchuk-Migdal effect).
Energy loss in QCD - II
Density of scattering centers
Scattering “power”
of QCD medium:
d
q dq
dq 2
2
qˆ
2
Property of medium
(range of color force)
For power law parton spectrum ( pT-v)
energy loss leads to an effective momentum
shift for fast partons (BDMS):
pT
Including expansion:
2
ˆ
qL
2
0 eff
qˆ L
k T2
s
2qˆ0
(r )
ˆ 2 pT /
qL
d
(r , )
Analytical model: Surface emission
dN
Quenching factor:
d 2 pT
(Q
dN
Q ( pT ) 2
d pT
partons
Q ( pT )
2( p0
R (
pT )
1) pT
RAA )
hadrons
= final dN/dy / volume
Volume / R = surface
= QCD energy loss parameter:
2
s
q 2 dq 2 (d / dq 2 )
3
2
0.5 ln(…) for gluons;
C2 (
2 2
s
2
) ln qmax
/
2
D
0.25 ln(…) for quarks
Jet correlations
E L
Q
R/R
Away-side jet
Q ' ( R / R) 2
Q Qasj
Back-to-back jets (leading hadrons)
are quadratically suppressed!
Quenching provides a
mechanism for generating
an anisotropy with respect
to the collision plane for
hadron production in noncentral collisions. The
predicted anisotropy is
less than 10%.
Part III
The initial state:
Structure of nuclei at small x
Au+Au Collision at RHIC
Space-time picture of a HI collision
Hadronization
Expansion
Equilibration
Hard scattering
Initial state: The naïve picture
For partons of flavour a in a nucleus the distribution is given by:
Nh
Fa (r , k )
PaNi (k , P, Q02 ) RaNi (r , R)
i 1
with the initial momentum distribution:
PaNi (k , P, Q02 )
FaNi ( x, Q02 ) ? aA g (k ) d( Pz
P ) d2 ( P )
(Q0: initial resolution scale, ?A optional shadowing, g: opt. primordial kT)
and the initial spatial distribution:
RaNi (r , R) d( RAB b )
haNi (r ) H Ni ( R)
boosted
• HN: distribution of nucleons in nucleus (e.g. Fermi-Distribution)
• ha: distribution of partons in hadron (based on elastic form factor)
Initial state II: Parton momenta
• flavour and x are sampled from
PDFs at an initial scale Q0 and low
x cut-off xmin
• initial kt is sampled from a
Gaussian of width Q0 (case of no
initial state radiation)
Initial State III: Spatial Distribution
rest frame
• partons are spatially distributed according to elastic form factor of nucleon:
N
a
h (r )
1
8
e
3
r/
with
0.24 fm
• Lorentz contraction utilizing y*; on-shell rapidity of partons, or rz~1/pz
Parton saturation at small x
DGLAP splitting:
~ 1/Q2
GLRMQ parton fusion:
parton density
2
sat
Q
xGA ( x, Q 2 )
s
area =
RA2
Q2
1/ 3
A x
A1/ 3 x
Q2
1
from HERA data
Parton saturation II
Saturation suggests a picture of quasiclassical glue fields at
small x, where gA k, and the perturbation expansion is in
powers of s, but not in powers of gA. In the extreme limit
(x 0) the probability distribution of classical color fields is
random and completely determined by the saturation scale:
P A
exp
d 2 x g 2 A2 ( x ) / Qs2
This ensemble of fields is called color glass condensate.
Qs evolves with x and satisfies a nonlinear RG equation,
generalizing the BFKL equation, which is universal in the
limit x 0, i.e. independent of the hadron species (meson,
baryon, or even nucleus).
Parton saturation III
How many of these partons are “liberated” due to interactions when
two nuclei collide?
In the limiting case (x 0
and s
) all partons are
liberated, but PCM
calculations suggest that
the liberation probability
drops for partons at small x
at fixed collision energy s.
Baryon “stopping”
Net baryon number content
of a hadron or nucleus:
B( x)
1
3
[ f q ( x)
f q ( x)]
q
RHIC
LHC
• net baryon contribution in the
initial state (valence quark
distribution) extends to small x,
and accounts for a net baryon
density at mid-rapidity dN/dy 5
• parton rescattering in the
PCM then fills up the midrapidity region to explain the
net baryon density observed in
Au+Au collisions at RHIC.
• At the LHC, the midrapidity
region is almost completely net
baryon free.
Part IV
Matter formation and breakup
Space-time picture of a HI collision
Hadronization
Expansion
Equilibration
Hard scattering
Equilibration and expansion
* Hard scattering: Occurs on short time scale t
and is described by pQCD.
1/Q < 1/Qs
* Equilibration: Can be described by multiple parton scattering
in the PCM or by chaotic dynamics of classical color fields.
Characteristic time scale: t 1/g2T.
* Expansion of the QGP: Described by relativistic fluid
dynamics. Simplest case = boost invariant longitudinal flow
(Bjorken model) gives cooling like T(t) 1/t1/3.
* Hadronization: Slow or fast – that is the question!
Hadron formation
q
q q
q
q
qq q
Fragmentation
Baryon
Meson
1
Recombination
Baryon
Meson
1
Sudden recombination model
Assumptions:
•
Quarks and antiquarks recombine into hadrons locally “at an instant”:
qq
M
qqq
B
•
Gluons get absorbed into valence quarks before hadronization
•
Competition between fragmentation and recombination;
fragmentation
recombination
p2 of
•
Hadron momentum P much larger than internal momentum
the quark wave function of the hadron;
•
Parton spectrum has thermal part (valence quarks) and a power law tail
(quarks and gluons) from pQCD.
Recombination of thermal quarks
Relativistic formulation using hadron light-cone frame:
w (r , p)
E
dN M
d 3P
dN
E 3B
d p
d
Quark distribution function at “freeze-out”
P u
(2 )3
P u
d
(2 )3
dxw ( R, xP )w ( R, (1 x) P )
M ( x)
2
,
dxdx ' w ( R, xP )w ( R, x ' P ) w ( R, (1 x x ') P )
B
( x, x ')
, ,
For a thermal distribution
w(r , p )
exp( p u / T )
w ( R, xP ) w ( R, (1 x) P ) exp
P u /T
Meson
w ( R, xP ) w ( R, x ' P ) w ( R, (1 x x ') P ) exp
P u /T
Baryon
2
Recombination vs. Fragmentation
1
Fragmentation:
dN
E 3h
d P
Recombination…
w (r , xP ) w (r , (1 x) P ) exp
P u /T
Meson
w (r , xP ) w (r , x ' P ) w (r , (1 x x ') P ) exp
P u /T
Baryon
P u dz
d
(2 )3 0 z 3
w (r , 1z P )D
h
( z)
… always wins over fragmentation for an exponential spectrum:
exp( P u / T ) exp( P u / zT ) w P / z
… but loses at large pT, where the spectrum is a power law ~ (pT)-b
Apparent paradox: At given value of pT …
• The average hadron is produced by recombination
• The average parton fragments
Model fit to hadron spectrum
R.J. Fries, BM, C. Nonaka, S.A. Bass (PRL in print)
shifted pQCD spectrum
Teff = 350 MeV
fitted to spectrum
2.2 GeV
Part V
Insights:
The first 3 years of RHIC
CM energy
500 GeV for p-p
200 GeV (per N-N) for Au-Au
RHIC & its detectors
Luminosity
Au-Au: 2 x 1026 cm-2 s-1
p-p : 2 x 1032 cm-2 s-1
STAR
The Solenoidal Tracker At RHIC
Magnet
Time
Projection
Chamber
Coils
Silicon
Vertex
Tracker *
TPC Endcap &
MWPC
FTPCs
ZCal
ZCal
Vertex
Position
Detectors
Endcap
Calorimeter
Central
Trigger Barrel
Barrel EM
Calorimeter
+ TOF patch
RICH
* yr.1 SVT ladder
2000
2001
2003
PHENIX (central part)
Not showing the North and South muon arms
PHOBOS & BRAHHMS
Flavour equilibration
The statistical (thermal) model for hadron abundances works well with T
Tc
Parametrization of transverse flow
Blast wave parametrization
fit for STAR data works
well for ,K,P, . Multiply
strange baryons , show
less, but still substantial
flow: These particles with
smaller interaction cross
section decouple earlier;
much flow is generated
before the hadronization.
,
STAR preliminary
,K,P,
tanh
0
spectra in peripheral AuAu and pp
R=
Yield Au+Au / N binary
Au+Au
Yield pp
Au+Au
Nbin =12.3 ±4.0
70-80% Peripheral
Suppression of high-pT hadrons in Au+Au collisions
PHENIX Data: Identified
0
Away side jet
Same side jet
STAR
Charged hadron suppression
suppression increases with centrality
Suppression patterns: baryons vs. mesons
What makes baryons
different from mesons ?
p/
ratio
HIGH-ENERGY PHYSICS:
Wayward Particles Collide
With Physicists' Expectations
Charles Seife
EAST LANSING --At a
meeting here last week, researchers announced results that, so
far, nobody can explain. By
slamming gold atoms together
at nearly the speed of light, the
physicists hoped to make gold
nuclei melt into a novel phase
of matter called a quark-gluon
plasma. But al-though the
experiment produced encouraging evidence that they had
succeeded, it also left them
struggling to account for the
behavior of the particles that
shoot away from the tremendously energetic smashups.
Central
Peripheral
Hadron spectra I
Hadron spectra II
Hadron dependence of high-pt suppression
• R+F model describes
different RAA behavior of protons and pions
• Jet quenching becomes universal in the fragmentation region
Azimuthal anisotropy v2
Mesons and baryons behave differently
Semiperipheral collision
Coordinate space:
initial asymmetry
Momentum space:
final asymmetry
y
px
x
v2
cos 2
,
tan
1
(
py
px
)
Collective flow behavior extends to higher
pT for baryons (p, ) than mesons ( ,K)
Does v2 reflect parton flow?
P. Sorensen (UCLA – STAR)
Recombination model
suggests that hadronic
flow reflects partonic
flow (n = number of
valence quarks):
v had
2
nv 2part
pThad
npTpart
Provides measurement
of partonic v2 !
d+Au compared with Au+Au
Proton/deuteron
nucleus
collision
Nucleusnucleus
collision
“Centrality” Dependence
Au + Au Experiment
Final Data
d + Au Control Experiment
Preliminary Data
• Dramatically different and opposite centrality evolution
of Au+Au experiment from d+Au control.
Azimuthal distributions
pedestal and flow subtracted
No back-side jet in central Au+Au
CONCLUSION
The strong suppression of the inclusive yield and
back-to-back correlations at high pT previously
observed in central Au+Au collisions are due to
final-state interactions with the dense medium
generated in such collisions.
Part VI
The LHC heavy ion programme
What’s different (better) at the LHC ?
Much larger “dynamic range” compared to RHIC
•
•
•
•
Higher energy density 0 at earlier time 0.
Jet physics can be probed to pT > 100 GeV.
b, c quarks are plentiful, good probes.
Increased lifetime of QGP phase (10-15 fm/c)
Initial state effects less important.
• QGP more dominant over final-state hadron
interactions.
ECM dependence of dN/dy, dE/dy
NLO pQCD with geometric parton saturation (Eskola et al. - EKRT)
Overestimate of growth of dN/dy, dE/dy with ECM ??
LHC
RHIC
LHC
RHIC
Jet quenching at the LHC
Hadron production at the LHC
R.J. Fries et al.
r
r
= 0,65
= 0.85
r
= 0.75
Includes
estimated
parton energy
loss
Photon tagged jets
q
g
High-energy photon defines energy of
the jet, but remains unaffected by the
hot medium.
Parton energy loss is measured by
the suppression of the fragmentation
function D(z) near z 1 .
Measuring the density
q+g
q+
q+q
g+
Backscattering probes the plasma
density and initial parton spectrum
g
q
d
dt
2
e
u
s q
s2
s
s
u
R.J. Fries, BM, D.K. Srivastava,
PRL 90 (2003) 132301
One dedicated HI experiment: ALICE
One pp experiment with a HI program: CMS
One pp experiment considering HI: ATLAS
LHC running conditions for Pb+Pb
•
CM energy: 5.5 TeV/NN
x 200
•
Luminosity:
Lmax = 1 1027 cm-2s-1
•
Charged multiplicity
– Estimates dN/dy = 2 – 3000
– Design for dNch/dy|max = 8000
•
Event rate:
– 8000 minimum bias coll./ s
– 109 events/year
– 1% recorded
The ALICE Experiment
HMPID
HMPID
PID
PID (RICH)
(RICH) @
@ high
high pptt
TOF
TOF
PID
PID
TRD
TRD
Electron
Electron ID
ID
PMD
PMD
multiplicity
multiplicity
TPC
TPC
Tracking,
Tracking, dEdx
dEdx
ITS
ITS
Low
Low pptt tracking
tracking
Vertexing
Vertexing
PHOS
PHOS
,,
00
MUONS
MUONS
ALICE central detector acceptance
2
ITS tracking
1
TRD TOF
0
PHOS
HMPID
TPC
-1
ITS multiplicity
-2
0
1
2
3
20
100
Muon arm: 2.4< <4 , PMD: 2.3< <3.5 , FMD: -5.4< <-1.6, 1.6< <3
pt
ALICE event display for Pb+Pb
HMPID
HMPID
TOF
TOF
TRD
TRD
TPC
TPC
2 slice of TPC
PHOS
PHOS
full TPC volume
Unstable particles: K*, D
Detection of unstable neutral
hadrons via “V” decays in TPC.
D0
K-
+
D0
K*0
K+
-
K*0
M(K+ -) (GeV/c2)
Quarkonia in ALICE
• M =94.5 MeV/ c2
at t he
• Separ at ion of , ’, “
• Tot al ef f iciency
~ 75%
• Expect ed st at ist ics
(kevent s – 1 mont h):
central
J/
’
‘
“
310
12
39
19
12
min. bias
574
23
69
35
22
Quarkonia in CMS
J/
f amily
Yield/month (kevents, 50% eff)
(including barrel and endcaps)
Pb+Pb
Sn+Sn
Kr+Kr
Ar+Ar
1027
1.7 1028
6.6 1028
1030
28.7
210
470
2200
0.8
5.5
12
57
22.6
150
320
1400
'
12.4
80
180
770
''
7
45
100
440
L
J/
'
Pb+Pb, 1 month at L=1027
Jet Reconstruction in CMS
Window
Algorithm
•
•
•
•
•
Subtract average pileup
Find jets with sliding window
Build a cone around ETmax
Recalculate pileup outside the
cone
Recalculate jet energy
Full jet reconstruction in Pb+Pb central collisions (dN/dy~8000)
Efficiency
Measured jet energy
Jet energy resolution
Balancing or Z0 vs Jets: Quark Energy Loss
,
ETjet, >120 GeV in the barrel
Z0
1 month at
1027 cm-2s-1
Pb+Pb
<E>=0 GeV
<E>=4 GeV
<E>=8 GeV
Background
Jet+
Z0
Isol.
0+jet
ET // 0-ETJet (GeV)
Conclusions
• ALICE, CMS, (and ATLAS ?) are nicely complementary
in their physics capabilities to study hot, ultradense matter
created in nuclear collisions.
• Hard probes (jets, heavy quarkonia) extend the range of
matter probes into regimes that allow for more reliable
calculations.
• Hadrons containing b- and c-quarks will become abundant
components in the final state.
• Soft probes are governed by quantitatively so different
parameters that conclusions drawn from RHIC data can be
put to a serious test.
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