Heavy Ion Physics at the LHC
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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 programmePart I QCD at high temperature: The quark-gluon plasma (QGP)
Matter under extreme conditions
1. Squeeze slowly Cold, dense matter
2. 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
LQCD 1
4 Ga Ga
a
g Aa t a
f a
mf
fDegrees of freedom
• At extreme (energy) density, particle masses can
be neglected relative to the kinetic energy:
d3 p E
with E p2 m2
( 2 )3 e E / T 1
2
4 7 / 8(fermions)
aT with a
30 1 (bosons)
Quarks: 2 2 NC N F 12 N F
Gluons: 2 ( N C2 1) 16Hadrons or quarks & gluons?
If QCD had NF light quark flavors, there would be
(NF2-1) nearly massless Goldstone bosons (“pions”):
2
N 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 4
30 T QGP = quark-gluon plasma
0
QCD equation
of state from
lattice QCD
Hadron gas
0Is 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 densityColor screening
2 a a
g G ( b) g a
Q ( b)
Induced color density
a a d3 p ( E g bt b ) / T
1
2 a
Tr t 3
e 1
(2 )
2 2 2 NF
with G ( gT ) , Q ( gT ) 2
6
a
Static color charge (heavy quark) generates potential ta s
e r
rColor 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 16 2 4 50 21 2
1 s
T 1 s
N FT 4
4 30 21 30
2 3 2 2
1 s
2 q ( T2 1
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.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
1 2 1 1 k k
D(k , ) k2 ( gT ) 2 1 ln
2 2 k k
k 0 1
mG* gT
Effective mass of gluon: 3
k 0 1
mG* gT
2QCD phase diagram
initial
LHC
state
RHIC
LHC
Color super-
conducting
quark matterPart 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 4
30 g DOFT T
E
Additional energy is
used up to liberate
new degrees of
freedom (color!) in
transition regionHadrons 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 1 + 2v2cos2( lab- plane)
Force P • Two-particle correlations
More flow in collision plane dN/d( 1- 2)
than perpendicular to it. 1 + 2v22cos(2[ 1- 2])
Elliptic flow “measures” the • Four-particle correlations
transverse pressure at very exp[i2( 1+ 4
2- 3- 4 )] = -v 2
early times ( < 3 fm/ c).Strangeness enhancement…
…probes chiral symmetry restoration and deconfinement
Mass (MeV)
1000000 NA57 data
Q CD mass
100000
Higgs mass
(sss)
10000
1000 (qss)
100
(qqs)
10
1
u d s c b t
FlavorCharmonium suppression…
VQQ(r) is screened at distance scales r > (gT)-1
heavy quark bound states dissolve above some Td:
J/ suppression.
But: J/ may survive
above Td as a narrow
resonance, as recent
lattice calculations of
the spectral function
Karsch et al.
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
q
q rescattering in dense, hot medium.
Radiative energy loss: dE / dx L kT 2
L
Scattering centers = color charges
q q
g
Can be described as medium effect on
parton fragmentation:
2 2 z
Dp h ( z , Q ) Dp h ( z , Q ) Dp h , Q2
1 E/EEnergy 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:
1 2 2d 2
c 2
ˆ
qL with qˆ q dq
dq 2
Energy loss spectrum for a fast parton is ( 2 s C2 / ) :
2 2
c c
D( ) exp
2 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” 2d 2
qˆ q dq k T2
of QCD medium: dq 2
Property of medium
For power law parton spectrum ( pT-v) (range of color force)
energy loss leads to an effective momentum
shift for fast partons (BDMS):
pT s
ˆ 2 pT /
qL
2 2 2qˆ0
Including expansion: ˆ
qL qˆ L
0 eff d (r , )
(r )Analytical model: Surface emission
dN dN (Q RAA )
Quenching factor: Q ( pT ) 2
d 2 pT d pT
partons hadrons
2( p0 pT )
Q ( pT )
R ( 1) pT
= final dN/dy / volume
Volume / R = surface
= QCD energy loss parameter:
2
s q 2 dq 2 (d / dq 2 ) 3
2 C2 ( 2 2
s
2
) ln qmax / 2
D
0.5 ln(…) for gluons; 0.25 ln(…) for quarksJet correlations
E L
Q R/R
Quenching provides a
Away-side jet mechanism for generating
an anisotropy with respect
Q ' ( R / R) 2 Q Qasj to the collision plane for
hadron production in non-
central collisions. The
Back-to-back jets (leading hadrons) predicted anisotropy is
are quadratically suppressed! less than 10%.Part III
The initial state:
Structure of nuclei at small xAu+Au Collision at RHIC
Space-time picture of a HI collision
Hadronization
Expansion
Equilibration
Hard scatteringInitial 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 1 r/
h (r )
a 3
e with 0.24 fm
8
• Lorentz contraction utilizing y*; on-shell rapidity of partons, or rz~1/pzParton saturation at small x
DGLAP splitting:
~ 1/Q2
GLRMQ parton fusion:
xGA ( x, Q 2 ) s A1/ 3 x
parton density area = 1
RA2 Q2 Q2
2 1/ 3
Q sat A x from HERA dataParton 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
1
of a hadron or nucleus: B( x) 3 [ f q ( x) f q ( x)]
q
• 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
RHIC PCM then fills up the mid-
rapidity region to explain the
net baryon density observed in
LHC 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 scatteringEquilibration and expansion * Hard scattering: Occurs on short time scale t 1/Q < 1/Qs and is described by pQCD. * 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
Recombination
Fragmentation
Baryon
Baryon 1
1 Meson
MesonSudden 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
• Hadron momentum P much larger than internal momentum p2 of
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) Quark distribution function at “freeze-out”
dN M P u 2
E d dxw ( R, xP )w ( R, (1 x) P ) M ( x)
d 3P (2 )3 ,
dN P u 2
E 3B d dxdx ' w ( R, xP )w ( R, x ' P ) w ( R, (1 x x ') P ) B ( x, x ')
d p (2 )3 , ,
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 BaryonRecombination vs. Fragmentation
1
dN P u dz
Fragmentation: E 3h d w (r , 1z P )D h ( z)
d P (2 )3 0 z 3
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
… 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 fragmentsModel 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 GeVPart V
Insights:
The first 3 years of RHICCM energy RHIC & its detectors
500 GeV for p-p
200 GeV (per N-N) for Au-Au
Luminosity
Au-Au: 2 x 1026 cm-2 s-1
p-p : 2 x 1032 cm-2 s-1
STARThe Solenoidal Tracker At RHIC
Magnet Time
Projection
Coils Chamber
Silicon
TPC Endcap & Vertex
MWPC Tracker *
FTPCs
ZCal ZCal
Vertex
Endcap Position
Calorimeter Detectors
Central
Barrel EM Trigger Barrel
Calorimeter
+ TOF patch
RICH * yr.1 SVT ladder
2000 2001 2003PHENIX (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
, STAR preliminary
well for ,K,P, . Multiply
strange baryons , show
less, but still substantial
flow: These particles with
,K,P,
smaller interaction cross
section decouple earlier;
much flow is generated
before the hadronization.
tanh0 spectra in peripheral AuAu and pp
Yield Au+Au / N binary Au+Au
R= Yield pp
Au+Au
Nbin =12.3 ±4.0
70-80% PeripheralSuppression of high-pT hadrons in Au+Au collisions
PHENIX Data: Identified 0
Away side jet
Same side jet
STARCharged 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, resear- chers announced results that, so far, nobody can explain. By slamming gold atoms together Central 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 encoura- Peripheral ging evidence that they had succeeded, it also left them struggling to account for the behavior of the particles that shoot away from the tremen- dously energetic smashups.
Hadron spectra I
Hadron spectra II
Hadron dependence of high-pt suppression • R+F model describesdifferent 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: Momentum space:
initial asymmetry final asymmetry
y
px
x
1
py
v2 cos 2 , tan ( )
px
Collective flow behavior extends to higher
pT for baryons (p, ) than mesons ( ,K)Does v2 reflect parton flow?
Recombination model
P. Sorensen (UCLA – STAR) 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
Nucleus-
nucleus
collision“Centrality” Dependence Au + Au Experiment d + Au Control Experiment Final Data 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+AuCONCLUSION 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 LHC
RHIC RHICJet quenching at the LHC
Hadron production at the LHC
R.J. Fries et al.
r = 0.85 Includes
estimated
parton energy
loss
= 0,65 r = 0.75
rPhoton tagged jets
High-energy photon defines energy of
q
g 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+ Backscattering probes the plasma
density and initial parton spectrum
q+q g+
g
q
2
d e
s q u s
dt s2 s u
R.J. Fries, BM, D.K. Srivastava,
PRL 90 (2003) 132301One 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% recordedThe 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 MUONS
MUONS
PHOS
PHOS
,, 00ALICE central detector acceptance
2
1 ITS tracking
TRD TOF
0 PHOS
HMPID
TPC
-1
ITS multiplicity
-2
0 1 2 3 20 100 pt
Muon arm: 2.4<ALICE event display for Pb+Pb
HMPID
HMPID
TOF
TOF
TRD
TRD
TPC
TPC
2 slice of TPC full TPC volume
PHOS
PHOSUnstable particles: K*, D
Detection of unstable neutral
D0 K- +
hadrons via “V” decays in TPC.
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 min. bias
J/ 310 574
’ 12 23
39 69
‘ 19 35
“ 12 22Quarkonia in CMS
J/ f amily
Yield/month (kevents, 50% eff)
(including barrel and endcaps)
Pb+Pb Sn+Sn Kr+Kr Ar+Ar
L 1027 1.7 1028 6.6 1028 1030
J/ 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
Pb+Pb, 1 month at L=1027Jet Reconstruction in CMS
• Subtract average pileup
• Find jets with sliding window
Window • Build a cone around ETmax
Algorithm • 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 resolutionBalancing or Z0 vs Jets: Quark Energy Loss
ETjet, >120 GeV in the barrel
, Z0
1 month at
1027 cm-2s-1
Pb+Pb
=0 GeV
=4 GeV
=8 GeV
Background
Isol. 0+jet
Jet+ Z0
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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