Introduction to ultra-relativistic heavy

Introduction to ultra-relativistic heavy-ion collisions
Measurement of global observables and the Glauber Model
• Centrality measurement
• Glauber calculations
• “Applications”
• Global observables
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
High-energy nucleus-nucleus collisions: the scope
• Study of:
– Phase diagram
chiral/deconfinement transition(s)
T
quark-gluon
plasma
~170
MeV
11
00
00
11
• Relevance for:
– early Universe (10−5 s, QGP)
– neutron stars
deconfined,
χ -symmetric
hadron gas
confined,
χ -SB
Braun-Munzinger, Wambach, Rev. Mod. Phys. 81 (2009)
1031
1
0
0
1
0
1
color
superconductor
µo
few times nuclear
matter density
Create in laboratory a chunk of deconfined matter and study its properties
(what we often call “medium”, also called Quark-Gluon Plasma, QGP/sQGP)
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
µ
Nucleus-nucleus collisions in the LHC era
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
...an era of deep questions and quantitative answers
• nature of confinement and deconfinement [what fingerprints of deconfined matter (QGP) we do see with hadrons?]
• breaking and restoration of chiral symmetry
• phase diagram of QCD [how is thermalization achieved (at partonic level)?]
• aim to determine:
– critical temperature (for deconfinement and chiral symmetry restoration)
– the equation of state of compressed nuclear (partonic) matter
– transport coefficients (ex.: viscosity)
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
How to ”measure” the early Universe in laboratory?
with collisions of heavy nuclei (Au,Pb) at relativistic energies
(Ex.: Energy per nucleon = 100 GeV → velocity 0.99996 × speed of light)
...and we need models to simulate the experiments
(theory intractable due to strength of the force)
Ultra-relativistic Quantum Molecular Dynamics
http://th.physik.uni-frankfurt.de/∼urqmd/
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
How to ”simulate” in laboratory the early Universe?
1. initial collisions (t ≤ tcoll = 2R/γcmc)
2. thermalization: equilibrium is established (t . 1 fm/c)
3. expansion and cooling (t < 10-15 fm/c)
4. hadronization
5. chemical freeze-out: inelastic collisions cease; yields are frozen
6. kinetic freeze-out: elastic collisions cease; spectra are frozen (t+ = 3-5 fm/c)
we measure at stages 5. and 6. want to know properties of stage 3.
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
Matter (nuclear force) at extremes
conditions in high-energy nucleus-nucleus collisions (extracted from data and
models ...“run the movie backwards” )
Temperature: T =100-1000 MeV (or up to a million times T at Sun’s center;
1 MeV≃10 billion degrees)
Pressure: P =100-300 MeV/fm3 (1 MeV/fm3=≃1028 atmospheres;
center of Earth: 3.6 million atm)
Density: ρ=1-10ρ0 (ρ0. density of a Au nucleus=2.7×1014 g/cm3;
density of Au = 19 g/cm3)
Volume: about 2000 fm3 (1 fm=10−15 m)
Duration: about 10 fm/c (or about 3×10−23 s)
trully “extreme”...
(a femto-world)
• What are the ”control parameters”:
– Energy of the collision
– Centrality of the collision (size of the nuclei)
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
Heavy ion accelerators
√
sN N =2.4 GeV, E/A=1.15 GeV
√
• AGS @ BNL, Brookhaven (1985-1995): sN N =4.8 GeV, E/A=10.5 GeV
√
• SPS @ CERN, Geneva (1987-2004): sN N =17.3 GeV, E/A=157 GeV
• Bevalac @ LBL, Berkeley (1980-1990):
√
• SIS @ GSI, Darmstadt: sN N =2.5 GeV, E/A=1.5 GeV
√
• RHIC @ BNL, Brookhaven: sN N =200 GeV, E/A=100 GeV
√
• LHC @ CERN, Geneva (2009): sN N =5500 GeV, E/A=2750 GeV
√
...running now at sN N =2.76 TeV, E/A=1.38 TeV
(collider, nr. of collisions = 8000 per sec.)
√
• FAIR @ GSI, Darmstadt (2018): sN N =8.3 GeV, E/A=35 GeV
(beam on fixed-target, nr. of collisions = 107 per sec.)
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
Participants and spectators
in AA collisions at high energies geometric concepts are applicable
N.Herrmann, J.P.Wessels, T.Wienold, Ann. Rev. Nucl. Part. Sci. 49 (1999) 581
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
Centrality
...defined by the impact parameter b (length of ~b, a 2D vector connecting the
centers of the 2 nuclei; points in x direction)
central collisions (small b): large participating zone (hot/dense, also called
fireball), large Npart (number of participating/wounded nucleons)
peripheral collisions (large b): large spectators (cold, flying away undisturbed)
b is not a directly measurable quantity
2
σ(b)
b
centrality fraction for b: σ(b ) = 4R2 (pure geometry; bmax = 2R)
max
10% most central Pb+Pb collisions (RP b ≃7 fm): b < b2 = 4.5 fm
R b2 2
b db
0
< b >= R b2
≃3 fm
0 bdb
assumed: nuclei as “black discs” (if overlap then interaction) → dσ = 2πbdb
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
Calculations on centrality
The Glauber Model (or “Wounded Nucleon” Model)
treats an AA collision as a superposition of elementary nucleon-nucleon (inelastic)
collisions
Assumptions:
• after an inelastic collision an excited (nucleon-like) hadron is created, which
interacts with the same cross section
• the nucleons travel along straight lines (at high energies)
Input:
• the nucleon density profile (nucleons are assumed to be randomly distributed
accordoing to this profile)
• the inelastic nucleon-nucleon cross section σinel
see http://www.gsi.de/∼misko/overlap/
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
-3
Nucleon density (fm )
Nuclear density profile
0.18
Au
0.16
0.14
0.12
Xc=0
0.1
0.08
Woods-Saxon
(parametrize e scattering measurements)
Xc=0.7 fm
0.06
Xc=1.2 fm
0.04
0.02
0
1
2
3
4
5
6
7
RA
8
9
10
Radius (fm)
• “core”: Ncoll > 1
• “corona”: Ncoll ≤ 1
(from MC Glauber: Xc=1.2 fm)
Corona fraction
0
1
Xc=0 fm
Au+Au
0.9
Xc=0.7 fm
Xc=1.2 fm
0.8
0.7
0.6
0.5
0.4
“bulk” may scale differently:
core: ∼ Npart,
corona: ∼ Ncoll (pp)
0.3
0.2
0.1
0
0
50
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
100
150
200
250
300
350
Npart
The total inelastic nucleon-nucleon cross section
ATLAS, arXiv:1104.0326
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
Glauber calculations
Nuclear thickness: TA(~s) =
R
ρ(~s, z)dz (Normalization:
R
TA(~s)d2s = A)
“Nucleon luminosity” in area d2s: TAB (~s) = TA(~s) · TB (~s − ~b)d2s
“Nucleon luminosity”
for collisions at impact parameter b:
R
TAB (b) = TA(~s) · TB (~s − ~b)d2s (nuclear overlap function)
Average occurence per event for a process X: < NX >= TAB · σX
Number of collisions: < Ncoll >= TAB · σinel
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
Measurement of centrality (ALICE)
obviously one needs (simple) observables which vary with centrality
...and are not correlated with the measurement intended as a function of
centrality
...and one wants a correlation of 2 different measurements to eliminate
background (beam-gas) and “pileup” (more events at the same time)
ALICE collab., arXiv:1011.3916
ALICE collab., arXiv:1011.3914
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
Measurement of centrality: Zero Degree Calorimeter (ALICE)
ZEM
ZN
IP
116 m
ZP
ALICE
Figure 5.1: Schematic top view of the side of the ALICE beam line opposite to the muon arm.
The locations of the neutron (ZN), proton (ZP) and forward electromagnetic (ZEM) calorimeters
are shown. The position of the beam line dipoles (Dx) and quadrupoles (Qx) are also indicated.
Beam pipes
ZP
ZN
Figure 5.2: Front view of one ZDC set placed on the lifting platform in data-taking position.
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
ALICE ZDC (JINST 3 (2008) S08002)
Figure 5.3: Front face of the ZN calorimeter;
the quartz fibres connecting the monitoring laser
system to PMTs are visible.
Figure 5.4: Front face of the ZP calorimeter.
Table 5.1: Dimensions and main characteristics of the detectors.
Dimensions (cm3 )
Absorber
ρabsorber (g cm−3 )
Fibre core diameter (µm)
Fibre spacing (mm)
Filling ratio
Length (in X0 units)
Length (in λI units)
Number of PMTs
ZN
ZP
ZEM
7.04 × 7.04 × 100
tungsten alloy
17.6
365
1.6
1/22
251
8.7
5
12 × 22.4 × 150
brass
8.5
550
4
1/65
100
8.2
5
7 × 7 × 20.4
lead
11.3
550
not applicable
1/11
35.4
1.1
1
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
An illustration of Glauber model
Ncoll
1800
participant nucleons:
suffered at least 1 collision
1600
LHC (σnn=60 mb)
1400
RHIC (σnn=42 mb)
spectators: Ncoll = 0
1200
• Npart =< Npart >
1000
• Ncoll =< Ncoll >
800
(for given centrality class)
600
400
200
0
0
50
100
150
200
250
300
350
400
for fluctuations one needs Monte
Carlo Glauber to account for the
finite nr. of nucleons
Npart
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
Monte Carlo Glauber
√
Au-Au, sN N =200 GeV
incoming nucleons are distributed radomly according to Woods-Saxon
p
2 nucleons collide if within a distance in transverse plane d ≤ σinel /π
many events are used to calculate average quantities (and rms) per collision
centrality interval
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
Two types of scaling
Npart (“soft”)
Ncoll (“hard”)
“bulk” particle production
“hard probes” (X: charm)
RAA =
RAA
4
dN ch /d η / 〈 N part〉 /2
200 GeV
3
AA/dy
dNX
pp
Ncoll · dNX /dy
2
1.8
RAA for pT > 0.3 GeV/c
1.6
Au+Au @ sNN = 200 GeV
1.4
Saturation Model
Hijing (1.35)
Two-Component Fit
1.2
1
0.8
2
19.6 GeV
0.6
0.4
1
0.2
0
100
200
PHOBOS collab., arXiv:nucl-ex/0405027
300
400
〈 N part〉
0
0
50
100
150
PHENIX collab., arXiv:1005.1627
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
200
250
300
350
Npart
Recall
E+pz
Rapidity: y = 12 ln E−p
= tanh−1(βz )
z
pz = q
longitudinal (beam direction) momentum
E=
m20 + p2 = total energy
Advantage: additive for Lorentz transformations
“Disdvantage”: needs particle identification (mass)
p+p
Pseudorapidity: η = 21 ln p−pzz = −ln tan θ2
θ = polar angle (of emission/scattering)
Phase space (invariant distribution):
d2 N
d3 N =
2πptdptdy
dx3
pt = p sin θ = transverse momentum
q
sometimes instead of pt transverse mass: mt = m20 + p2t
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
Overall (charged) particle production vs. pseudorapidity
dNch/dη
800
62.4 GeV
19.6 GeV
130 GeV
200 GeV
600
400
200
0
-5
0
5
η
-5
0
5
-5
0
η
5
-5
0
η
Phobos collaboration (from Miller, Reygers, Sanders, Steinberg, Ann.Rev.Nucl.Part.Sci.57 (2007) 205 [arXiv:nucl-ex/0701025])
larger particle densities: i) for more central collisions ii) for higher energies
broader distributions for higher energies
(averages over many events of a given centrality class)
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
5
η
“Bulk” particle production (in the LHC era)
dNch/dy ≃ 1.1 × dNch/dη (colliders)
dNch /dy
Nch “scaling” with Npart (at η=0)
E895, E877
Npart=350
NA49,NA44
NA50,NA60
10
3
PHOBOS,BRAHMS
ALICE
148⋅√s0.30
ALICE collab., arXiv:1011.3914
10
(hep-ph/0402291)
2
AGS SPS
clearly, particle production is different
in AA than in pp
10
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012
RHIC
10
LHC
2
10
3
10
√sNN (GeV)
4
Multiplicity vs. centrality
ALICE collab., arXiv:1012.1657
same centrality dependence at LHC as at RHIC (just a factor 2.1 larger)
TU Darmstadt — Fachbereich Physik — Introduction to Relativistic Heavy Ion Collisions — SS 2012