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Hard Scattering and Jets in Heavy-Ion Collisions Naturwissenschaftlich-Mathematisches Kolleg der Studienstiftung des deutschen Volkes Kaiserslautern 30.9. – 5.10.2007. PD Dr. Klaus Reygers Institut für Kernphysik Universität Münster. Content. 1 Introduction 1.1 Quark-Gluon Plasma - PowerPoint PPT Presentation
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Hard Scattering and Jetsin Heavy-Ion Collisions
Naturwissenschaftlich-Mathematisches Kollegder Studienstiftung des deutschen Volkes
Kaiserslautern 30.9. – 5.10.2007
PD Dr. Klaus ReygersInstitut für Kernphysik Universität Münster
2 Hard Scattering and Jets in Heavy-Ion Collisions
Content
1 Introduction1.1 Quark-Gluon Plasma
1.2 Kinematic Variables
2 Lepton-Nucleon, e+e-, and Nucleon-Nucleon Collisions2.1 Deep-Inelastic Scattering and the Quark-Parton Model
2.2 Jets in e+e- Collisions
2.3 Jets and High-pT Particle Production in Nucleon-Nucleon Collisions
2.4 Direct Photons
3 Nucleus-Nucleus Collisions3.1 Parton Energy Loss
3.2 Point-like Scaling
3.3 Particle Yields at Direct Photons at High-pT
3.4 Further Tests of Parton Energy Loss
3.5 Two-Particle Correlations
3.6 Jets in Pb+Pb Collisions at the LHC
3 Hard Scattering and Jets in Heavy-Ion Collisions
Links
Slides will be posted at
http://www.uni-muenster.de/Physik.KP/Lehre/HS-2007
Lectures on Heavy-Ion Physics (from experimentalist‘s viewpoint):
http://www.uni-muenster.de/Physik.KP/Lehre/QGP-SS06
User: qgp, password: ss06
Many useful talks/lectures on Hard Scattering and Jets:
http://cteq.org
(→ summer schools)
4 Hard Scattering and Jets in Heavy-Ion Collisions
Paper on Hard Scattering and Jets
M. Tannenbaum,Review of hard scattering and jet analysisnucl-ex/0611008
A. Accardi et al.,Hard Probes in Heavy Ion Collisions at the LHC: Jet Physicshep-ph/0310274
5 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma
1.1 Quark-Gluon Plasma
6 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma
Confinement:Isolated quarks and gluons cannot be observed, only color-neutral hadrons
Meson Asymptotic freedom:Coupling s between color charges gets weaker for high momentum transfers, i.e., for small distances (r < 1/10 fm)
Limit of low particle densities and weak coupling experimentally well tested ( QCD perturbation theory)
Strong Interaction
Nucleus-Nucleus collisions: QCD at high temperatures and density („QCD thermodynamics“)
Nobel prize 2004 in physics
David J. Gross H. David Politzer Frank Wilczek
7 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma
Confinement
( )4Heavy quark potential ( ) : ( )
3s r c
cc V r k rr
Dominant at small distances (1-gluon exchange)
Dominant at large distances (Confinement)
8 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma
Asymptotic Freedom
QCD perturbation theory (pQCD):
2
2
2
12( )
(33 2 ) ln
:number of quark flavors
: QCD scale parameter
( 250 MeV/ )
s
f
f
n
n
c
pQCD works for s << 1.
This is the case for Q2 >> 2 0,06 (GeV/c)2
Asymptotic freedom: 2 2( ) 0 für s Q Q
In the limit Q2 quarks behave as free particles
9 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma
Predictions from First principles: Lattice QCD
F. Karsch, E. Laermann, hep-lat/03050252
4SB
30mit 37
g T
g
pe = × ×
=
2 quark flavors:
Tc = (160 - 190) MeV
c 0.7 – 1.0 GeV/fm3
only 20% deviation:qgp is an ideal gas
not
10 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma
QCD Phase Diagram
Measure of net baryon density ρ
Early universe (t 10-6 s)
RHIC, LHC
(?)
11 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma
Brief History of QCD and Jets
12 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma
A Jet in a p+p Collision
13 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma
Jet-Quenching in Nucleus-Nucleus Collisions
14 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma
Brief History of Heavy Ion Physics
StartStart AcceleratorAccelerator ProjectileProjectile Energy (Energy (s) per s) per NN pairNN pair
~1985 AGS (BNL) Si ~5 GeV
~1985 SPS (CERN) O, S ~20 GeV
1994 SPS (CERN) Pb 17 GeV
2000 RHIC (BNL) Au 200 GeV
2008 LHC (CERN) Pb 5500 GeV
15 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma
CERN SPS (1985 - 2004)
SPS
West area (WA)
North area (NA)
NA35/44NA38/50/50NA49NA45(CERES)NA57
WA80/98, WA97→NA57
Circumference: 6,9 km
16 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma
RHIC: Relativistic Heavy Ion Collider
Circumference 3,83 km
2 independent rings
120 „bunches“
~109 Au-Ions per bunch
„Bunch Crossings“ every 106 ns
Collisions of different particle species possible
Maximum energy:
200 GeV for Au+Au
500 GeV for p+p
Design luminosity
Au-Au: 2 x 1026 cm-2 s-1
p-p: 1,4 x 1031 cm-2 s-1
)GeV 500(A
ZsNN
17 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma
RHIC beamtimes:
Run 1 (2000): Au+Au, sNN
= 130 GeV
Run 2 (2001-2002): Au+Au, p+p, sNN
= 200 GeV
Run 3 (2003): d+Au, p+p, sNN
= 200 GeV
Run 4 (2003-2004): Au+Au, (p+p) sNN
= 62, 200 GeV
Run 5 (2005): Cu+Cu, p+p sNN
= 22, 62, 200 GeV
Run 6 (2006): p+p sNN
= 22, 62, 200 GeV
Run 7 (2007): Au+Au sNN
= 200 GeV
18 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma
CERN: Large Hadron Collider (LHC)
p+p collisions:s = 14 TeVcollision rate: 800 MHz
Pb+Pb collisions:s = 5,5 TeVcollision rate: 10 kHz
circumference: 27 kmB-Field: 8 T100 m beneath the surfacefirst collisions: 2008
19 Hard Scattering and Jets in Heavy Ion Collisions – 1.1 Quark-Gluon-Plasma
FAIR at GSI
UNILACSIS
FRS
ESR
SIS 100/300
HESRSuperFRS
NESR
CR
RESR FLAIR
Currently availablebeam particles:Z = 1 – 92(protons up to uranium)up to 2 GeV/nucleon
Planned facility:100 – 1000 times higher beam intensities,Z = -1 – 92(protons up to uranium, antiprotons),up to 35 GeV/nucleon
2007 begin of construction2012 first experiments2014 completion
20 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables
1.2 Kinematic Variables
21 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables
Energy and Momentum
„Length“ of a 4-vector is invariant under Lorentz transformation:
2 2 2 2 2( , , , )x ct x y z x x c t x y z
Relativistic momentum and relativistic energy:
2
2
1, , rest mass, = ,
1-
vp m v E m c m
c
����������������������������
Relativistic energy momentum relation:
12 2 4 2 2 2 2 2cE m c p c E m p
Energy-Momentum four vector:
( / , , , )x y zp E c p p p
22 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables
Energy and Momentum Conservation
Der energy-momentum four-vector is conserved in all components. For a reaction A+B C+D one has:
1. energy conservation:
2. 3-momentum conservation
A B C DE E E E
A B C Dp p p p ��������������������������������������������������������
Mandelstam variables:
AP
BPDP
CP2 2
2 2
2 2
( ) ( )
( ) ( )
( ) ( )
A B C D
A C B D
A D B C
s P P P P
t P P P P
u P P P P
2 2 2 2 .A B C Ds t u m m m m const
energy-momentum four-vectors, , , :A B C DP P P P
23 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables
Interpretation of s und t
Center-of-mass system (CMS) defined by:
3
A B
vectors
p p
����������������������������
Interpretation of s: 2 * * 2
Total energy in CMS
( ) ( )A B A Bs P P E E
is the total energy in the center-of-mass system s
Interpretation of t: 2( )A Ct P P
is the momentum transfer (square of four-momentum transfer) t
24 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables
s for Fixed-Target and Collider Experiments
1p
Target
1 1, labm E
2 2, 0labm p
1 1 2
2 21 2 1 2
,
1 2
2
2lab
lab
E m mlab
s m m E m
E m
1 1, labm E 2 2, labm E
1 2 1 2
2 21 2 1 2 1 2
,
1
2 2
2
lab lab lab lab
p p m mlab
s m m E E p p
E
Fixed-Target-Experiment:
Collider:
Example: Anti-proton production in a fixed-target experiment:
p p p p p p Minimum energy required for the production of an anti-proton: All produced particles at rest in CMS-frame, i.e s = 4 mp , therefore
2 2,min
1
(4 ) 27
2p plab
pp
m mE m
m
25 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables
Rapidity
Lp Tp
p
beam axis
2 2 2 2, :L T T Tp p p m m p
,y yL L
L L
E p E pe e
E p E p
cosh , sinh
tanh
T L T
LL
E m y p m y
py
E
y is additive under Lorentz transformation:
2
2
2cos1 cos 1 1 cos 1 2ln ln ln ln tan :2 cos 2 1 cos 2 22sin
2
p mE py
E p
Pseudorapidity :
'' Sy y y rapidity in system S rapidity of S‘ measured in S
rapidity in S‘
11 1ln ln
2 2 1L L
L L
E py
E p
rapidity
for 1L Ly
for 0y m In particular:
26 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables
Summary: Kinematic Variables
2
pp
T
0
1
2
1
2
Transverse momentum
Rapidity
Pseudorapidity
T sinp p J= ×
Latanhy b=
( )ln tan / 2h Jé ù=- ë û
(~40)
(~15)
27 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables
Example of a Pseudorapidity Distribution
p+p at 200 GeVs
dNch
/d
Beam rapidity:
beam ln 5,4E p
ym
Average number of charged particles:
20chch
dNN d
d
beamybeamy
28 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables
Lorentz Invariant Phase Space Element
Lorentz transformation of phase space element 3x y zd p dp dp dp
��������������
( )
( )x x
x
y y
z z
p p E
E E p
p p
p p
( , , )
( , , )x y z
x y z x y zx y z
p p pdp dp dp dp dp dp
p p p
0 0
( , , )0 0
( , , )
0 0
x
x
x y z y
x y z y
z
z
p
p
p p p p E
p p p p E
p
p
3d p
E
��������������
Invariant phase space element:
notLorentzInvariant!
3 3/
d dE
d p E d p
����������������������������Invariant cross section:
29 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables
Invariant Cross Section
cosh
/
3 3 3
3 3
3
2
1
1
1
2
LT
T T L
dpm y E
dy
T T
symmetry
T T
d d dE E
dp E dp p dp dp d
d
p dp dy d
d
p dp dy
Example: production
0.35 0.35y
Integral of the inv. cross section:3
inel3d d dT T
dp p y E N
dp
Average particlemultiplicity per event
Total inel.cross section
p+p at 200 GeVs
30 Hard Scattering and Jets in Heavy Ion Collisions – 1.2 Kinematic Variables
Invariant Mass
Consider decay of a particle with mass M into two daughter particles
2
1 22 2 21 2 1 2
1 2
2 21 2 1 2 1 2
2 21 2 1 2 1 2
( ) ( )
2 2
2 2 cos
E EM E E p p
p p
m m E E p p
m m E E p p
��������������������������������������������������������
����������������������������
0
1
2
Example: 0 - Decay 01 2( : 98,8%), 0, i iBR m m E p
1 22 (1 cos )M E E
M (GeV/c2)
coun
ts
Background of -pairs, whichdon‘t originate from the same 0 decay
Signal: Number of entries over combinatorial background(Peak width determined by energy resolution of the detector)Momentum
of the 0
Invariant Mass: