Hard Scattering and Jets in Heavy-Ion Collisions Naturwissenschaftlich-Mathematisches Kolleg der...

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


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)


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


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


Confinement

( )4Heavy quark potential ( ) : ( )

3s r c

cc V r k rr

Dominant at small distances (1-gluon exchange)

Dominant at large distances (Confinement)


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

QQ

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


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


QCD Phase Diagram

Measure of net baryon density ρ

Early universe (t 10-6 s)

RHIC, LHC

(?)


Brief History of QCD and Jets


A Jet in a p+p Collision


Jet-Quenching in Nucleus-Nucleus Collisions


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


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


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


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


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


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


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


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


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


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


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:


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)


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


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:


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


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:

Hard Scattering and Jets in Heavy-Ion Collisions Naturwissenschaftlich-Mathematisches Kolleg der...

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