High Energy Physics
• Lecture 7
• Part 1: LHC Experiments
• Part 2: Cross Section and Luminosity
HEP Lecture 7
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About 100 years ago Ernest
Rutherford was experimenting with
alpha particles (which he himself had
discovered), bombarding gold foils.
Comparing his results with the then
known theory he discovered the nuclear
structure of atoms. He had one very
capable glassblower and one
assistant.
Today’s experiments require a very different scale.
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Today’s experiments require worldwide collaboration
36 countries collaborate in the LHC experiment ATLAS
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The LHC tunnel
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LHC Parameters
Circumference
26 659 m
Beam energy
7 TeV
Injection energy
0.45 TeV
Filling time
6 minutes
Acceleration period
1200 s
Beam lifetime
10 hours
Bunches per ring
2835
Bunch length
7.5 cm
Bunch radius
16 μm
Time between bunch crossings
25 ns
Particles per bunch
10.5x1010
up to 20 pp collisions per bunch crossing
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Access
shafts
Atlas
detector
Service
tunnel
Beam
tunnel
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The ATLAS Detector
Inner
Detector
Beam
Beam
muon
chambers
muon
chambers
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Cross section of the ATLAS detector
hadronic
calorimeter
Beam pipe
muon
chambers
tracking
detector
solenoidal
magnet
electromagnetic
calorimeter
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Transition
radiation
tracker
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ATLAS Transition Radiation
Tracker (TRT)
Participating institutes from countries:
CERN, Denmark, Poland, Russia, Sweden,
Turkey, USA.
Russian institutes:
FIAN, MEPhI, MSU-SNPI, PNPI, JINR
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Slice through a Sector of the CMS
Detector at LHC
0
1m
5m
7m
4 Tesla
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Muon Chamber Assembly
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Assembly of
hadronic calorimeter
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Hadronic calorimeter during construction
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Monte Carlo simulation of a proton-proton collision event
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Monte Carlo simulation of tracks in the tracking chamber
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Reaction Cross Section
• WHERE THEORY MEETS EXPERIMENT
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Differential cross section:
definition:
where
N (θ ) d Ω
dσ (θ ) =
N0
N (θ ) d Ω is the number of particles passing every second through
the element of solid angle
dΩ
and N0 is the number of beam
of beam particles per sq. cm and second.
scattered
particles
beam
θ
θ is the scattering angle
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As a result of a collision the particles can either remain
unchanged (elastic collision) or transform into different
particles (inelastic collision).
The different reactions are called channels.
Each reaction takes place with a different probability.
If the number of events in the ith channel is Ni, then
Ni d Ω
dσ i =
N0
is the differential cross section of channel i
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When the elastic diff cs is integrated over all angles we get the
elastic cross section:
1
σ el =
N0
v∫ N (θ )d Ω
S
where S is the surface of the unit sphere.
Similarly we get the cross sections for all other channels, σi.
The sum of the elastic cs and all channel cross sections is the
total cross section:
σ = σ el + ∑ σ i
i
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Total and elastic proton-proton cross sections as a function
of the LAB momentum in GeV/c
ISR
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Total and elastic proton-antiproton cross sections as a function
of the LAB momentum in GeV/c
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Total and elastic pion-proton cross sections as a function
of the LAB momentum in GeV/c
First nucleon
resonance Δ++
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Total and elastic K --proton cross sections as a function
of the LAB momentum in GeV/c
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Cross sections have by definition the dimension of an area.
They are sometimes given in cm2, but more frequently in
barns, millibarns, microbarns, etc.
1 barn = 10-28 m2
Of interest are reactions which occur with small probability
and hence with low cross sections, such as a few nanobarns
or even picobarns.
To be able to see collisions with such small cross sections
one must make sure to have a sufficiently large number of
collisions within a reasonable time.
The quantity that characterises the number of collisions in a collider
is called luminosity.
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Definition of Luminosity:
The interaction rate R (i.e. the number of interactions per second)
is proportional to the cross section; the constant of proportionality
is the luminosity L:
R=Lσ
If two bunches containing n1 and n2 particles collide with
frequency f then
L = f n1 n2 /4π σxσy
where σx and σy are the Gaussian horizontal and vertical
widths, respectively.
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The luminosity is measured by observing the
interaction rate of a process that is theoretically
well understood and convenient to measure.
A process that is well understood is
ud → W + → A +ν A
Its cross section σ+ is about 20 nb = 20x10-33 cm2
The design luminosity of LHC is L = 1034 cm-2 s-1
Therefore we should see about 200 such events per second.
The accuracy of this method is limited by a poor knowledge
of the momentum distribution of quarks in the proton, which
is not better than about 10%. So one needs other methods as well.
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The LHC is expected to have initially a luminosity of
1033 cm-2 s-1 and to reach its design luminosity of
1034 cm-2 s-1 after 2 to 3 years, i.e. by 2009 or 2010.
With L = 1034 cm-2 s-1 one can record 1 event per day
of a reaction that has a cross section of about 0.14 pb
(assuming 20 hours of beam time per day)
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