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Luminosity and ATLAS
Boštjan Maček
Adviser: prof. Marko Mikuž
Overview
introduction
definition of luminosity
the need for high luminosity
LHC (Large Hadronic Collider) and luminosity
ATLAS (A Toroidal LHC AparatuS) measurements
detectors: BCM (Beam Conditions Monitor)
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Luminosity and ATLAS
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Introduction
particle identity
protons
available energy
E=2*7 TeV =14 TeV
luminosity
L=1034cm-2s-1
data analysis
quantitative measurements of
particle physics world
experimental conditions
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Luminosity
scattering experiment
d N
d
L
ddt
d
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luminosity – experimental conditions
differential cross-section - description of physics
•experimental conditions
measurements
luminosity  rate
dN
R
 L
dt
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•rate of interactions
•amount of data
N   Rdt    Ldt  
integrated luminosity  number of scattered particles
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LHC - ATLAS
Luminosity and ATLAS
larger statistics  bigger precision
higher luminosity  larger statistics
The race for high luminosity
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LHC and luminosity
luminosity defined by parameters of collider
protons grouped in bunches
number of protons in a bunch - 1.15 1011
number of bunches - 2808
revolution frequency - 11.2 kHz
relativistic  factor - 7461
N n f rev r
L
F
4
2
b b
beam optics parameters
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Beam optics I
for high L bigger proton density is needed
squeezing the beam
typically systems of quadrupol magnets are used
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Beam optics II
beam parameterization:
x
x’=dx/ds
...
...
distance from optical axis
inclination toward optical axis
particle dynamics in quadrupol magnet
C x’
magnet
B
B
A
particle trajectory
A
optical axis
C
magnet
magnetic field, charge momentum
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x
2
 x' 
2

x
a
 
K
Luminosity and ATLAS
initial conditions
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Beam optics III
• passage trough magnet  ellipse in x’-x plane
• 1011 protons in a bunch  bunch area
x’
x’
x
x’
x
x
• Liouville’s theorem  bunch area is preserved
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x’
x’max
Beam optics IV
• goal: minimal xmax
x
xmax
– minimal  (shape)
– minimal emittance 
xmax

x'max
(area)
large
smal 

N n f 
L  b b rev r F
4
2
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reduction by
factor F=0.8
big x’ means that protons
collide under 35
angle
Luminosity and ATLAS
rad
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Luminosity measurements
d 2N
d
L
ddt
d
relate measured rate to cross-section
feedback to the LHC
fast measurements needed
data preprocessing
all four experiments have their luminosity measuring
devices + LHC monitoring
several complementary methods are used
absolute luminosity measurements  limited, calibration
luminosity monitoring
 high luminosities
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Calculation from beam
parameters
hard to measure F, , and 
N b2 nb f rev r
L
F
4
transversal bunch size  van der Meer scan
beam-beam interactions
limited by resolution of beam position monitor
expected precision 5-10%
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Well calculable processes
analyzing recorded data
processes that can be precisely calculated
most promising processes
pp  ppe+e- or
W/Z production
pp  pp+-
d 2N
d
L
ddt
d
expected precision around 10%
not a real-time measurement
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Optical theorem
incident plain wave
distance to the detector
ikr
e
 (r , )  eikz  f ( )
r
overall scattering
scattering angle
small angles
x2  y2
r  z
2z
z
detector response
cross-section
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area of the detector
  (r, ) dS  S 
2
4
Im[ f (0)]
k
 tot  4 Im[ f (0)]
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Small angle scattering
tot=Rtot/L
scattering under zero angle
Re[f(0)]/Im[f(0)]
2
d el

2
(  0)  f (0)  Im 2 [ f (0)](1   2 )  tot2 (1   2 )
d
16
2
Rtot
1
L
(1   2 )
16 dRel / dp
measuring:
elastic rate at small angles and extrapolating to zero
total rate (elastic rate + inelastic rate)
Elastic
Strong
extremely small angles
expected precision: 2%
Elastic
EM
Inelastic
no total rate needed !!!
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Luminosity monitoring
only option for high luminosity
measuring inelastic rate
number of interactions in pp collision  Poisson
counting only ‘empty events’
0 1 2 3 ... n
 ALi
i
BC
n n e
i
pp
possible bunch luminosity measurement
needs to be calibrated (A)
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ATLAS detectors
for W/Z analysis whole detector will contribute
dedicated detectors
absolute luminosity measurements
ZDC (Zero Degree Calorimeter)
Roman Pots
luminosity monitoring
BCM (Beam Conditions Monitor)
LUCID (LUminosity measurement using a Cherenkov Integrating Detector)
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Beam Conditions
Monitor
• relative luminosity measurement
– bunch luminosity measurement  fast electronics
– close to interaction point  radiation hard
• background suppression  t + coincidences
4 modules on each side of IP
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Beam Conditions Monitor
• something on both sides
• rate of coincidences

L
R( L)   P N ,  1  e rTR P N 1  e rTR (1 P ) N
L0 
N 0 


Poisson distribution


probability for anything on + side
simulation
probability for particle detection on + side
P 
N
N  N
changes with interaction
point position
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Conclusion
luminosity is a parameter of collider
detector must be adapted to measure in high luminosity
precise measurement of luminosity is essential for
physics interpretation of experiment
for measuring more complementary approaches are
needed
ATLAS will be able to monitor luminosity to high
precision
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Thank you ☺
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