project-atlas-lucid Site - CERN

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0000 1111
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1111 0000
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Report from the luminosity
measurement taskforce
WLS fibers
16 Plastic
Scintillators
MBTS
EMEC
Moderator shielding
FCAL
Pump
HEC
(front)
ZDC
HEC
(back)
FCal 1 FCal 2 FCal 3
(EM) (Had) (Had)
LAr Calorimeter
shielding plug
TAS
BCM
LUCID
ZDC
140 m
237 m
ALFA
http://project-atlas-lucid.web.cern.ch/project-atlas-lucid/taskforce/main.html

ATLAS
The basic principle
ATLAS
The luminosity (L) can be calculated from the rate of all inelastic interactions (R in )
and the total inelastic cross section ( in ) by using the simple relation:
L = R in
in
The inelastic interaction rate is given by the average number of inelastic interactions
per bunch crossing () and the bunch crossing rate (f BX ):
R in = x f BX = x
The Number of filled Bunch crossings
3564
x 40 MHz
Conclusion: To provide a luminosity the detector must estimate correctly
from a measured rate and the inelastic cross section has to be known.
V. Hedberg Luminosity Working Group 03.12.2009 2

ATLAS
The inelastic cross section
ATLAS
Predicted cross section in mb from Phojet 1.12 and Pythia 6.420
14 TeV:
Phojet Pythia
Inelastic 83.1 79.3
Elastic 34.4 22.2
Total 117.5 101.5
10 TeV:
Phojet Pythia
Inelastic 79.8 75.3
Elastic 32.0 20.8
Total 111.8 96.1
Phojet Pythia
Non diff. 68.0 (82%) 54.7 (69%)
Double diff. 4.1 (5%) 10.3 (13%)
Single diff. 11.0 (13%) 14.3 (18%)
Phojet Pythia
Non diff. 64.9 (81%) 51.6 (68%)
Double diff. 4.0 (5%) 9.8 (13%)
Single diff. 10.8 (14%) 14.0 (19%)
}
}
Phojet Pythia
Minimum bias 72.1 65.0
Phojet Pythia
Minimum bias 68.9 61.3
0.9 TeV:
Phojet Pythia
Inelastic 54.0 52.5
Elastic 14.1 12.8
Total 68.1 65.3
Phojet Pythia
Non diff. 40.0 (74%) 34.4 (66%)
Double diff. 3.5 (7%) 6.4 (12%)
Phojet Pythia
Minimum bias 43.5 40.8
Single diff. 10.5 (19%) 11.7 (22%)
(Note: double pomeron processes were not included in PHOJET cross sections).
}
V. Hedberg Luminosity Working Group 03.12.2009 3

ATLAS
Measuring
ATLAS
The average number of interactions per bunch crossing () is estimated from
a rate measured by the detectors.
The measured rate that is used to estimate can be of three main types:
1) Event rate
2) Hit rate
3) Particle rate
The different detectors measure different quantities while requiring different
combinations of signals in the two detectors. This lead to a long list of different
luminosity methods.
V. Hedberg Luminosity Working Group 03.12.2009 4

I
Type of events
A C
Hits = 0 Hits = 0
Measured
quantity
EVENTS
BCM
MBTS
LUCID
Name
ZERO COUNTING - AND
II
Hits = 0 Hits = 0
Hits 1
Hits = 0
EVENTS
MBTS
LUCID
ZERO COUNTING - OR
III
Hits = 0 Hits 1
Hits 1 Hits 1
EVENTS
HITS
BCM
ZDC
MBTS
LUCID
EVENT COUNTING - AND
HIT COUNTING - AND
PART.
FCAL
PARTICLE COUNTING - AND
IV
Hits 1 Hits 1
Hits 1
Hits = 0
Hits = 0 Hits 1
EVENTS
HITS
Not used
MBTS
LUCID
EVENT COUNTING - OR
HIT COUNTING - OR
V
Hits 1
Hits = 0
EVENTS
HITS
BCM
Not used
EVENT COUNTING - XOR SIDE A
HIT COUNTING - XOR SIDE A
VI
Hits = 0 Hits 1
EVENTS
HITS
BCM
Not used
EVENT COUNTING - XOR SIDE C
HIT COUNTING - XOR SIDE C
VII
Hits 1 Hits 1
Hits 1
Hits = 0
EVENTS
PART.
ZDC
FCAL
EVENT COUNTING - OR SIDE A
PARTICLE COUNTING - OR SIDE A
VIII
Hits 1 Hits 1
Hits = 0 Hits 1
EVENTS
PART.
ZDC
FCAL
EVENT COUNTING - OR SIDE C
PARTICLE COUNTING - OR SIDE C

ATLAS
Measuring by particle counting
ATLAS
If a true number of particles is counted in the detectors without any requirement on
a minimum number of particles then
N
part/BX
= =
N part/pp
The average number of detected particles per bunch crossing
The average number of detected particles per inelastic pp interaction
The average number of detected particles per inelastic pp interaction (N part/pp )
has to be obtained from simulations or from a reference data sample recorded at
low luminosity (low ).
Another possibility is to measure the luminosity with for example ALFA and calibrate
the detector:
ALFA
f BX
L =
in
x N part/BX
N part/pp
in
x N part/pp =
L
N part/BX
x
fBX
Detector
V. Hedberg Luminosity Working Group 03.12.2009 6

ATLAS
Particle counting with coincidence
ATLAS
In order to reduce background it is an advantage to do particle counting while requiring at
least one particle in each detector. In this case is no longer proportional to N part/BX .
If only events with particles in both detectors are used then the relationship between
N part/bx and becomes:
N
Coinc
part/BX N part/pp
-
e
C
A
N part/pp N Coinc
C
+ part/pp N part/pp
-
+
Coinc
N part/pp
e
A
5 parameters needed to describe the dependence on
What is needed is as a function of N part/BX i.e. = f(Npart/BX) but the expression
above cannot be inverted analytically.
V. Hedberg Luminosity Working Group 03.12.2009 7

ATLAS
Measuring by hit counting
ATLAS
Most detectors do not measure particles. If hits are measured instead without
any requirement on a minimum number of hits in each detector there is no longer
a linear relationship between and N hits/BX :
N hits/BX
=
N tubes
N hits/pp
[ 1 - ( 1- ) ] N hits/pp for

ATLAS
Hit counting with coincidence
ATLAS
In order to reduce background it is an advantage to do also hit counting while requiring
at least one particle in each detector.
The relationship between the number of hits and particles:
N part = - N tubes x
N hits
ln ( 1- )
N tubes
can be used together with the relationship between and the number of particles
N part/BX
A
N part/pp
e
A
Coinc
N part/pp
2e
A
if
A
N part/pp
C
N part/pp
and
A
C
to obtain a relationship between N hits and :
N hits = N tubes[1 - e
A
N part/pp
e
A Coinc
N part/pp N 2e A
] tubes
However, there is no way of analytically express as a function of N hits in this case !
V. Hedberg Luminosity Working Group 03.12.2009 9

ATLAS
Hit counting - AND versus OR
ATLAS
AND
N hits = N
tubes[1-e
OR
N hits/BX
30
25
20
15
10
5
0
A
N part/pp
HitcountingAND
HitcountingOR
LUCID
A Coinc
e N part/pp N 2e A
tubes ]
= N tubes [ 1 - ]
( 1- N hits/pp N tubes )
13% Difference
70% Difference
1% Difference
0 5 10 15 20 25
N hits/BX
The dependence of on N hits is only linear for small .
The largest difference between AND and OR is at low
N hits/BX
V. Hedberg Luminosity Working Group 03.12.2009 10
1,6
1,4
1,2
1
0,8
06 0,6
0,4
0,2
0,16
0,14
0,12
0,1
0,08
0,06 006
0,04
0,02
0
0
HitcountingAND
HitcountingOR
0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6
HitcountingAND
HitcountingOR
N hits/BX
OR
sing
N hits/BX N hits/pp
AND
coinc
N hits/BX N hits/pp
0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 0,16

ATLAS
Hit counting - linear extrapolation
ATLAS
AND
N hits = N
tubes[1-e
AND
coinc
N hits/BX N hits/pp
30
25
20
15
10
5
0
A
N part/pp
A Coinc
e N part/pp N 2e A
tubes ]
Hitcounting
AND
Hitcounting
Linear
0 5 10 15 20 25
N hits/BX
1,6
1,4
1,2
1
0,8
0,6
04 0,4
0,2
0
0,16
0,14
0,12
0,1
0,08
0,06
0,04 004
0,02
0
HitcountingAND
HitcountingLinear
0 0,2 0,4 0,6 0,8 1 1,2
N hits/BX
HitcountingAND
Hitcountinglinear
0 0,02 0,04 0,06 0,08
N hits/BX
V. Hedberg Luminosity Working Group 03.12.2009 11

ATLAS
Event counting
ATLAS
The simplest quantity to measure is the number of events per bunch crossing.
Different requirements can be made on the signals seen in the two detectors
and different system uses different requirement.
Some of these event topologies are not independent with respect to each other.
Probability( Zero-counting-AND ) = 1 - Probability( Event-counting-OR)
Probability( Zero-counting-OR ) = 1 - Probability( Event-counting-AND)
It is possible to calculate the probability (rate) of any event topology at any
if three basic parameters ( 0 , 1 and 2 ), that describe the probability when there
is one pp interaction, are known.
A problem with event counting is that at high the event rate tends to saturate
and an increase in does then not give a significant increase in the event rate.
V. Hedberg Luminosity Working Group 03.12.2009 12

ATLAS
Event counting
ATLAS
Name
Event type
ZERO COUNTING - AND Hits = 0 Hits 0
EVENT COUNTING - XOR - A Hits 1 Hits = 0
EVENT COUNTING - XOR - C Hits = 0 Hits 1
EVENT COUNTING - AND Hits 1 Hits 1
Propability for 1 pp
0 = 1- 1 - 2 - 3
= e ( 0 -1)
1 = A - coinc
2 = C - coinc
e( 0 + 1 -1)
-
e -
( 0-1)
- -
e ( 0 + 2-1)
e ( 0-1)
3 = coinc
Probability for interactions
(
e 0 + 2 -1)
+e
( 0 -1)
1- e ( 0 + 1-1)
-
EVENT COUNTING - OR
Hits 1 Hits 1
Hits 1 Hits = 0
Hits = 0 Hits 1
sing = 1 - 0
1-e ( 0 -1) -
ZERO COUNTING - OR
Hits = 0 Hits = 0
Hits 1
Hits = 0
Hits = 0 Hits 1
-
e ( 0+ 1 -1)
+
(
e 0 + 2 -1)
-e
( 0 -1)
EVENT COUNTING - OR - A
Hits 1 Hits 1
Hits 1 Hits = 0
A = 1 - 0 - 2
1- e ( 0 + 2-1)
EVENT COUNTING - OR - C
Hits 1 Hits 1
Hits = 0 Hits 1
C = 1 - 0 - 1
1- e ( 0 + 1-1)
V. Hedberg Luminosity Working Group 03.12.2009 13

ATLAS
Event counting
ATLAS
Efficiencies for one pp interaction at 14 TeV
A C
0
Hits = 0 Hits = 0
Hits 1
Hits = 0
Hits = 0 Hits 1
Hits 1 Hits 1
1
= 0.442
= 0.212
= 0.212
3 = 0.135
2
LUCID BCM MBTS
0.711
0.125
0.125
0.040
0
0.004
0.004
0.992
ZDC
0.472
0.215
0.215
0.098
sing = 1 - 0 = 0.559 0.290 1.000
= A 1 - 0 - 2
= C 1 - 0 - 1
LUCID BCM MBTS ZDC
= 0.347 0.165
= 0.347 0.165
0.528
0.998 0.313
0.998 0.313
coinc =1- 0 - 1 - 2 = 0.135 0.040 0.992 0.098
LUCID: GEANT3 + PHOJET (non-diff + diff, 16 + 16 tubes, cut = 50 p.e. )
BCM: GEANT4 + PYTHIA (non-diff + diff, 4 + 4 modules )
MBTS: GEANT4 + PYTHIA (only non-diff, 16 + 16 sectors, cut = 40 mV )
ZDC: ATL-LUM-INT-2009-002, A = C = coinc
V. Hedberg Luminosity Working Group 03.12.2009 14

ATLAS
Event versus hit counting
ATLAS
30
28
OR
N events/BX =
1-e - sing
Event counting OR
OR
N hits/BX
30
28
g
Hit counting OR
= N tubes [ 1 - ( 1- N hits/pp N tubes ) ]
26
24
22
LUCID
MBTS
BCM
ZDC
26
24
22
LUCID
20
18
16
14
12
10
8
6
4
2
0
Saturation
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
20
18
16
14
12
10
8
6
4
2
0
0 2 4 6 8 10 12 14 16 18 20 22 24
N events/BX
N hits/BX
Conclusions:
Hit counting suffers less from saturation than event counting.
A small acceptance gives less saturation (but less statistics)
V. Hedberg Luminosity Working Group 03.12.2009 15

ATLAS
Event counting - AND versus OR
ATLAS
N Events
AND
N events/BX = 1-e - A -
OR
N events/BX =
1-e - sing
e C -
+e sing
20
15
OR
AND
LUCID
N BX
1,2
1
LUCID
inverted
10
5
0,8
0,6
0,4 04
0,2
0
OR
0 5 10 15 20
Conclusions:
OR counting saturates before AND counting
OR counting is described by 1 parameter
AND counting is described by 3 parameters
If

ATLAS
Zero counting - AND versus OR
ATLAS
N Zero
N BX
1
0,8
OR
N zero/BX = e - A +
AND
N events/BX =
LUCID
e - sing
e C -
-e sing
OR AND
inverted
20
15
10
5
LUCID
OR AND
AND OR
0,6
0,4
0,2
0
0 5 10 15 20
Conclusions:
AND counting saturates before OR counting
AND counting is described by 1 parameter
OR counting is described by 3 parameters
If

ATLAS
Zero counting - linear extrapolation
ATLAS
Compare Zero-OR counting with a
linear extrapolation from the low
limit:
OR
N zero/BX = e - A +
OR
N zero/BX =
1-
Coin
e C -
-e sing
20
18
16
14
12
ORlinear
OR
4
3,5
3
2,5
ORlinear
OR
14% difference
10
2
8
1,5
6
1
4
2
0,5
3% difference
0
0 0,2 0,4 0,6 0,8 1
N zero/BX
0
0,5 0,6 0,7 0,8 0,9 1
N zero/BX
V. Hedberg Luminosity Working Group 03.12.2009 18

ATLAS
Zero counting - more extrapolation
ATLAS
Compare Zero-OR counting with a
linear extrapolation from the low
limit and an exponential extrapolation:
20
18
16
14
12
10
8
6
ORlinear
OR
ORln
OR
N zero/BX = e - A +
OR
N zero/BX = e - Coin
OR
N zero/BX =
4
3,5
3
2,5
2
1-
Coin
e C -
-e sing
ORlinear
OR
ORln
4
1,5
2
1
0
0 0,2 0,4 0,6 0,8 1
0,5
N zero/BX
0
0,5 0,6 0,7 0,8 0,9 1
N zero/BX
V. Hedberg Luminosity Working Group 03.12.2009 19

ATLAS
Migration
ATLAS
6
10
5
10
4
10
3
10
2
10
PMT
Entries 640000
Mean 3.08
RMS 14.8
Underflow 0
Overflow 36
Cut
GAS
Entries 640000
Mean 3.16
RMS 14.8
Underflow 0
Overflow 48
PMT+GAS
Entries 640000
Mean 6.07
RMS 24.1
Underflow 0
Overflow 244
Primaries
Entries 640000
Mean 0.633
RMS 8.07
Underflow 0
Overflow 34
μ = 1.00
PMT
GAS
PMT+GAS
Primaries
3
10
2
10
PMT
Entries 25600
Mean 76.2
RMS 71.7
Underflow 0
Overflow 62
Cut
GAS
Entries 25600
Mean 78
RMS 70.8
Underflow 0
Overflow 78
PMT+GAS
Entries 25600
Mean 144
RMS 105
Underflow 0
Overflow 662
Primaries
Entries 25600
Mean 15.8
RMS 39.2
Underflow 0
Overflow 41
μ = 25.00
PMT
GAS
PMT+GAS
Primaries
10
1
0 50 100 150 200 250 300 350 400 450 500
p.e./tube/event
Migration:
When events are piled up at large ,
particles that give a small signal combines
with other small signals to give a hit above
the threshold.
The effect in LUCID is large
- 1)[%]
true
/μ
meas
(μ
10
0 50 100 150 200 250 300 350 400 450 500
p.e./tube/event
100
80
60
40
20
0
true
Hit Counting (coincidence)
True
Thr = 40 p.e.
Thr = 50 p.e.
Thr = 60 p.e.
Thr = 70 p.e.
inel
B
10
10 1 10
V. Hedberg Luminosity Working Group 03.12.2009 μ = σ inel 20 × L B
-2
-1
true

ATLAS
The Beam Condition Monitor
ATLAS
The BCM has four modules on each side.
2+2 modules are at present read out
separately from the other 2+2 modules.
The detector will do event counting and
not hit counting. Since the detector
read-out is split in two one can make
two independent measurements for each
methods.
Zero-counting-AND:
=
N 00
ln ( )
N BX
0 -1
- C - A - sing
Function tested
with MC data:
BCM detector
modules
Function
inverted:
YES YES
Event-counting-AND:
N AND ( 0 + 1 -1)
= 1-e (0 +
-e
2 -1)
+e
( 0 -1)
N BX
YES NO
Event-counting-XOR Side A:
N A ( 0 + 1 -1) ( 0 -1)
= e -e
N BX
N C ( 0 + 2 -1) ( 0 -1)
Event-counting-XOR Side C: = e -e
N BX
NO NO
NO NO
V. Hedberg Luminosity Working Group 03.12.2009 21

ATLAS
The Beam Condition Monitor
ATLAS
The BCM has so far only been studied with 14 TeV PYTHIA/GEANT4 events and assuming
a read-out of 4 modules on each side.
Efficiency
A C
Hits = 0 Hits = 0
0
= 0.711
Hits 1 Hits = 0
1 = 0.125
Hits = 0 Hits 1
2
= 0.125
Hits 1 Hits 1
3
= 0.040
Event-counting-AND:
N AND ( 0 + 1 -1)
= 1-e (0 +
-e
2 -1)
+e
( 0 -1)
N BX
N AND
N 00
1-
N BX
N BX
Zero-counting-AND:
N 00
1- = 1- e
N BX
( 0 -1)
V. Hedberg Luminosity Working Group 03.12.2009 22

ATLAS
The Beam Condition Monitor
ATLAS
What needs to be done ?
The Event-Counting-AND formula needs to be inverted.
The Event-Counting-XOR formula needs to be tested with simulated events and
inverted (perhaps inclusive OR would be easier ?)
The efficiencies needs to be calculated at lower energies than 14 TeV.
V. Hedberg Luminosity Working Group 03.12.2009 23

ATLAS
The Zero Degree Calorimeter
ATLAS
The ZDC has two calorimeters that will
measure the total energy. A cut will be made
on this energy and three rates will be
measured:
Zero Degree Calorimeter
32 ch
3+3ch
PMT
Had. mod.
32+1 chs
PMT
Had. mod.
1 chs
PMT
Had. mod.
1 chs
LHCf
Ionization
chamber
ZDC12Rate: Inclusive single rate on Side 12
ZDC81Rate: Inclusive single rate on Side 81
4+4 ch
96 ch
PMT
32 ch
PMT
PMT
PMT
ZDCcoincRate: Coincidence rate
EM mod.
96+1 chs
Had. mod.
32+1 chs
Had. mod.
1 chs
Had. mod.
1 chs
Ionization
chamber
The methods that will be used are:
Event-counting-AND:
N AND ( 0 + 1 -1)
= 1-e (0 +
-e
2 -1)
+e
( 0 -1)
N BX
=
ZDCcoincRate
BX rate
Event-counting-OR Side A:
Event-counting-OR Side C:
N A
N BX
=
N C
N BX
=
1- e ( 0 + 2-1)
1- e ( 0+ 1 -1)
ZDC12Rate
BX rate
ZDC81Rate
BX rate
V. Hedberg Luminosity Working Group 03.12.2009 24
=
=
=
=
ZDC12Rate
ln(1- )
BX rate
0 + 2 -1
ZDC81Rate
ln(1- )
BX rate
0 + 1 -1

ATLAS
The Zero Degree Calorimeter
ATLAS
Double Arm Acceptance
ZDC performance at Low Energy, neutron yield¥acceptance
0.10
0.08
0.06
0.04
0.02
ATL-LUM-INT-2009-002
0.00
0 1000 2000 3000 4000 5000 6000 7000
LHC Beam EnergyHGeVL
20
15
10
5
ZDCOR
ZDCAND
Assumptions:
coinc = 0.10
A = C = coinc = 0.31
What about migration ? Accidentals ?
A simulation is needed !
0
0 0,2 0,4 0,6 0,8 1
N events/BX
V. Hedberg Luminosity Working Group 03.12.2009 25

ATLAS
The Zero Degree Calorimeter
ATLAS
What needs to be done ?
A simulation of the detector is badly needed.
The probability functions have to be tested with simulated data.
Functions for = f(ZDC rate) have to be constructed at various energies.
V. Hedberg Luminosity Working Group 03.12.2009 26

ATLAS
LUCID
ATLAS
LUCID has 15 working Cherenkov
tubes in each detector.
The signals are discriminated and
provide a hit pattern that are
used to do four measurements.
Zero-counting-AND, Zero-counting-OR, Hit-counting-AND, Hit-counting-OR.
Monte Carlo studies have shown that none of the probability functions describe the
Monte Carlo data sufficiently well. The reason for this is migration which cannot be
described in these functions.
LUCID plots as a function of the probability (P) of events or hits and fit a polynomial
function so that can be expressed as
N
= p 0
0 + p 1 P + p 2 P 2 + p 3 P 3 where P = or or and p 0 , p 1 , p 3
N BX
N 00
N BX
N hits
N BX
are constants.
Sometimes the fit is done in two regions of P in order to get a good agreement between
the fit and the Monte Carlo data.
V. Hedberg Luminosity Working Group 03.12.2009 27

ATLAS
LUCID 900 GeV
ATLAS
Zero counting (OR)
Zero counting g( (AND)
P 0 > 0.75
P 0 >0.25
P 0

ATLAS
LUCID 900 GeV
ATLAS
Hit counting g( (OR)
Hit counting (AND)
N hits < 0.7
N hits >0.7
V. Hedberg Luminosity Working Group 03.12.2009 29

ATLAS
Low approximation for LUCID at 0.9 TeV
ATLAS
OR
N zero/BX = e - A +
AND
N events/BX =
e - sing
e C -
-e sing
= 1- sing
= e - coin = 1- coin
OR
=(1-N zero/BX ) /
AND
= (1-N events/BX )/
coin
sing
Threshold A C sing coin
10 pe 0.269 0.273 0.463 0.0788
15 pe 0.239 0.243 0.420 0.0625
50 pe 0.104 0.107 0.199 0.0124
AND
N hits = N tubes [1-e
OR
N hits/BX
A
N part/pp
A Coinc
e N part/pp N 2e A
tubes ]
= N tubes [ 1 - ( 1- N hits/pp N tubes ) ]
sing
N hits/pp
coinc
N hits/pp
=
OR
= N hits/BX
AND
N hits/BX
/
/
coinc
N hits/pp
sing
N hits/pp
A
N hits/pp
C
N hits/pp
sing
N hits/pp
coinc
N hits/pp
Threshold
10 pe 0.550 0.559 0.856 0.2530
15 pe 0.450 0.458 0.719 0.1890
50 pe 0.138 0.142 0.250 0.0299
V. Hedberg Luminosity Working Group 03.12.2009 30

ATLAS
Measured for LUCID at 0.9 TeV
ATLAS
Selection of MBTS events using pulseheight and timing cuts and requiring hits
on both sides.
Monte Carlo Data
sing
A
C
coinc
for loser cuts )
coinc
N hits/pp
Monte Carlo Data
sing
N hits/pp
V. Hedberg Luminosity Working Group 03.12.2009 31

ATLAS
LUCID 14 TeV
ATLAS
Zero Counting - AND
Zero Counting - OR
Efficiency
A C
Hits = 0 Hits = 0
0
= 0.442
Hits 1 Hits = 0
1 = 0.212
Hits = 0 Hits 1
2
= 0.212
Hits 1 Hits 1
3
= 0.135
Hit Counting - AND
N hits/BX < 1
Hit Counting - OR
N hits/BX < 15
Hit Counting - AND
N hits/BX > 1
Hit Counting - OR
N hits/BX > 15
V. Hedberg Luminosity Working Group 03.12.2009 32

ATLAS
LUCID
ATLAS
What needs to be done ?
Fits for all possible LHC energies are needed.
Study of systematic errors.
Studies using real event samples at low .
Studies of the detector response using real event samples.
V. Hedberg Luminosity Working Group 03.12.2009 33

ATLAS
MBTS
ATLAS
MBTS has 16 plastic scintillators one each side. They are arranged
in two rings and read-out by WLS fibers via the TileCal electronics.
The signals are discriminated and provide a hit pattern that are used
to do four measurements:
WLS fibers
16 Plastic
Scintillators
Zero-counting-AND
Hit-counting-AND
Zero-counting-OR
Hit-counting-OR
The efficiency of the detector is very high for non-diff. events:
0
= 0 1 = 0.004 2 = 0.004 3
= 0.992 (14 TeV, only non-diff.)
For the two zero-counting-methods, MBTS uses the following function that is fitted to the event
probability (P):
N 00 N
0
= -p 0 - p 1 ln(P) where P = or and p 0 , p 1 are constants
N BX
N BX
For hit counting, MBTS plot as a function of the hit probability (P) and fit a ratio of two polynomial
functions so that can be expressed as
=
p 3 + p 4 P + p 5 P 2 + p 6 P 3
p 0 + p 1 P + p 2 P 2
N hits
where P = and p 0 ,....,p 6 are constants
N BX
V. Hedberg Luminosity Working Group 03.12.2009 34

ATLAS
MBTS 900 GeV - Only non-diff.
ATLAS
N 0
-ln( )
N
-ln( 00
)
N BX
N BX
N hits
N hits
N BX
V. Hedberg Luminosity Working Group 03.12.2009 35
N BX

ATLAS
MBTS 10 TeV - Only non-diff.
ATLAS
N
-ln( 0
)
N BX
N
-ln( 00
)
N BX
N hits
N BX
N hits
N BX
V. Hedberg Luminosity Working Group 03.12.2009 36

ATLAS
MBTS
ATLAS
What needs to be done ?
Monte Carlo samples with a mixture including diffractive events have to be used.
Fits for all possible LHC energies are needed.
Studies of the detector response using real event samples.
Studies where only a few of the 32 segments are used.
Correct for pulses that are longer than the bunch separation time.
V. Hedberg Luminosity Working Group 03.12.2009 37

ATLAS
Beam separation scans
ATLAS
For Event-Counting-AND
the probability function is
N AND/BX =
- A - C -( A C Coin
1-e - e +e
Assume that A = C and that coin = A x
C N
- A -(2 A A A
AND/BX = 1-2e +e
Fit
N
N
AND
BC
LUCID
ε AC /
= 0.3430 ± 0.0007
2
χ = 1.10
Deviations from fit
μ
The fit works surprisingly well !
μ
V. Hedberg Luminosity Working Group 03.12.2009 38

ATLAS
Beam separation scans
ATLAS
A separation scan done at >1 will be distorted by the non-linear behaviour of
the rate measurement.
Beam separation scan with LUCID
Assumptions:
= 3
= 90 m
A Gaussian fit gives = 87.4 m
-
A fit with N AND/BX = 1-2e A -(2
+e
A A A
gives:
True Measured Difference
3 3.2 8%
: 90 m 90.8 m 0.9%
A : 0.343 0.321 7%
Backg. = 30%
Σ( μm)
The fit works better at higher where the
distortions are larger !
-
A second fit with N OR/BX = 1- e
sing
to Event-Counting-OR events give sing .
V. Hedberg Luminosity Working Group 03.12.2009 39

ATLAS
Final remarks
ATLAS
All detectors have done a lot of progress towards the goal of
having realistic luminosity algorithms.
But we are not there yet !
Due to a lack of manpower the progress is slow (and LHC running
does not help).
We will have a lot of work to do also in 2010 !
V. Hedberg Luminosity Working Group 03.12.2009 40

LIST OF METHODS

ATLAS
Zero-counting-AND
ATLAS
Zero-counting-AND events are events with no signals in both detectors:
A C
Hits = 0 Hits = 0
The probability to have a zero-AND event is
N 00/BX = e ( 0-1) = ē
sing =
N 00
N BX
=
Number of measured zero-AND events
Number of bunch crossings
This function can easily be inverted so that can be obtained from the measured events:
=
N 00
ln ( )
N BX
0 -1
N 00
ln ( )
N BX
= where only one parameter ( 0 ) has to be determined from Monte Carlo
- sing
The instantaneous luminosity is the obtained from
L = R in
in
= f BX
in
x
N 00
ln ( )
N BX
0 -1
where in = 79-83 mb at 14 TeV
0 = 0.442 (LUCID) = 0.711 (BCM) = 0 (MBTS) all at 14 TeV
V. Hedberg Luminosity Working Group 03.12.2009 42

ATLAS
Zero-counting-AND
ATLAS
Even if one can find a simple expression of as a function of the number of measured empty events,
this does not mean that this expression gives a perfect estimation of .
LUCID:
- 1)[%]
true
/μ
meas
(μ
25
20
15
10
Zero Counting (single AND side)
True
Thr = 40 p.e.
Thr = 50 p.e.
Thr = 60 p.e.
Thr = 70 p.e.
5
0
-5
-2
10
-1
10 1 10
B
μ = σ inel
× L
true
The reason for the error in the -determination above is migration i.e. the effect of particles with a
low pulseheight (below the discriminator threshold) that add up at large and produce a total signal
above threshold.
V. Hedberg Luminosity Working Group 03.12.2009 43

ATLAS
Event-counting-OR
ATLAS
Event-counting-OR events are events with a signal in at least one detector:
Probability( Zero-counting-AND ) = 1 - Probability( Event-counting-OR)
A C
Hits 1 Hits 1
Hits 1
Hits = 0
Hits = 0 Hits 1
The probability to have an event-counting-OR event is
N OR/BX = 1 - e ( 0 -1) = 1 - e -sing =
N OR
N OR/BX Sing if

ATLAS
Zero-counting-OR
ATLAS
A C
Zero-counting-OR events are events with no signals in one or two detectors:
The probability to have a zero-AND event is given by
Hits = 0 Hits = 0
Hits 1
Hits = 0
Hits = 0 Hits 1
N 0/BX = N 0
N BX
=
Number of measured zero-OR events
Number of bunch crossings
( 0 + 1 -1) (
N 0/BX = e +e 0 + 2 -1)
-e
( 0 -1) - A - C -( A C Coin
= e + e -e
( 0 + 1 -1) (
N 0/BX = 2e -e 0 -1) -
= 2e A -(2
-e
A Coin N 0
= if 1 = 2
N BX
=
N 0
N BX
and A C
This function cannot be inverted analytically and it depends on two parameters .
0 and 1 ).
V. Hedberg Luminosity Working Group 03.12.2009 45

ATLAS
Event-counting-AND
ATLAS
Event-counting-AND events are events with a signals in both detectors:
Probability( Zero-counting-OR ) = 1 - Probability( Event-counting-AND)
A C
Hits 1 Hits 1
The probability to have an event-counting-AND event is given by
N AND/BX = N AND
N BX
=
Number of measured event-counting-AND events
Number of bunch crossings
Sing
(
N AND/BX = 1-e 0 + 1 -1) (
-e 0 + 2 -1)
+e
( 0 -1) - A - C -( A C Coin
= 1-e - e +e
(
N AND/BX = 1-2e 0 + 1 -1)
+e
( 0 -1) -
= 1-2e A -(2
+e
A Coin if 1 = 2 and A C
This function cannot be inverted analytically and it depends on two parameters .
0 and 1 ).
N AND/BX = Coin if

ATLAS
Event-counting-XOR
ATLAS
Event-counting-XOR events are events with signals in only one detector:
A C
Hits 1
or
Hits = 0
Hits = 0 Hits 1
The probability to have an event-counting-XOR event on side A is given by
N A/BX = N A
N BX
=
Number of measured event-counting-XOR-side A events
Number of bunch crossings
( 0 + 1 -1) ( 0 -1)
N A/BX = e -e
and for side C one gets
( 0 + 2 -1) ( 0 -1)
N C/BX = e -e
These functions cannot be inverted analytically and they depends on two parameters.
V. Hedberg Luminosity Working Group 03.12.2009 47

ATLAS
Hit-counting-OR
ATLAS
Hit-counting-OR is a method which uses the hits in any detector:
A C
Hits 1 Hits 1
Hits 1
Hits = 0
Hits = 0 Hits 1
If the detectors counted the true number of particles then
N
part/BX
= =
N part/pp
The average number of detected particles per bunch crossing
The average number of detected particles per inelastic pp interaction
Instead the detectors count hits and at large there will be several particles in each detector element.
The number of particles can, however, be estimated from the number of hits:
N part = - N tubes x
and so
=
ln
ln
(
(
1-
1-
N hits/BX
N tubes
N hits/pp
)
)
N hits
ln ( 1- )
N tubes
where N tubes is the number of detector elements i.e. tubes in
the case of LUCID and scintillator segments in the case of MBTS.
N tubes
V. Hedberg Luminosity Working Group 03.12.2009 48

ATLAS
Hit-counting-AND
ATLAS
Hit-counting-AND is a method which uses the hits under the condition that both
sides have hits:
A C
Hits 1 Hits 1
The average number of particles in a bunch crossing can be estimated in this mode from the expected
number of hits for one inelastic pp interaction and the efficiencies. Assuming that the detector response
on side A and side C are identical one gets
N part/BX
A
N part/pp
e
A
Coinc
N part/pp
2e
A
if
A Npart/pp
C
N part/pp
and
A
C
where N part is obtained from N hits by
N part = - N tubes x
N hits
ln ( 1- )
N tubes
N hits/BX = N tubes[ 1 - e
A
N part/pp
e
A Coinc
N part/pp N 2e A
] tubes
What is needed is expressed as N hits but the function above cannot be inverted analytically.
N hits/BX = N tubes[ 1 - e
N Coinc
part/pp
A
N part/pp N tubes
]
for large
N hits/BX = Coinc
N part/pp
for small
V. Hedberg Luminosity Working Group 03.12.2009 49

ATLAS
Statistics at low
ATLAS
Zero-AND
Event-OR
Compare the methods zero-counting-AND with event-counting-OR: Hits = 0 Hits = 0 Hits 1 Hits 1
Zero-counting-AND:
= N 00
e ( 0 -1)
N BX
Event-counting-OR: 1 - e ( 0-1)
=
N OR
N BX
Hits 1
Hits = 0
Hits = 0 Hits 1
Conclusion: N 00 = N BX - N OR
where N BX is a constant and so both methods have the same
statistical uncertainty.
Event-AND
Event-OR
Compare the methods event-counting-AND with event-counting-OR: Hits 1 Hits 1 Hits 1 Hits 1
Conclusion: N OR > N AND
Hits 1
Hits = 0
Hits = 0 Hits 1
Compare the methods event-counting-OR with hit-counting-OR:
N OR/BX = 1 - e ( 0 -1)
N hits/BX
N hits/pp
[ 1 - ( 1- ) ] N hits/pp = 1.20 for