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Selection
of
W­Pair­Production
in
DELPHI
with
Feed­Forward
NEURAL
NETWORKS
#
ffl
Introduction
ffl
Hadronic
Analysis
ffl
Optimization
of
the
NN
ffl
Determination
of
Systematic
Errors
ffl
Summary
Karl­Heinz
Becks,
J¨
urgen
Drees,
Uwe
M¨
uller,
Helmut
Wahlen
Bergische
Universit¨
at­GH
Wuppertal,
Delphi
Kollaboration
Selection
of
W­Pairs
with
Feed­Forward
NN
ACAT2002
­
Moscow
­
June
24­28
2002
Uwe
M¨
uller

Introduction
\Delta Z
0
=fl
e
\Gamma
e
+
W
+
W
\Gamma
\Theta š
e
\Gamma
e
+
W
\Gamma
W
+
ffl
W­pair­production
e
+
e
\Gamma
!W
+
W
\Gamma
at
LEP
(CERN)
at
center­of­mass
energies
161
­
209
GeV
ffl
decay
channels:
hadronic
:
W
+
W
\Gamma
!
qqqq
(45:9%)
semileptonic
:
W
+
W
\Gamma
!
qqlš
(43:7%)
leptonic
:
W
+
W
\Gamma
!
lšlš
(10:4%)
ffl
measurements
of
production
cross
sections,
W­mass
and
width
as
well
as
branching
ratios
ffl
tests
of
Standard
Model
predictions
and
cross
checks
with
earlier
electroweak
measurements
possible
Selection
of
W­Pairs
with
Feed­Forward
NN
ACAT2002
­
Moscow
­
June
24­28
2002
Uwe
M¨
uller

Hadronic
WW­Candidate
DELPH
I
R
u
n
:
E
v
t
:
B
e
am
:
DAS
:
P
r
o
c
:
S
c
a
n
:
1
0
4
.
4
GeV
2
9
­
Ap
r
­
2
0
0
0
2
9
­
Ap
r
­
2
0
0
0
1
1
:
4
3
:
3
4
2
9
­
Ap
r
­
2
0
0
0
109372
8483
Tan
a
g
r
a
Selection
of
W­Pairs
with
Feed­Forward
NN
ACAT2002
­
Moscow
­
June
24­28
2002
Uwe
M¨
uller

Semileptonic
and
Leptonic
WW­Candidate
DELPH
I
R
u
n
:
E
v
t
:
B
e
am
:
DAS
:
P
r
o
c
:
S
c
a
n
:
9
8
.
1
GeV
2
8
­
J
un
­
1
9
9
9
2
8
­
J
un
­
1
9
9
9
0
4
:
1
4
:
0
9
2
­
J
u
l
­
1
9
9
9
103302
4779
Tan+DST
DELPH
I
R
u
n
:
E
v
t
:
B
e
am
:
DAS
:
P
r
o
c
:
S
c
a
n
:
9
8
.
1
GeV
2
7
­
J
un
­
1
9
9
9
2
7
­
J
un
­
1
9
9
9
0
8
:
0
3
:
1
5
2
­
J
u
l
­
1
9
9
9
103279
20825
Tan+DST
Selection
of
W­Pairs
with
Feed­Forward
NN
ACAT2002
­
Moscow
­
June
24­28
2002
Uwe
M¨
uller

Signal
and
Main
Background
Processes
ffl
signal
:
e
+
e
\Gamma
!W
+
W
\Gamma
!
qqqq
)
4­jet
event
topology
with
similar
quark
jets:
--
small
differences
in
jet
energies
--
large
angles
between
jets
--
high
total
jet
multiplicity
ffl
dominating
background
at
all
energies:
e
+
e
\Gamma
!
Z
0
=fl
?
!
qq(g)
--
cross
section
higher
by
one
order
of
magnitude
--
4­jet
events
with
two
quark
jets
and
two
gluon
jets
or
two
jets
from
a
gluon
decay
--
initial
state
photon
radiation
(Z­returns)
ffl
difficult
background
above
182
GeV:
e
+
e
\Gamma
!
Z
0
Z
0
!
qqqq
--
cross
section
lower
by
one
order
of
magnitude
--
same
topology
like
signal
and
very
similar
)
hardly
to
reject
Selection
of
W­Pairs
with
Feed­Forward
NN
ACAT2002
­
Moscow
­
June
24­28
2002
Uwe
M¨
uller

Neural
Network
vs.
Linear
Cuts
ffl
conventional
analysis
based
on
linear
cuts
(used
until
1998)
--
effective
center­of­mass
energy
p
s
0
--
number
of
jets
n
jet
--
total
jet
multiplicity
N
jet
all
--
D
=
E
jet
min
\Delta\Theta
jet
min
E
jet
max
\Delta(E
jet
max
\GammaE
jet
min
)
ffl
feed­forward
network
with
standard
backpropagation
algorithm
(first
use
at
189
GeV
in
1998)
--
loose
preselection
against
non­4­jet­events
and
Z­returns
--
13
jet­
or
event­variables
as
input
nodes:
p
s
0
,
\Theta
jet
min
,
N
jet
all
,
d
join
(4
!
3),
E
jet
max
\Gamma
E
jet
min
,
b
min
,
P
7
i=1
j~ p
3
i
j,
probability
from
constrained
fit,
rapidity,
sphericity,
thrust,
H3,
H4
--
architecture
13
­
7
­
1
--
2500
training
events
from
signal
and
QCD­background
simulation
--
test
with
additional
training
sample
of
simulated
ZZ
events
and
3
output
nodes
)
more
CPU
time
,
result
not
improved
Selection
of
W­Pairs
with
Feed­Forward
NN
ACAT2002
­
Moscow
­
June
24­28
2002
Uwe
M¨
uller

Selection
Results
@
189
GeV
DELPHI
data
WW5
qqqq
WW5
qqln
4­fermion­background
2­fermion­background
Output
value
of
the
Feed­Forward­network
number of events
NN
cuts
signal
efficiency
[%]
88.74
85.58
remaining
bg
[pb]
1.886
2.228
selection
purity
[%]
77.84
74.14
eff
\Theta
pur
[%]
69.08
63.45
selected
events
1298
1342
)
clear
improvement
in
selection
quality,
similar
at
all
other
LEP­energies
)
NN
chosen
as
Delphi
cross
section
analysis
Selection
of
W­Pairs
with
Feed­Forward
NN
ACAT2002
­
Moscow
­
June
24­28
2002
Uwe
M¨
uller

Requirements
for
Final
Publication
ffl
best
possible
separation
between
signal
and
background
with
consistent
analyses
at
all
energies
from
183
to
207
GeV
ffl
energy
dependent
preselection
ffl
same
neural
network
(architecture,
parameter
settings)
at
all
energies
ffl
different
trainings
for
all
energies
Selection
of
W­Pairs
with
Feed­Forward
NN
ACAT2002
­
Moscow
­
June
24­28
2002
Uwe
M¨
uller

Optimization
of
the
Neural
Network
ffl
variation
of
preselection:
too
loose
and
too
hard
preselection
)
worse
selection
small
variations
)
deviations
within
statistical
uncertainties
ffl
variation
of
network
parameters
or
configuration:
--
use
of
different
numbers
of
training
events
and
different
training
samples
--
j
(learning
rate,
0:0025
+0:015
\Gamma0:0015
,
with
and
without
decrease)
and
ff
(momentum
term,
0:56
\Sigma
0:3)
)
in
both
cases
results
compatible
within
statistical
uncertainties
)
contribution
to
systematic
errors
neglected
Selection
of
W­Pairs
with
Feed­Forward
NN
ACAT2002
­
Moscow
­
June
24­28
2002
Uwe
M¨
uller

Pruning
in
the
first
analysis
architecture
13­7­1
was
selected
by
trial­and­error
now
test
of
a
pruning
procedure
(implemented
in
Jetnet)
to
verify
or
find
an
optimal
architecture
ffl
pruning
by
adding
complexity
term
to
fitness
error
E
!
E
+
–
P
ij
!
2
ij
=!
2
0
1+!
2
ij
=!
2
0
ffl
parameters
–
and
!
2
0
also
used
for
updating
the
weights
additional
parameter
D
as
threshold
for
procedure
(i.e.
how
much
pruning)
ffl
number
of
hidden
nodes
was
reduced
depending
on
value
of
D
ffl
when
starting
with
more
than
4
nodes
in
hidden
layer
and
D
=
1
number
was
reduced
to
4
ffl
4
hidden
nodes
were
reduced
to
3
)
in
all
tests
selection
quality
(''
\Theta
p)
much
better
than
cut
anlysis
but
slightly
worse
than
NN
without
pruning
Selection
of
W­Pairs
with
Feed­Forward
NN
ACAT2002
­
Moscow
­
June
24­28
2002
Uwe
M¨
uller

Systematic
Studies
@
189
GeV
systematic
errors
of
signal
efficiency
and
remaining
background
necessary
basis
for
error
of
cross
section
systematic
studies
using
NN
like
mathematical
function
(black
box)
fixed
training,
always
the
same
cut
ffl
comparison
of
MC
generators
with
different
hadronisation
models,
different
parameter
settings
and
fsi
models
ffl
data­MC­agreement
using
the
technique
of
mixed
Lorentz­boosted
Z
0
ffl
smearing
of
input
variables
taking
detector
resolution
into
account
Selection
of
W­Pairs
with
Feed­Forward
NN
ACAT2002
­
Moscow
­
June
24­28
2002
Uwe
M¨
uller

Final
Result
@
189
GeV
ffl
systematic
effect
on
efficiency
and
background
for
each
method
ffl
combination
of
different
systematics
taking
into
account
correlations
between
methods
ffl
determination
of
cross
section
from
binned
maximum
likelihood
fit
to
output
distribution
taking
into
account
the
expected
background
final
result
for
NN
analysis:
oe
W
+
W
\Gamma
!qqqq
=
7:36
\Sigma
0:26
(stat)
\Sigma
0:10
(syst)
pb
as
comparison
result
for
linear
cuts:
oe
W
+
W
\Gamma
!qqqq
=
7:56
\Sigma
0:28
(stat)
pb
(systematic
error
expected
to
be
compatible
to
NN
analysis)
Selection
of
W­Pairs
with
Feed­Forward
NN
ACAT2002
­
Moscow
­
June
24­28
2002
Uwe
M¨
uller

Summary
ffl
successful
application
of
feed­forward
neural
network
in
direct
selection
of
hadronic
WW­candidates
at
Delphi
ffl
significant
improvement
in
selection
quality
compared
to
old
standard
analysis
)
final
Delphi
cross
section
analysis
based
on
this
selection
procedure
ffl
different
tests
of
network
stability
--
variation
of
preselection
--
change
of
network
parameters,
configuration
and
architecture
ffl
complete
determination
of
systematic
error
for
publication
--
tests
of
network
stability
found
to
be
negligible
--
based
on
ideas
for
linear
cut
analyses
--
neural
network
as
mathematical
function
Selection
of
W­Pairs
with
Feed­Forward
NN
ACAT2002
­
Moscow
­
June
24­28
2002
Uwe
M¨
uller