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NN
PD
F:
Fai
thfu
l N
NP
DF
: F
aith
ful
Par
tons
Par
tons
•P
arto
nF
itti
ng:
Pro
ble
ms
and S
olu
tions
•D
IS f
its:
NN
PD
F 1
.0 –
1.2
•G
lobal
fit
ting:
NN
PD
F 2
.0
RD
B,
Lu
igi
Del
Deb
bio
, S
tefa
no
Fort
e, A
lber
to G
uff
anti
,
Jose
Lat
orr
e, A
ndre
a P
icci
on
e, J
uan
Rojo
, M
aria
Ub
iali
(Bar
celo
na,
Ed
inburg
h, F
reib
urg
, M
ilan
)
Cam
bri
dge
June
2009
PD
Fs
for
LH
C
To f
ull
y e
xplo
it L
HC
dat
a, w
e nee
d:
•P
reci
se r
elia
ble
fai
thfu
l P
DF
s
•N
o t
heo
reti
cal
bia
s (b
eyond N
LO
pQ
CD
, et
c.)
No
bia
s d
ue
to f
un
ctio
nal
form
No
bia
s du
e to
im
pro
per
sta
tist
ical
pro
cedure
•G
enuin
e st
atis
tica
l co
nfi
den
ce l
evel
Fu
ll i
ncl
usi
on
of
corr
elat
ion
s in
exp
syst
emat
ics
No
res
cali
ng
of
exp
erim
enta
l er
rors
Un
iform
tre
atm
ent
of
un
cert
ain
ties
PD
Fs
for
LH
C
To f
ull
y e
xplo
it L
HC
dat
a, w
e nee
d:
•P
reci
se r
elia
ble
fai
thfu
l P
DF
s
•N
o t
heo
reti
cal
bia
s (b
eyond N
LO
pQ
CD
, et
c.)
No
bia
s d
ue
to f
un
ctio
nal
form
No
bia
s du
e to
im
pro
per
sta
tist
ical
pro
cedure
•G
enuin
e st
atis
tica
l co
nfi
den
ce l
evel
Fu
ll i
ncl
usi
on
of
corr
elat
ion
s in
exp
syst
emat
ics
No
res
cali
ng
of
exp
erim
enta
l er
rors
Un
iform
tre
atm
ent
of
un
cert
ain
ties
Zer
o T
ole
ran
ce!
hep
-ph
/051
1119
HE
RA
-LH
C B
ench
mar
k3163 D
IS d
ata →
773 d
ata
•B
ench
mar
k p
arto
ns
and g
lobal
par
tons
dis
agre
e!
•∆
χ2
glo
bal=
50 b
ut
∆χ
2b
ench
=1:
stat
isti
cal
trea
tmen
t tu
ned
HE
RA
-LH
C B
ench
mar
k3163 D
IS d
ata →
773 d
ata
•N
NP
DF
: ben
chm
ark p
arto
ns
and g
lobal
par
tons
agre
e!
•N
NP
DF
:∆
χ2
glo
bal=
∆χ
2b
ench
=1:
stat
isti
cal
trea
tmen
t co
nsi
sten
t
Th
eory
PD
F E
nse
mble
s
Fo
rte,
Gar
rid
o, L
ato
rre
& P
icci
on
e, h
ep-p
h/0
20
42
32
Gie
le, K
elle
r an
d K
oso
wer
, h
ep-p
h/0
10
405
2
Pro
duci
ng t
he
PD
F E
nse
mble
s
•G
ener
ate
by M
onte
Car
lo N
rep
lica
s o
f th
e
exp
erim
enta
l dat
a se
ts, d
istr
ibu
ted
acc
ord
ing t
o
the
exp
erim
enta
l un
cert
ain
ties
.
N.B
. use
all
kno
wn
corr
elat
ed u
nce
rtai
nti
es
Pro
duci
ng t
he
PD
F E
nse
mble
s
•G
ener
ate
by M
onte
Car
lo N
rep
lica
s o
f th
e
exp
erim
enta
l dat
a se
ts, d
istr
ibu
ted
acc
ord
ing t
o
the
exp
erim
enta
l un
cert
ain
ties
.
N.B
. use
all
kno
wn
corr
elat
ed u
nce
rtai
nti
es
•F
it a
pd
fto
eac
h r
epli
ca. T
he
resu
ltin
g
ense
mb
le o
f p
dfs
mu
st t
hen
rep
rod
uce
th
e d
ata
wit
h c
om
bin
ed u
nce
rtai
nti
es p
rov
idin
g t
he
fitt
ing
is
itse
lf u
nb
iase
d.
Unb
iase
d f
itti
ng
req
uir
es
(a)
a re
du
nd
ant
par
amet
riza
tion
(lar
ge
num
ber
s of
‘fla
t’ d
irec
tio
ns)
: n
eura
l n
ets
(b)
a st
opp
ing
cri
teri
on (
so a
s no
t to
fit
stat
isti
cal
flu
ctuat
ion
s)
Flo
w c
har
t
Dat
a R
epli
cas
Fit
ting
NL
O p
QC
D
PD
F E
nse
mble
In a
sta
ndar
d f
it, m
inim
ise
a χ
2w
ith a
giv
en p
aram
etri
zati
on
•If
the
bas
is i
s to
o l
arge,
the
fit
nev
er c
onver
ges
•If
the
bas
is i
s to
o s
mal
l, t
he
fit
is b
iase
d
Q.
How
can
we
be
sure
that
the
com
pro
mis
e is
unbia
sed?
A.U
se a
neu
ral
net
work
: sm
ooth
nes
s dec
reas
es a
s fi
t
qual
ity i
mpro
ves
Why N
eura
l N
etw
ork
s?
Model
χ2∼
2
Why N
eura
l N
etw
ork
s?
In a
sta
ndar
d f
it, m
inim
ise
a χ
2w
ith a
giv
en p
aram
etri
zati
on
•If
the
bas
is i
s to
o l
arge,
the
fit
nev
er c
onver
ges
•If
the
bas
is i
s to
o s
mal
l, t
he
fit
is b
iase
d
Q.
How
can
we
be
sure
that
the
com
pro
mis
e is
unbia
sed?
A.U
se a
neu
ral
net
work
: sm
ooth
nes
s dec
reas
es a
s fi
t
qual
ity i
mpro
ves
Model
χ2∼
1
Why N
eura
l N
etw
ork
s?
In a
sta
ndar
d f
it, m
inim
ise
a χ
2w
ith a
giv
en p
aram
etri
zati
on
•If
the
bas
is i
s to
o l
arge,
the
fit
nev
er c
onver
ges
•If
the
bas
is i
s to
o s
mal
l, t
he
fit
is b
iase
d
Q.
How
can
we
be
sure
that
the
com
pro
mis
e is
unbia
sed?
A.U
se a
neu
ral
net
work
: sm
ooth
nes
s dec
reas
es a
s fi
t
qual
ity i
mpro
ves
Model
χ2∼
0
Q.
How
do w
e know
wh
en t
o s
top t
he
fitt
ing (
‘tra
inin
g’)
A.
Use
cro
ss-v
alid
atio
n
•D
ivid
e dat
a (r
andom
ly)
into
‘tr
ainin
g’
and ‘
val
idat
ion’
sets
•T
rain
net
on ‘
trai
nin
g’
set,
monit
ori
ng f
it t
o ‘
val
idat
ion’
set
•S
top w
hen
fit
to ‘
val
idat
ion’
set
is n
o l
onger
im
pro
vin
g .
Sto
ppin
g
Too L
ate!
Hig
h f
inal
χ2
mea
ns
dat
a er
rors
under
esti
mat
ed
Low
fin
al χ
2m
eans
dat
a er
rors
over
esti
mat
ed
Res
ult
s
NN
PD
F1.0
Aug
2008
DIS
dat
a:•
Fix
ed T
arg
et
•H
ER
A N
C &
CC
•N
eutr
ino
(C
HO
RU
S)
Cuts
:Q
2>
2 G
eV2
W2
> 1
2.5
GeV
2
NL
O p
QC
D
ZM
-VF
NS
Fit
5 P
DF
sat
Q0
2=
2 G
eV2:
Assum
e
5 ×
37
=1
85
par
amet
ers!
3161
dat
a p
ts
Glu
ons
: in
div
idual
rep
lica
s
…an
d r
elat
ive
unce
rtai
nty
•N
NP
DF
: G
enu
ine
68%
CL
•E
rro
r no
t ar
tifi
cial
ly i
nfl
ated
Zero
To
lera
nce!
•E
rro
r n
atura
lly l
arg
e
in e
xtr
apola
tio
n r
egio
n
Sta
nd
ard
Can
dle
s at
LH
C
Incl
ud
es h
eav
y q
uar
k m
ass
effe
cts
NN
PD
F1.2
Ju
n 2
009
Add t
o D
IS d
ata
NuT
evdim
uon
dat
a: s
ensi
tive
to
stra
ngen
ess
Use
I-Z
MV
FN
S
(slo
w r
esca
ling e
tc)
for
dim
uo
nxse
c
(sen
siti
ve
to c
har
m m
ass)
Fit
7 P
DF
sat
Q0
2=
2 G
eV2:
7 ×
37
=2
59
par
amet
ers!
3372
dat
a p
ts
wit
ho
ut
dim
uo
nd
ata
wit
h d
imu
on
dat
a
no
su
m r
ule
sum
ru
le
Sin
gle
t
Glu
on
Sta
bil
ity
Str
ange
mom
entu
m f
ract
ion
Co
mple
te p
robab
ilit
y d
istr
ibuti
on:
larg
e as
ym
met
ric
erro
r
CK
M e
lem
ents
Vcd
and V
cs
Des
pit
e la
rge
unce
rtai
nty
in s
+, ca
n s
till
det
erm
ine
Vcs
Bes
t dir
ect
det
erm
inat
ion o
f V
cs
Val
ence
Str
ang
enes
s
Par
amet
riza
tion
ver
y f
ree:
≥1
cro
ssin
g
Ver
y l
arge
unce
rtai
nty
NuT
eVA
nom
aly
GO
NE
!
NN
PD
F2.0
(tr
uly
glo
bal
fit
)P
reli
min
ary
Add t
o D
IS d
ata
dim
uon
dat
a:
•D
Y d
ata
.
•W
/Z a
sym
md
ata
•In
clu
siv
e je
ts
.
No K
-fac
tors
: U
se F
astN
LO
for
jets
Hav
e new
Fas
tNL
O-t
ype
code
for
DY
Pre
lim
inar
y
NB
: N
NP
DF
1.2
fit
alr
eady g
ood…
Pre
lim
inar
y
Pre
lim
inar
y
Val
ence
dbar
Red
uce
d u
nce
rtai
nti
es i
n v
alen
ce s
ecto
r
Sum
mar
y &
Outl
ook
Sum
mar
y &
Outl
ook
•N
NP
DF
work
s :
1.0
(D
IS),
1.2
(+
dim
uon)
See
for
yours
elf:
htt
p:/
/pro
ject
s.hep
forg
e.org
/lhap
df
•N
ew d
irec
t det
erm
inat
ion o
f V
cs:
no N
uT
eVan
om
aly
•G
lobal
fit
s :
2.0
(+
DY
+W
/Z+
jets
)
ET
A:
Sep
2009
•F
or
the
futu
re:
hea
vy q
uar
ks,
res
um
mat
ion, N
NL
O, et
c, e
tc,
Sum
mar
y &
Outl
ook
Sum
mar
y &
Outl
ook
•N
NP
DF
work
s :
1.0
(D
IS),
1.2
(+
dim
uon)
See
for
yours
elf:
htt
p:/
/pro
ject
s.hep
forg
e.org
/lhap
df
•N
ew d
irec
t det
erm
inat
ion o
f V
cs:
no N
uT
eVan
om
aly
•G
lobal
fit
s :
2.0
(+
DY
+W
/Z+
jets
)
ET
A:
Sep
2009
•F
or
the
futu
re:
hea
vy q
uar
ks,
res
um
mat
ion, N
NL
O, et
c, e
tc,
Watc
h t
his
space
!W
atc
h t
his
space
!
Pap
ers
•U
nb
iase
d D
eter
min
atio
n o
f th
e P
roto
n S
tru
ctu
re F
un
ctio
n F
2p
wit
hF
aith
ful
Un
cert
ain
ty E
stim
atio
n
JHE
P 0
50
3(2
00
5)0
80
; h
ep-p
h/0
50
106
7
•N
eura
l N
etw
ork
Ap
pro
ach
to
Par
ton
Dis
trib
uti
on
Fit
tin
g
Nu
cl.I
nst
r.M
eth
. A
55
9(2
00
6)2
03
; h
ep-p
h/0
50
906
7
•N
eura
l N
etw
ork
Det
erm
inat
ion
of
Par
ton
Dis
trib
uti
on
s: T
he
No
nsi
ng
let
Cas
e
JHE
P 0
70
3(2
00
7)0
39
; h
ep-p
h/0
70
112
7
•A
Det
erm
inat
ion
of
Par
ton
Dis
trib
uti
on
s w
ith
Fai
thfu
l U
nce
rtai
nty
Est
imat
ion
[NN
PD
F1
.0]
Nu
cl. P
hys.
B8
09
(20
09
)1;
arX
iv:0
80
81
23
1
•U
pd
ate
on
Neu
ral
Net
wo
rk P
arto
nD
istr
ibu
tio
ns
[N
NP
DF
1.1
]
arX
iv:0
81
1.2
28
8
•P
reci
sio
n D
eter
min
atio
n o
f E
lect
row
eak
Par
am
eter
s an
d t
he
Str
ang
e C
on
ten
t
of
the
Pro
ton
fro
m N
eutr
ino
Dee
p I
nel
asti
c S
catt
erin
g [
NN
PD
F1
.2]
arX
iv:0
60
9??
? (i
mm
inen
t)
Ex
tra
slid
es
NN
PD
F1.0
Ben
chm
ark
Aug
2008
Str
ang
enes
s: N
NP
DF
1.1
N
ov
2008
Sam
e dat
a: a
dd t
wo m
ore
pdfs
Pre
pro
cess
ing:
Sto
ppin
g
Q.
How
do w
e know
wh
en t
o s
top t
he
fitt
ing (
‘tra
inin
g’)
?
A.
Use
cro
ss-v
alid
atio
n
•D
ivid
e dat
a (r
andom
ly)
into
‘tr
ainin
g’
and ‘
val
idat
ion’
sets
Rea
l F
2dat
a
Sto
ppin
g
Q.
How
do w
e know
wh
en t
o s
top t
he
fitt
ing (
‘tra
inin
g’)
A.
Use
cro
ss-v
alid
atio
n
•D
ivid
e dat
a (r
andom
ly)
into
‘tr
ainin
g’
and ‘
val
idat
ion’
sets
•T
rain
net
on ‘
trai
nin
g’
set,
monit
ori
ng f
it t
o ‘
val
idat
ion’
set
GO
!
Sto
ppin
g
Q.
How
do w
e know
wh
en t
o s
top t
he
fitt
ing (
‘tra
inin
g’)
A.
Use
cro
ss-v
alid
atio
n
•D
ivid
e dat
a (r
andom
ly)
into
‘tr
ainin
g’
and ‘
val
idat
ion’
sets
•T
rain
net
on ‘
trai
nin
g’
set,
monit
ori
ng f
it t
o ‘
val
idat
ion’
set
•W
hen
fit
to ‘
trai
nin
g’
set
bet
ter
than
fit
to ‘
val
idat
ion’
set.
..
ST
OP
Q.
How
do w
e know
wh
en t
o s
top t
he
fitt
ing (
‘tra
inin
g’)
A.
Use
cro
ss-v
alid
atio
n
•D
ivid
e dat
a (r
andom
ly)
into
‘tr
ainin
g’
and ‘
val
idat
ion’
sets
•T
rain
net
on ‘
trai
nin
g’
set,
monit
ori
ng f
it t
o ‘
val
idat
ion’
set
•W
hen
fit
to ‘
trai
nin
g’
set
bet
ter
than
fit
to ‘
val
idat
ion’
set
.
Sto
ppin
g
Too L
ate!
Hig
h χ
2m
eans
bad
dat
a, n
ot
bad
fit