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