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First global NNPDF analysis

Maria Ubiali

University of Edinburgh& Universite Catholique de Louvain

Rencontres de Moriond, QCD session19th March 2010

TH

E

UN I V E

RS

IT

Y

OF

ED

I N BU

R

GH

“A first unbiased global NLO determination of parton distribution functions”arXiv:1002.4407

The NNPDF CollaborationR.D.Ball1, L.Del Debbio1 , S.Forte2, A.Guffanti3 , J.I.Latorre4, J. Rojo2 , M.U.1,5

1 PPT Group, School of Physics, University of Edinburgh2 Dipartimento di Fisica, Universita di Milano

3 Physikalisches Institut, Albert-Ludwigs-Universitat Freiburg4 Departament d’Estructura i Constituents de la Materia, Universitat de Barcelona

5 CP3, Universite Catholique de Louvain, Chemin du Cyclotron, 1348 Louvain-la-Neuve, Belgium

Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 1 / 53

Outline

1 Introduction

2 NNPDF method

3 NNPDF2.0: a global fit

4 Conclusions and outlook


IntroductionParton Distribution Functions

Factorization Theorem (Q2 ≫ Λ2QCD):

dσH

dX=

∑

a,b

∫

dx1dx2fa(x1, µf )fb(x2, µf )⊗d σab

dX(αs(µr ), µr , µf , x1, x2,Q

2)

DGLAP equations:

d

dt

(

q

g

)

=αs

2π

(

Pqq Pqg

Pgq Pgg

)

⊗

(

q

g

)

+O(α2s )

PDFs and their associated uncertainties willplay a crucial role in the full exploitation ofthe LHC physics potential.


IntroductionIssues in the standard approach

Given a set of data points we must determine a set of functions with errors.

We need an error band in the space of functions, i.e. a probability density P[f (x)] inthe space of PDFs, f(x). For an observable F depending on PDFs :

〈F [f (x)]〉 =

∫

[Df ]F [f (x)]P[f (x)]

Standard approach

1 Choose a specific functional form

qi (x,Q20 ) = Aix

bi (1 − x)ci (1 + ...)

2 Determine best-fit values of parameters whichdefine the functions

3 Errors determined via gaussian linear errorpropagation and large tolerance

∆χ2 ≫ 1

Issues

1 Parametrization: how can we know that it isflexible enough and does not introduce atheoretical bias?

2 Large tolerance T =√

∆χ2 means that errorsare blown up by

S =√

∆χ2/2.7

3 Benchmark partons do not agree with globalpartons within errors


MotivationHistorical overview

Monte Carlo representation ofthe probability measure in thespace of functions

Use of neural network asredundant and unbiasedparametrization

Structure functions [hep-ph/0501067]

Non-singlet PDF q− = u + d − (u + d) [hep-ph/0701127]

DIS global analysis: NNPDF1.0 [arXiv:0808.1231]

Determination of the strange content: NNPDF1.2 [arXiv:0906.1958]

Global (DIS+DY+JET) analysis: NNPDF2.0 [arXiv:1002.4407]

All sets are available in the LHAPDF interface


MotivationWhat’s nice about NNPDF #1

1) Monte Carlo behaves in a statistically con-sistent way

Generate a Monte Carlo ensemble in thespace of data

N pseudo–data reproduce the probabilitydistribution of the original experimentaldata.

Precision of estimators scales as the size ofthe sample.

x-510 -410 -310 -210 -110 1

) 02xg

(x,

Q

-2

-1

0

1

2

3

4CTEQ6.5MRST2001E

Alekhin02

NNPDF1.0

x-510 -410 -310 -210 -110 1

) 02xg

(x,

Q

-2

-1

0

1

2

3

4

Gluon PDF

CTEQ6.5

MRST2001E

Alekhin02

NNPDF08 prelim.

Gluon PDF

0.0001

0.001

0.01

0.1

1

10

100

0.0001 0.001 0.01 0.1 1 10

Mon

te C

arlo

rep

licas

Experimental data

NNPDF1.2 - Errors

Nrep=10 Nrep=100 Nrep=1000

2) Results are shown to be independent ofthe parametrization and even stable upon theaddition of independent PDFs parametriza-tions

7x37 pars → 7x31 pars



3) PDFs behave as expected upon theaddition of new data

HERA-LHC benchmark: DIS data

x-510 -410 -310 -210 -110 1

)2 (

GeV

2Q

1

10

210

310

410 NNPDF1.0

NNPDF_bench_H-Lx

-210 -110 1

)2 0xu

(x,Q

0

0.2

0.4

0.6

0.8

1

1.2NNPDF1.0

NNPDF1.0 [bench*]

MRST2001E

MRST bench

x-510 -410 -310 -210 -110 1

)2 0xu

(x,Q

0

0.2

0.4

0.6

0.8

1

1.2NNPDF1.0

NNPDF1.0 [bench*]

MRST2001E

MRST bench

4) Control on PDFs uncertainties: NuteV anomalysolved AND Vcs precise determination at the same time[NNPDF1.2 [arXiv:0906.1958]]


NNPDF approachGeneral scheme

Frepi

(k) = S(k)i,N

Fexpi

1 + r(k)i

σstati +

Nsys∑

j=1

r(k)i,j

σsysi,j

r(k)i,j

= r(k)

i′,jif i and i’ correlated

Experimental Data

MC generation

NN parametrization

Fi i=1,...,Ndata

NMC,BCDMS,SLAC,HERA,CHORUS...

Fi(1) Fi(2) Fi(N)Fi(N-1)

q0net(1) q0net(2) q0net(N-1) q0net(N)

REPRESENTATION OF

PROBABILITY DENSITY

EVOLUTION

TRAINING


NNPDF approachMain Ingredients

1 Monte Carlo determination of errors:

〈F [f (x)]〉 =1

Nrep

Nrep∑

k=1

F [f (k)(net)(x)]

σF [f (x)] =√

〈F [f (x)]2〉 − 〈F [f (x)]〉2

-2

-1

0

1

2

3

4

1e-05 0.0001 0.001 0.01 0.1 1

xg(x

,Q02 )

x

Nrep=100

2 Neural Networks as redundant and unbiased parametrisation of PDFs:Σ(x) 7−→ NNΣ(x) 2-5-3-1 37 pars

g(x) 7−→ NNg (x) 2-5-3-1 37 pars

V (x) 7−→ NNV (x) 2-5-3-1 37 pars

T3(x) 7−→ NNT3(x) 2-5-3-1 37 pars

∆S (x) ≡ d(x) − u(x) 7−→ NN∆(x) 2-5-3-1 37 pars

s+(x) ≡ (s(x) + s(x))/2 7−→ NN(s+)(x) 2-5-3-1 37 pars

s−

(x) ≡ (s(x) − s(x))/27−→ NN(s−)(x) 2-5-3-1 37 pars

3 Dynamical stopping criterion in order to fit data and not statistical noise (259 pars).

GA generations0 5000 10000 15000 20000 25000 30000 35000 40000 45000 500001

1.5

2

2.5

3

3.5

DYE605

trE valE

targetE

DYE605

* Divide data in two sets: training and validation.

* Minimisation is performed only on the training set.The validation χ2 for the set is computed.

* When the training χ2 still decreases while thevalidation χ2 stops decreasing → STOP.


NNPDF2.0Data sets

x-510 -410 -310 -210 -110 1

]2 [

GeV

2 T /

p2

/ M

2Q

1

10

210

310

410

510

610 NMC-pdNMCSLACBCDMSHERAI-AVCHORUSFLH108NTVDMNZEUS-H2DYE605DYE886CDFWASYCDFZRAPD0ZRAPCDFR2KTD0R2CON

NNPDF2.0 dataset

3477 data points

For comparison MSTW08 includes 2699 data points

OBS Data sets

Fp2

NMC,SLAC,BDCMS

Fd2 SLAC,BCDMS

Fd2 /Fp2

NMC-pd

σNC HERA-I AV, ZEUS-H2

σCC HERA-I AV, ZEUS-H2

FL H1

σν, σν CHORUS

dimuon prod. NuTeV

dσDY/dM2dy E605

dσDY/dM2dxF E886

W asymmetry CDF

Z rap. distr. CDF,D0

incl. σ(jet) D0(cone) Run II

incl. σ(jet) CDF(kT ) Run II

Kinematical cuts on DIS dataQ2 >2 GeV2

W 2 = Q2(1 − x)/x >12.5 GeV2

No cuts on hadronic data


NNPDF2.0FastKernel

NLO computation of hadronic observablestoo slow for parton global fits.

MSTW08 and CTEQ include Drell-YanNLO as (local) K factors rescaling the LOcross section

K-factor depends on PDFs and it is notalways a good approximation.

0 0.5 1 1.5 2 2.5

y

0.00001

10ˉ⁴

10ˉ³

10ˉ²

0.1

E605

E886p

E886r

Wasy

Zrap

FastKernel METHOD

* NNPDF2.0 includes full NLOcalculation of hadronic observables.

* Use available fastNLO interface for jetinclusive cross-sections.[hep-ph/0609285]

* Built up our own FastKernelcomputation of DY observables.

Both PDFs evolution and doubleconvolution sped up

Use high-orders polynomialinterpolation

Precompute all Green Functions

∫

1

x0,1

dx1

∫

1

x0,2

dx2 fa(x1)fb (x2)Cab

(x1, x2) →

Nx∑

α,β=1

fa(x1,α)fb (x2,β )

∫

1

x0,1

dx1

∫

1

x0,2

dx2 I(α,β)(x1, x2)C

ab(x1, x2)


ResultsStatistical features: global χ2

tr(k)

E1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

0

0.1

0.2

0.3

0.4

0.5

distribution for MC replicastrE distribution for MC replicastrE

2(k)χ1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8

0

0.1

0.2

0.3

0.4

0.5

0.6

distribution for MC replicas2(k)χ distribution for MC replicas2(k)χ

Training lenght [GA generations]0 5000 10000 15000 20000 25000 30000

0

0.05

0.1

0.15

0.2

0.25

0.3

Distribution of training lenghtsDistribution of training lenghts

χ2tot 1.21

〈E〉 ± σE 2.32 ± 0.10〈Eval〉 ± σEval

2.29± 0.11〈Eval〉 ± σEval

2.35± 0.12〈TL〉 ± σTL 16175 ± 6275

⟨

χ2(k)⟩

± σχ2 1.29± 0.09


ResultsStatistical features: individual experiments

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

for sets2χDistribution of

NMC-pd

NMC

SLACp

SLACd

BCDMSp

BCDMSd

HERA1-NCep

HERA1-NCem

HERA1-CCep

HERA1-CCem

CHORUSnu

CHORUSnb

FLH108

NTVnuDMN

NTVnbDMN

Z06NC

Z06CC

DYE605

DYE886p

DYE886r

CDFWASY

CDFZRAP

D0ZRAP

CDFR2KT

D0R2CON

for sets2χDistribution of

No obvious data incompatibility


ResultsComparison to data included in the fit

x-210 -110 1

)2=1

5 G

eV2

(x,

Qp 2F

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8NNPDF1.0

NNPDF1.2

NNPDF2.0

DATA

Fx0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

)2=2

5 G

eV2

, M F (

x2

/dM

F/d

xD

Yσ

d

0

2

4

6

8

10

12

14

16

18

20

22NNPDF1.0

NNPDF1.2

NNPDF2.0

DATA

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 20 40 60 80 100

( D

ata

- T

heor

y )

/ Err

or

Data Point

D0 Run II Inclusive jet production

NNPDF2.0Experimental data

2x0.05 0.1 0.15 0.2 0.25 0.3

) 2 (

x2

/dM

F/d

xp

p,D

Yσ

)/2d

2 (

x2

/dM

F/d

xp

d,D

Yσd 0.8

0.9

1

1.1

1.2

1.3

1.4NNPDF1.0

NNPDF1.2

NNPDF2.0

DATA


ResultsPartons

x-510 -410 -310 -210 -110 1

) 02xg

(x,

Q

-2

-1

0

1

2

3

4 NNPDF2.0

NNPDF1.0

NNPDF1.2

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02xg

(x,

Q

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7NNPDF2.0

NNPDF1.0

NNPDF1.2

x-510 -410 -310 -210 -110 1

) 02 (

x, Q

Σx

0

1

2

3

4

5

6NNPDF2.0

NNPDF1.0

NNPDF1.2

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02

(x,

Q3

xT

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5NNPDF2.0

NNPDF1.0

NNPDF1.2

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02xV

(x,

Q

0

0.2

0.4

0.6

0.8

1

1.2NNPDF2.0

NNPDF1.0

NNPDF1.2

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

)02

(x,

QS

∆x

-0.02

0

0.02

0.04

0.06

0.08

0.1NNPDF2.0

NNPDF1.0

NNPDF1.2

x-510 -410 -310 -210 -110 1

) 02 (

x, Q

+xs

-1

-0.5

0

0.5

1

1.5

2NNPDF2.0

NNPDF1.0

NNPDF1.2

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02 (

x, Q

+xs

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3NNPDF2.0

NNPDF1.0

NNPDF1.2

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

)02

(x,

Q-

xs

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06NNPDF2.0

NNPDF1.0

NNPDF1.2


ResultsPartons

x-510 -410 -310 -210 -110 1

) 02xg

(x,

Q

-2

-1

0

1

2

3

4 NNPDF2.0CTEQ6.6

MSTW 2008

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02xg

(x,

Q

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7NNPDF2.0CTEQ6.6

MSTW 2008

x-510 -410 -310 -210 -110 1

) 02 (

x, Q

Σx

0

1

2

3

4

5

6NNPDF2.0CTEQ6.6

MSTW 2008

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02

(x,

Q3

xT

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5NNPDF2.0CTEQ6.6

MSTW 2008

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02xV

(x,

Q

0

0.2

0.4

0.6

0.8

1

1.2 NNPDF2.0CTEQ6.6

MSTW 2008

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

)02

(x,

QS

∆x

-0.02

0

0.02

0.04

0.06

0.08

0.1NNPDF2.0CTEQ6.6

MSTW 2008

x-510 -410 -310 -210 -110 1

) 02 (

x, Q

+xs

-1

-0.5

0

0.5

1

1.5

2NNPDF2.0CTEQ6.6

MSTW 2008

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02 (

x, Q

+xs

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3NNPDF2.0CTEQ6.6

MSTW 2008

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

)02

(x,

Q-

xs

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06NNPDF2.0CTEQ6.6

MSTW 2008


ResultsPartons

x-510 -410 -310 -210 -110

) 02xg

(x,

Q

0

1

2

3

4

5

6NNPDF2.0CTEQ6.6

MSTW 2008

x-510 -410 -310 -210 -110

) 02 (

x, Q

+xs

0

0.5

1

1.5

2

2.5

3

3.5

4NNPDF2.0CTEQ6.6

MSTW 2008

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

) 02

(x,

Q3

xT

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045NNPDF2.0CTEQ6.6

MSTW 2008

Reduction of uncertainties with respect toolder NNPDF sets.

Small uncertainties due to excellent datacompatibility.

Uncertainty larger than other groups whenMSTW/CTEQ parametrizations are toorestrictive.


Impact of modificationsA quantitative assessment

A quantitative assessment is possible

d(qj ) =

√

√

√

√

√

⟨(

〈qj〉(1) − 〈qj〉(2))2

σ21 [qj ] + σ2

2 [qj ]

⟩

Npart

d(σj ) =

√

√

√

√

√

⟨(

〈σj 〉(1) − 〈σj 〉(2))2

σ21 [σj ] + σ2

2 [σj ]

⟩

Npart

Comparisons performed in NNPDF2.0 analysis

1 Start from NNPDF1.2

2 NNPDF1.2 vs. NNPDF1.2 + minimization/training improvements

3 Improved NNPDF1.2 vs. Improved NNPDF1.2 + t0-method

4 Fit to DIS dataset with H1/ZEUS data vs. Fit with HERA-I combined

5 Fit to DIS dataset vs. Fit to DIS+JET

6 Fit to DIS+JET vs. NNPDF2.0 final


Impact of modificationsHERA-I combined dataset

Fit NNPDF1.2 NNPDF1.2+IGA NNPDF1.2+IGA+t0 2.0 DIS

χ2tot 1.32 1.16 1.12 1.20〈E〉 2.79 2.41 2.24 2.31

〈χ2(k)〉 1.60 1.28 1.21 1.29HERAI 1.05 0.98 0.96 1.13

HERA-I combined more precise.

Quality of other data unchanged.

Overall fit quality to the whole dataset isgood

σ+NC

dataset has relatively high

χ2 ∼ 1.3σ−CC

dataset has very low χ2 ∼ 0.55

Same χ2-pattern observed in theHERAPDF1.0 analysis

Impact on PDFs, mainly Singlet andGluon at small-x

x-510 -410 -310 -210 -110 1

) 02xg

(x,

Q

-4

-3

-2

-1

0

1

2

3

4

5

NNPDF2.0 DIS(HERAold)

NNPDF2.0 DIS

x-510 -410 -310 -210 -110 1

) 02 (

x, Q

Σx

0

1

2

3

4

5

6

NNPDF2.0 DIS(HERAold)

NNPDF2.0 DIS


Impact of modificationsTevatron inclusive Jet data

Fit NNPDF1.2 NNPDF1.2+IGA NNPDF1.2+IGA+t0 2.0 DIS 2.0 DIS+JET

χ2tot 1.32 1.16 1.12 1.20 1.18

〈E〉 2.79 2.41 2.24 2.31 2.28

〈χ2(k)〉 1.60 1.28 1.21 1.29 1.27CDFR2KT 1.10 0.95 0.78 0.91 0.79D0R2CON 1.18 1.07 0.94 1.00 0.93

Tevatron Run-II inclusive jet dataprovide a valuable constrain onlarge-x gluon.

No incompatibility.

Run-I data not included butcompatibility with the outcome ofthe fit has been checked.

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02xg

(x,

Q

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

NNPDF2.0 - DIS

NNPDF1.2 - DIS + JET

x-510 -410 -310 -210 -110 1

) 02 (

x, Q

Σx

0

1

2

3

4

5

6

NNPDF2.0 DIS+JET

NNPDF2.0 DIS


Impact of modificationsDrell-Yan and Vector Boson production data

Fit NNPDF1.2 NNPDF1.2+IGA NNPDF1.2+IGA+t0 2.0 DIS 2.0 DIS+JET NNPDF2.0

χ2tot 1.32 1.16 1.12 1.20 1.18 1.21

〈E〉 2.79 2.41 2.24 2.31 2.28 2.32

〈χ2(k)〉 1.60 1.28 1.21 1.29 1.27 1.29

DYE605 11.19 22.89 8.21 7.32 10.35 0.88

DYE866 53.20 4.81 2.46 2.24 2.59 1.28

CDFWASY 26.76 28.22 20.32 13.06 14.13 1.85

CDFZRAP 1.65 4.61 3.13 3.12 3.31 2.02

D0ZRAP 0.56 0.80 0.65 0.65 0.68 0.47

Good description of fixed targetDrell-Yan data (E605 proton and E886proton and p/d ratio)

Vector boson production at colliders(CDF W-asymmetry and Z rapiditydistribution) harder to fit

All valence-type PDF combinations areaffected by these data

Sizable reduction in the uncertainty ofthe strange valence (possible impact onNuTeV anomaly)

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02

(x,

Q3

xT

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

NNPDF2.0 DIS+JET

NNPDF2.0

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02xV

(x,

Q

0

0.2

0.4

0.6

0.8

1

1.2 NNPDF2.0 DIS+JET

NNPDF2.0




χ2tot 1.32 1.16 1.12 1.20 1.18 1.21

〈E〉 2.79 2.41 2.24 2.31 2.28 2.32

〈χ2(k)〉 1.60 1.28 1.21 1.29 1.27 1.29

DYE605 11.19 22.89 8.21 7.32 10.35 0.88

DYE866 53.20 4.81 2.46 2.24 2.59 1.28

CDFWASY 26.76 28.22 20.32 13.06 14.13 1.85

CDFZRAP 1.65 4.61 3.13 3.12 3.31 2.02

D0ZRAP 0.56 0.80 0.65 0.65 0.68 0.47

Good description of fixed targetDrell-Yan data (E605 proton and E886proton and p/d ratio)

Vector boson production at colliders(CDF W-asymmetry and Z rapiditydistribution) harder to fit

All valence-type PDF combinations areaffected by these data

Sizable reduction in the uncertainty ofthe strange valence (possible impact onNuTeV anomaly)

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

)02

(x,

QS

∆x

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

NNPDF2.0 DIS+JET

NNPDF2.0

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

)02

(x,

Q-

xs

-0.02

-0.01

0

0.01

0.02

0.03

0.04

NNPDF2.0 DIS+JET

NNPDF2.0


Conclusion and outlook

Monte Carlo ensemble* Any statistical property of PDFs can be calculated using standard statistical methods.* No need of any tolerance criterion.

The Neural Network parametrization* Small uncertainties come from the data, not from bias due to functional form.* Inconsistent data or underestimated uncertainties do not require a separate treatment

and are automatically signalled by a larger value of the χ2.

The NNPDF2.0 is the fist unbiased global NLO fit [FastKernel].

Same consistent statistical behaviour under addition of hadronic data.

No signs of incompatibility between data!!!!

Available on the common LHAPDF interface (http://projects.hepforge.org/lhapdf)

The NNPDF2.X with FONLL (see Ref.ArXiv:1001.2312) with better treatment ofheavy quarks mass will be soon available.

The NNPDF2.Y NNLO fit is a work in progress.

THANK YOU!!


BACK-UP


IntroductionParton Distribution Functions

) (nb)ν± l→ ± B(W⋅ ±Wσ

20 20.5 21 21.5 22 22.5 23

) (

nb

)- l

+ l→ 0

B(Z

⋅ 0Zσ

1.9

1.92

1.94

1.96

1.98

2

2.02

2.04

2.06

2.08

2.1

W and Z total cross sections at the LHC

R(W/Z) = 10.5 10.6 10.7

MSTW08 NNLO

MRST06 NNLO

MRST04 NNLO

Alekhin02 NNLO

MSTW08 NLO

MRST06 NLO

MRST04 NLO

Alekhin02 NLO

CTEQ6.6 NLO

) (nb)ν± l→ ± B(W⋅ ±Wσ

20 20.5 21 21.5 22 22.5 23

) (

nb

)- l

+ l→ 0

B(Z

⋅ 0Zσ

1.9

1.92

1.94

1.96

1.98

2

2.02

2.04

2.06

2.08

2.1

) (nb)ν+ l→ + B(W⋅ +Wσ

11.6 11.8 12 12.2 12.4 12.6 12.8 13

) (

nb

)ν- l

→ - B

(W⋅ -

Wσ

8.5

8.6

8.7

8.8

8.9

9

9.1

9.2

9.3

9.4

9.5

total cross sections at the LHC- and W+W

) = -/W+R(W 1.30 1.35

1.40

MSTW08 NNLO

MRST06 NNLO

MRST04 NNLO

Alekhin02 NNLO

MSTW08 NLO

MRST06 NLO

MRST04 NLO

Alekhin02 NLO

CTEQ6.6 NLO

James Stirling ArXiv:0812.2341

For some standard candle processes at LHC the uncertainty on PDFs is thedominant one.

σ(Z 0) at LHC: δσPDG ∼ 2-3%, δσpert ∼ 1%

σ(W +,−) at LHC: δσPDG ∼ 3-4%


NNPDF approachIngredient ♯1: Monte Carlo Errors

Generate a Nrep Monte Carlo sets of artificial data, or ”pseudo-data” of the original Ndata

data points

F(art)(k)i (xp ,Q

2p) ≡ F

(art)(k)i,p i = 1, ...,Ndata

k = 1, ...,Nrep

Multi-gaussian distribution centered on each data point:

F(art)(k)i,p = S

(k)p,N F

exp

i,p

1 + r(k)p σstat

p +

Nsys∑

j=1

r(k)p,j σ

sys

p,j

If two points have correlated systematic uncertainties

r(k)p,j = r

(k)

p′,j

Correlations are properly taken into account.


NNPDF approachIngredient ♯1: Monte Carlo Errors

〈F [f (x)]〉 =1

Nrep

Nrep∑

k=1

F [f (k)(net)(x)]

σF [f (x)] =√

〈F [f (x)]2〉 − 〈F [f (x)]〉2

-2

-1

0

1

2

3

4

1e-05 0.0001 0.001 0.01 0.1 1

xg(x

,Q02 )

x

Nrep=25

-2

-1

0

1

2

3

4

1e-05 0.0001 0.001 0.01 0.1 1

xg(x

,Q02 )

x

Nrep=100

Even though individual replicas may fluctuate significantly, average quantities such ascentral values and error bands are smooth inasmuch as stability is reached due to thedimension of the ensemble increasing.


NNPDF approachIngredient ♯2: Neural Network as unbiased parametrization

Each independent PDF at the initial scale Q20 = 2GeV

2 is parameterized by an individualNN.

* Each neuron receives input from neurons inpreceding layer.

* Activation determined by weights andthresholds according to a non linear function:

ξi = g(∑

j

ωijξj − θi ), g(x) =1

1 + e−x

In a simple case (1-2-1) we have,

ξ(3)1 =

1

1 + eθ(3)1 −

ω(2)11

1+eθ(2)1

−ξ(1)1

ω(1)11

−ω(2)12

1+eθ(2)2

−ξ(1)1

ω(1)21

7 parameters

...Just a convenient functional formwhich provides a redundant and flex-ible parametrization.

We want the best fit to be indepen-dent of any assumption made on theparametrization.


NNPDF approachIngredient ♯2: Neural Network as unbiased parametrization

Basis set: Q20 = 2 GeV2

Singlet : Σ(x) 7−→ NNΣ(x) 2-5-3-1 37 pars

Gluon : g(x) 7−→ NNg (x) 2-5-3-1 37 pars

Total valence : V (x) ≡ uV (x) + dV (x) 7−→ NNV (x) 2-5-3-1 37 pars

Non-singlet triplet : T3(x) 7−→ NNT3(x) 2-5-3-1 37 pars

Sea asymmetry : ∆S(x) ≡ d(x)− u(x) 7−→ NN∆(x) 2-5-3-1 37 pars

Total strangeness : s+(x) ≡ (s(x) + s(x))/2 7−→ NN(s+)(x) 2-5-3-1 37 pars

Strangeness valence : s−(x) ≡ (s(x)− s(x))/2 7−→ NN(s−)(x) 2-5-3-1 37 pars

259 parameters


NNPDF approachIngredient ♯3: Training and dynamical stopping

Our fitting strategy is very different from that used by other collaborations: instead of aset of basis functions with a small number of parameters, we have an unbiased basis offunctions parameterized by a very large and redundant set of parameters.

CTEQ,MSTW,AL

O(20) parm

NNPDF

O(200) parm

Not trivial because ...

A redundant parametrization mightadapt not only to physical behavior butalso to random statistical fluctuations ofdata.

Ingredients of fitting procedure

1 Flexible and redundantparametrization

2 Genetic Algorithm minimization

3 Dynamical stopping criterion:cross-validation technique


NNPDF approachIngredient ♯3: Dynamical stopping

* GA is monotonically decreasing by construction.

* The best fit is not given by the absolute minimum.

* The best fit is given by an optimal training beyond which the figure of meritimproves only because we are fitting statistical noise of the data.

Cross-validation method

* Divide data in two sets: trainingand validation.

* Random division for each replica(ft = fv = 0.5).

* Minimisation is performed only onthe training set. The validation χ2

for the set is computed.

* When the training χ2 still decreaseswhile the validation χ2 stopsdecreasing → STOP. GA generations

0 5000 10000 15000 20000 25000 30000 35000 40000 45000 500001

1.5

2

2.5

3

3.5

DYE605

trE valE

targetE

DYE605



x-510 -410 -310 -210 -110 1

) 02xg

(x,

Q

-2

-1

0

1

2

3

4CTEQ6.5MRST2001E

Alekhin02

NNPDF1.0

x-510 -410 -310 -210 -110 1

) 02xg

(x,

Q

-2

-1

0

1

2

3

4

Gluon PDF

CTEQ6.5

MRST2001E

Alekhin02

NNPDF08 prelim.

Gluon PDF

Results are statistically independent of thechoice of the parametrization

Data Extrapolation

Σ(x, Q20 ) 5 10−4 ≤ x ≤ 0.1 10−5 ≤ x ≤ 10−4

〈d [f ]〉 0.62 0.88〈d [σ]〉 0.87 0.95

g(x, Q20 ) 5 10−4 ≤ x ≤ 0.1 10−5 ≤ x ≤ 10−4

〈d [f ]〉 1.07 0.87〈d [σ]〉 0.86 0.78

T3(x, Q20 ) 0.05 ≤ x ≤ 0.75 10−3 ≤ x ≤ 10−2

〈d [f ]〉 1.00 1.11〈d [σ]〉 1.24 1.61

V (x, Q20 ) 0.1 ≤ x ≤ 0.6 3 10−3 ≤ x ≤ 3 10−2

〈d [f ]〉 1.30 0.90〈d [σ]〉 0.90 0.78

∆S (x, Q20 ) 0.1 ≤ x ≤ 0.6 3 10−3 ≤ x ≤ 3 10−2

〈d [f ]〉 0.84 1.02〈d [σ]〉 1.02 1.12

37 pars → 31 pars



x-310 -210 -110

) 02V

(x,

Q

0

10

20

30

40

50

60CTEQ6.5MRST2001E

Alekhin02

NNPDF1.0

x-310 -210 -110 1

) 02V

(x,

Q

0

10

20

30

40

50

60

ValTot PDF

CTEQ6.5

MRST2001E

Alekhin02

NNPDF08 prelim.

ValTot PDF

Results are statistically independent of thechoice of the parametrization

Data Extrapolation

Σ(x, Q20 ) 5 10−4 ≤ x ≤ 0.1 10−5 ≤ x ≤ 10−4

〈d [f ]〉 0.62 0.88〈d [σ]〉 0.87 0.95

g(x, Q20 ) 5 10−4 ≤ x ≤ 0.1 10−5 ≤ x ≤ 10−4

〈d [f ]〉 1.07 0.87〈d [σ]〉 0.86 0.78

T3(x, Q20 ) 0.05 ≤ x ≤ 0.75 10−3 ≤ x ≤ 10−2

〈d [f ]〉 1.00 1.11〈d [σ]〉 1.24 1.61

V (x, Q20 ) 0.1 ≤ x ≤ 0.6 3 10−3 ≤ x ≤ 3 10−2

〈d [f ]〉 1.30 0.90〈d [σ]〉 0.90 0.78

∆S (x, Q20 ) 0.1 ≤ x ≤ 0.6 3 10−3 ≤ x ≤ 3 10−2

〈d [f ]〉 0.84 1.02〈d [σ]〉 1.02 1.12

37 pars → 31 pars



PDFs are stable upon the addition of new independent PDFsparametrizations

NNPDF1.0: flavor assumptions, symmetric strange sea proportional to non strangesea according to Cs ∼ 0.5 suggested by neutrino DIS data.

s(x) = s(x) s(x) =Cs

2(u(x) + d(x))

NNPDF1.1: independent parametrization of the strange content of the nucleon.

Total strangeness : s+(x) ≡ (s(x) + s(x))/2 7−→ NN(s+)(x) 2-5-3-1 37 pars

Strangeness valence : s−(x) ≡ (s(x) − s(x))/2 7−→ NN(s−)(x) 2-5-3-1 37 pars

Added two unconstrained PDFs.

185 → 259 parameters

Only strange (and Σ) affected. Gluon and statistical features remain unchanged.


NNPDF1.1

PDFs are stable upon the addition of new independent PDFsparametrizations

x-510 -410 -310 -210 -110 1

) 02xg

(x,

Q

-2

-1

0

1

2

3

4CTEQ6.6

MRST2001ENNPDF1.0

NNPDF1.1 Larger in extrapolation region due tomore flexibility (+ 60 pars).

Same χ2 and statistical features of thefit. Same gluon shape and error band.

x-410 -310 -210 -110 1

) 02 (

x, Q

+xs

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2CTEQ6.6

MRST2001ENNPDF1.0

NNPDF1.1

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02 (

x, Q

-xs

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2CTEQ6.6

MRST2001ENNPDF1.0

NNPDF1.1



Define second momentum of PDFs f: [F ] =∫ 10 dx x f (x ,Q2).

Discrepancy ≥ 3σ between indirect and direct determination from NuTeV measurementassuming [S−] = 0 and isospin symmetry.

EW fit

sin2 θW = 0.2223± 0.0002

NuTeV

sin2 θW = 0.2276 ± 0.0014

δs sin2 θW ∼ −0.240

[S−]

[Q−]

δs sin2 θW = −0.0005±0.0096PDFs±sys

0.215

0.22

0.225

0.23

0.235

0.24

0.245

sin2 θ W

Determinations of the weak mixing angle sin2θW

NuTeV01 NuTeV01 Global EW fit+ NNPDF1.2 [S-]



Control on PDFs uncertainties: NuteV anomaly solved ANDprecision studies at the same time

52

54

56

58

60

62

0.8 0.85 0.9 0.95 1 1.05 1.1

χ2

|Vcs|

NNPDF1.2, Nrep = 500, |Vcd|=0.2256

NuTeV DimuonParabolic fit (5 points)Parabolic fit (3 points)

48

50

52

54

56

58

60

62

0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28

χ2

|Vcd|

NNPDF1.2, Nrep = 500, |Vcs|=0.97334

NuTeV DimuonParabolic fit (5 points)Parabolic fit (3 points)

CKM fit

Vcs = 0.97334 ± 0.00023, ∆Vcs ∼ 0.02%

Direct Determination

Vcs = 1.04± 0.06, ∆Vcs ∼ 6% D/B decays

Vcs > 0.59 DIS fit

NNPDF1.2 analysis

Vcs = 0.97 ± 0.07, ∆Vcs ∼ 6%


NNPDF2.0A first unbiased global NLO parton determination

DIS data are insufficient to determine accurately PDFs.Flavor decomposition of quark–antiquark sea and large–x gluon distribution.

Rpd =

dσd/dM2dxF

dσp/dM2dxF∝

(

1 + d/u)

AW =

dσ+W/dy − dσ−

W/dy

dσ+W/dy − dσ−

W/dy

∝ud − du

ud + du

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02g

(x,

Q

-310

-210

-110

1

10CTEQ6.5MRST2001E

Alekhin02

NNPDF1.0

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

)02

(x,

QS

∆x

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1CTEQ6.5MRST2001E

Alekhin02

NNPDF1.0

NNPDF2.0 includes most of the available hadronic data.


NNPDF2.0New features

1 GLOBAL: Includes fixed target Drell-Yan, Tevatron jets and weak bosons data.

2 Improvements in training/stopping

Target Weighted Training

Improved stopping

3 Improved treatment of normalization errors (t0 method)For details see [arXiv:0912.2276]

4 Fast DGLAP evolution based on higher-order interpolating polynomials

5 NLO: Fast computation of Drell-Yan observables based on higher-order interpolatingpolynomials.

6 Enforced positivity constraints


New FeaturesFastKernel

New strategy to solve DGLAPevolution equation

Implementation benchmarked againstthe Les Houches tables

Gain in speed by a factor 30 (for a fitto 3000 datapoints)

0 0.5 1 1.5 2 2.5

y

0.00001

10ˉ⁴

10ˉ³

10ˉ²

0.1

E605

E886p

E886r

Wasy

Zrap

FastKernel METHOD

x (50 pts) erel (uv ) erel (Σ) erel (g)

1 · 10−7 2.1 · 10−4 2.7 · 10−5 4.7 · 10−6

1 · 10−6 8.9 · 10−5 3.0 · 10−5 2.1 · 10−5

1 · 10−5 9.3 · 10−5 2.3 · 10−5 2.0 · 10−5

1 · 10−4 4.5 · 10−5 4.4 · 10−5 4.2 · 10−5

1 · 10−3 3.0 · 10−5 4.0 · 10−5 3.5 · 10−5

1 · 10−2 7.9 · 10−5 4.5 · 10−5 5.8 · 10−5

1 · 10−1 1.7 · 10−4 1.6 · 10−5 3.9 · 10−5

3 · 10−1 9.1 · 10−6 1.1 · 10−5 1.9 · 10−7

5 · 10−1 2.4 · 10−5 2.2 · 10−5 2.2 · 10−5

7 · 10−1 9.1 · 10−5 7.8 · 10−5 1.2 · 10−4

9 · 10−1 1.0 · 10−3 8.0 · 10−4 2.8 · 10−3

Drell–Yan fast computation exploitslinear interpolation

Accuracy below 1% for all pointsincluded in the fit

Increasing number of points in the gridone can improve accuracy;

A truly NLO analysis


Impact of modifications


χ2tot 1.32 1.16 1.12 1.20 1.18 1.21

〈E〉 2.79 2.41 2.24 2.31 2.28 2.32〈Etr〉 2.75 2.39 2.20 2.28 2.24 2.29〈Eval〉 2.80 2.46 2.27 2.34 2.32 2.35

〈χ2(k)〉 1.60 1.28 1.21 1.29 1.27 1.29

NMC-pd 1.48 0.97 0.87 0.85 0.86 0.99NMC 1.68 1.72 1.65 1.69 1.66 1.69SLAC 1.20 1.42 1.33 1.37 1.31 1.34

BCDMS 1.59 1.33 1.25 1.26 1.27 1.27HERAI 1.05 0.98 0.96 1.13 1.13 1.14

CHORUS 1.39 1.13 1.12 1.13 1.11 1.18FLH108 1.70 1.53 1.53 1.51 1.49 1.49

NTVDMN 0.64 0.81 0.71 0.71 0.75 0.67ZEUS-H2 1.52 1.51 1.49 1.50 1.49 1.51DYE605 11.19 22.89 8.21 7.32 10.35 0.88DYE866 53.20 4.81 2.46 2.24 2.59 1.28

CDFWASY 26.76 28.22 20.32 13.06 14.13 1.85CDFZRAP 1.65 4.61 3.13 3.12 3.31 2.02D0ZRAP 0.56 0.80 0.65 0.65 0.68 0.47CDFR2KT 1.10 0.95 0.78 0.91 0.79 0.80D0R2CON 1.18 1.07 0.94 1.00 0.93 0.93


Impact of modificationsHERA-I combined dataset

0

1

2

3

4

5

6

7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

d[ q

(x,Q

02 ) ]

x

Distance between central values

NNPDF 2.0-DIS vs. 2.0-DIS-HERAoldΣg

T3V

∆Ss+s-

0

1

2

3

4

5

6

7

1e-05 0.0001 0.001 0.01 0.1 1

d[ q

(x,Q

02 ) ]

x



T3V

∆Ss+s-

0

1

2

3

4

5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

d[ σ

q(x,

Q02 )

]

x

Distance between PDF uncertainties


T3V

∆Ss+s-

0

1

2

3

4

5

1e-05 0.0001 0.001 0.01 0.1 1

d[ σ

q(x,

Q02 )

]

x



T3V

∆Ss+s-



0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

d[ q

(x,Q

02 ) ]

x


NNPDF 2.0-DIS vs. 2.0-DIS+JETΣg

T3V

∆Ss+s-

0

1

2

3

4

5

6

1e-05 0.0001 0.001 0.01 0.1 1

d[ q

(x,Q

02 ) ]

x



T3V

∆Ss+s-

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

d[ σ

q(x,

Q02 )

]

x



T3V

∆Ss+s-

0

0.5

1

1.5

2

2.5

3

3.5

4

1e-05 0.0001 0.001 0.01 0.1 1

d[ σ

q(x,

Q02 )

]

x



T3V

∆Ss+s-


Impact of modificationsTevatron inclusive Jet data

0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

d[ q

(x,Q

02 ) ]

x



T3V

∆Ss+s-

0

1

2

3

4

5

6

1e-05 0.0001 0.001 0.01 0.1 1

d[ q

(x,Q

02 ) ]

x



T3V

∆Ss+s-

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

d[ σ

q(x,

Q02 )

]

x



T3V

∆Ss+s-

0

0.5

1

1.5

2

2.5

3

3.5

4

1e-05 0.0001 0.001 0.01 0.1 1

d[ σ

q(x,

Q02 )

]

x



T3V

∆Ss+s-


New FeaturesPositivity constraints

We want the fitting procedure to explore only the subspace of acceptable physicalsolutions.

We wantFL positive.Dimuon cross–section positive.Momentum and valence sum rules.

Modify the training function witha ddition of a Lagrangian multiplier:

E (k) −→ E (k) − λpos

Ndat,pos∑

I=1

Θ(

F(net)(k)I

)

F(net)(k)I

Ndat,pos : number of pseudodata points used to implement positivity constraints.

λpos : associated Lagrangian multiplier (1010)


ResultsImpact of positivity

x-510 -410 -310 -210 -110 1

) 02 (

x, Q

Σx

0

1

2

3

4

5

6

NNPDF2.0 (NO POS)

NNPDF2.0

x-510 -410 -310 -210 -110 1

) 02xg

(x,

Q

-4

-3

-2

-1

0

1

2

3

4

5

NNPDF2.0 (NO POS)

NNPDF2.0

x-510 -410 -310 -210 -110 1

) 02 (

x, Q

+xs

-1

-0.5

0

0.5

1

1.5

2

NNPDF2.0 (NO POS)

NNPDF2.0

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02 (

x, Q

+xs

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

NNPDF2.0 (NO POS)

NNPDF2.0


ResultsGaussian behaviour

x-510 -410 -310 -210 -110 1

) 02 (

x, Q

Σx

0

1

2

3

4

5

6)σNNPDF2.0 (1-

NNPDF2.0 (68% C.L.)

x-510 -410 -310 -210 -110 1

) 02xg

(x,

Q

-2

-1

0

1

2

3

4 )σNNPDF2.0 (1-

NNPDF2.0 (68% C.L.)

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02

(x,

Q3

xT

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5)σNNPDF2.0 (1-

NNPDF2.0 (68% C.L.)

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

) 02xV

(x,

Q

0

0.2

0.4

0.6

0.8

1

1.2)σNNPDF2.0 (1-

NNPDF2.0 (68% C.L.)


Some phenomenologyThe proton strangeness revisited

]D + U ] / [ + = [ SSK0 0.5 1 1.5 2

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

= 1000rep

, N2 = 20 GeV2NNPDF1.2, Q = 1000rep

, N2 = 20 GeV2NNPDF1.2, Q

]D + U ] / [ + = [ SSK0.3 0.4 0.5 0.6 0.7 0.8 0.9

0

0.02

0.04

0.06

0.08

0.1

0.12

= 1000rep

, N2 = 20 GeV2NNPDF2.0, Q = 1000rep

, N2 = 20 GeV2NNPDF2.0, Q

0.215

0.22

0.225

0.23

0.235

0.24

0.245

sin2 θ W

Determinations of the weak mixing angle sin2θW

NuTeV01 NuTeV01 EW fit+ NNPDF1.2 [S-]

NuTeV01+ NNPDF2.0 [S-]

KS =

0.71+0.19−0.31

stat± 0.26syst (NNPDF1.2)

0.503 ± 0.075stat ; (NNPDF2.0)

RS =

{

0.006 ± 0.045stat ± 0.010syst (NNPDF1.2)

0.019 ± 0.008stat (NNPDF2.0)

Uncertainty reduced by addiction ofDY data

Striking agreement with EW fits


ResultsParton Luminosities

Φgg

(

M2X

)

=1

s

∫

1

τ

dx1

x1

g(

x1,M2X

)

g(

τ/x1,M2X

)

Φgq

(

M2X

)

=1

s

∫

1

τ

dx1

x1

[

g(

x1, M2X

)

Σ(

τ/x1,M2X

)

+ (1 → 2)]

Φqq

(

M2X

)

=1

s

∫

1

τ

dx1

x1

Nf∑

i=1

[

qi

(

x1, M2X

)

qi

(

τ/x1,M2X

)

+ (1 → 2)]

1e-10

1e-08

1e-06

0.0001

0.01

1

50 100 200 500 1000 2000 5000

Par

ton

lum

inos

ities

[GeV

-2]

MX [GeV]

PDF Luminosities at the LHC - NNPDF2.0

GGGQQQ

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

50 100 200 500 1000 2000 5000

Rel

ativ

e P

DF

unc

erta

inty

MX [GeV]

QQ luminosity

S = (14 TeV)2NNPDF2.0

CTEQ6.6MSTW08

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

50 100 200 500 1000 2000 5000

Rel

ativ

e P

DF

unc

erta

inty

MX [GeV]

GG luminosity

S = (14 TeV)2NNPDF2.0

CTEQ6.6MSTW08


ResultsImpact of αs

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

) 02xg

(x,

Q

0

0.5

1

1.5

2

2.5

3

dependence in NNPDF2.0sα

) = 0.1192

Z(Msα

) = 0.1152

Z(Msα

) = 0.1172

Z(Msα

) = 0.1212

Z(Msα

) = 0.1232Z

(Msα


x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

) 02 (

x, Q

Σx

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5


) = 0.1192

Z(Msα

) = 0.1152

Z(Msα

) = 0.1172

Z(Msα

) = 0.1212

Z(Msα

) = 0.1232Z

(Msα


x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

) 02xV

(x,

Q

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5) = 0.1192

Z(Msα

) = 0.1152

Z(Msα

) = 0.1172

Z(Msα

) = 0.1212

Z(Msα

) = 0.1232Z

(Msα

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

) 02

(x,

Q3

xT

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5) = 0.1192

Z(Msα

) = 0.1152

Z(Msα

) = 0.1172

Z(Msα

) = 0.1212

Z(Msα

) = 0.1232Z

(Msα

Greater sensitivity to αs than NNPDF1.2

Greater NLO corrections for Drell-Yan observables.


Some phenomenologyLHC standard candles

11

11.2

11.4

11.6

11.8

12

12.2

12.4

12.6

12.8

σ(W

+)B

lν [n

b]

W+ Cross Section at the LHC [MCFM]

NNPDF2.0 NNPDF1.2 CTEQ6.6 MSTW08 1.8

1.85

1.9

1.95

2

2.05

2.1

σ(Z

0 )Bl+

l- [nb

]

Z0 Cross Section at the LHC [MCFM]

NNPDF2.0 NNPDF1.2 CTEQ6.6 MSTW08 7.8

8

8.2

8.4

8.6

8.8

9

9.2

9.4

σ(W

- )Blν

[nb]

W- Cross Section at the LHC [MCFM]

NNPDF2.0 NNPDF1.2 CTEQ6.6 MSTW08

34

35

36

37

38

39

σ(H

) [p

b]

H Cross Section at the LHC [gg fusion, MH=120 GeV, MCFM]


800

820

840

860

880

900

920

940

σ(ttb

ar)

[pb]

ttbar Cross Section at the LHC [MCFM]


HQ treatment?

Impact of K factorapproximation?

Impact of rigidparametrization?


Some applications of the NNPDF techniquePredictions on future experimental constraints on PDFs.

Generate LHeC pseudo-data.

Add them to the data set.

Fit them (or reweight)

x-610 -510 -410 -310 -210 -110 1

)2 (

GeV

2Q

1

10

210

310

410

510

610 NMC-pdNMCSLACBCDMSZEUSH1CHORUSFLH108NTVDMNXF3GZZEUS-H2LHeCtot

LHeC Linac(150 GeV)-Ring, Scenario E

Same settings: no tuning

HIgh predictivity.


Impact of modificationsTo conclude...

* Precise HERA data→ Small x gluon & singlet

* Tevatron W asymmetry data→ Small x flavor separation

* Fixed Target DIS data, Drell-Yan, neutrino inclusive→ Small x flavor separation

* Neutrino dimuon→ Strangeness

* Tevatron jets→ Large x gluon

No signs of tension between datasets included in the analysis!!!


first global nnpdf analysisnnpdf.mi.infn.it/wp-content/uploads/2017/10/moriond2010.pdf · outline 1...

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