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Transcript of First global NNPDF analysisnnpdf.mi.infn.it/wp-content/uploads/2017/10/moriond2010.pdf · Outline 1...
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
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I N BU
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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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 2 / 53
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.
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 3 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 4 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 5 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 6 / 53
MotivationWhat’s nice about NNPDF #2
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]]
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 7 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 8 / 53
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.
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 9 / 53
NNPDF2.0Data sets
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]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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 10 / 53
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)
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 11 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 12 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 13 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 14 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 15 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 16 / 53
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.
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 17 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 18 / 53
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
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) 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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 19 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 20 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 21 / 53
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,
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 22 / 53
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!!
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 23 / 53
BACK-UP
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 24 / 53
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%
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 25 / 53
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.
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 26 / 53
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.
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 27 / 53
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.
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 28 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 29 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 30 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 31 / 53
MotivationWhat’s nice about NNPDF #2
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 32 / 53
MotivationWhat’s nice about NNPDF #2
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 33 / 53
MotivationWhat’s nice about NNPDF #3
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.
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 34 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 35 / 53
MotivationWhat’s nice about NNPDF #5
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-]
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 36 / 53
MotivationWhat’s nice about NNPDF #5
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%
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 37 / 53
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.
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 38 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 39 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 40 / 53
Impact of modifications
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〈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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 41 / 53
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
Distance between central values
NNPDF 2.0-DIS vs. 2.0-DIS-HERAoldΣg
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
NNPDF 2.0-DIS vs. 2.0-DIS-HERAoldΣg
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
Distance between PDF uncertainties
NNPDF 2.0-DIS vs. 2.0-DIS-HERAoldΣg
T3V
∆Ss+s-
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 42 / 53
Impact of modificationsDrell-Yan and Vector Boson production 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
Distance between central values
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
Distance between central values
NNPDF 2.0-DIS vs. 2.0-DIS+JETΣg
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
Distance between PDF uncertainties
NNPDF 2.0-DIS vs. 2.0-DIS+JETΣg
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
Distance between PDF uncertainties
NNPDF 2.0-DIS vs. 2.0-DIS+JETΣg
T3V
∆Ss+s-
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 43 / 53
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
Distance between central values
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
Distance between central values
NNPDF 2.0-DIS vs. 2.0-DIS+JETΣg
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
Distance between PDF uncertainties
NNPDF 2.0-DIS vs. 2.0-DIS+JETΣg
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
Distance between PDF uncertainties
NNPDF 2.0-DIS vs. 2.0-DIS+JETΣg
T3V
∆Ss+s-
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 44 / 53
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)
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 45 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 46 / 53
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.)
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 47 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 48 / 53
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
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 49 / 53
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
dependence in NNPDF2.0sα
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
dependence in NNPDF2.0sα
) = 0.1192
Z(Msα
) = 0.1152
Z(Msα
) = 0.1172
Z(Msα
) = 0.1212
Z(Msα
) = 0.1232Z
(Msα
dependence in NNPDF2.0sα
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.
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 50 / 53
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]
NNPDF2.0 NNPDF1.2 CTEQ6.6 MSTW08
800
820
840
860
880
900
920
940
σ(ttb
ar)
[pb]
ttbar Cross Section at the LHC [MCFM]
NNPDF2.0 NNPDF1.2 CTEQ6.6 MSTW08
HQ treatment?
Impact of K factorapproximation?
Impact of rigidparametrization?
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 51 / 53
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.
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 52 / 53
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!!!
Maria Ubiali (University of Edinburgh & Universite Catholique de Louvain)First global NNPDF analysis Rencontres de Moriond, QCD session 53 / 53