Parton distributions with LHC data - PhD Physics...
Transcript of Parton distributions with LHC data - PhD Physics...
Parton distributions with LHC dataThe new generation of PDFs
Stefano Carrazza
Università di Milano and INFN
Mini-workshop 2012
in collaboration with S. Forte, R. Ball, L. Del Debbio et al.
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 1 / 14
Outline
1 IntroductionDefinitionMotivation
2 NNPDF approachOverview on current PDF providersThe NNPDF methodology
3 NNPDF with LHC dataThe new datasetPDF results with LHC dataComparing results between different PDF providersPhenomenology at
√s = 8 TeV
4 Conclusion and outlook
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 2 / 14
Outline
1 IntroductionDefinitionMotivation
2 NNPDF approachOverview on current PDF providersThe NNPDF methodology
3 NNPDF with LHC dataThe new datasetPDF results with LHC dataComparing results between different PDF providersPhenomenology at
√s = 8 TeV
4 Conclusion and outlook
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 2 / 14
Introduction - PDF definition
What are parton distribution functions?
PDF definition:The probability density of finding aconstituent of the proton, called parton,with a momentum fraction x of the protonat momentum transfer Q2.
Partons are gluons, quarks and antiquarks⇒ g,u, u,d , d , s, s, ...
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 3 / 14
Introduction - PDF definition
What are parton distribution functions?
PDF definition:The probability density of finding aconstituent of the proton, called parton,with a momentum fraction x of the protonat momentum transfer Q2.
Partons are gluons, quarks and antiquarks⇒ g,u, u,d , d , s, s, ...
Facts about PDFs:I Not calculable: reflect non-perturbative physics of confinementI Extracted by comparing theoretical predictions to experimental data:
Deep InelasticScattering
Drell-Yanprocess
Electroweakdistributions
Jetdistributions
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 3 / 14
Introduction - PDF definition
What are parton distribution functions?
PDF definition:The probability density of finding aconstituent of the proton, called parton,with a momentum fraction x of the protonat momentum transfer Q2.
Partons are gluons, quarks and antiquarks⇒ g,u, u,d , d , s, s, ...
PDF ≠PDF ≠
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 3 / 14
Motivation - Computing observables
Why do we need parton distribution functions?Following the factorization theorem in QCD, the observable of a hardprocess (Q � ΛQCD)can be written as
dσdxdQ2 =
nf∑i=1
d σi
dQ2 ⊗ fi/p(x ,Q2),
the sum over all PDF flavors nf of the convolution product between:
d σi
dQ2
the elementary “hard” crosssection which is computed in QCD,depends on the physical process.
⊗
fi/p(x ,Q2)
the PDF of parton i inside a protonp, carrying a momentum fraction xat the energy scale Q2.
Remark: PDFs are essential for theoretical predictions.
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 4 / 14
Motivation - Computing observables
Why do we need parton distribution functions?Following the factorization theorem in QCD, the observable of a hardprocess (Q � ΛQCD)can be written as
dσdxdQ2 =
nf∑i=1
d σi
dQ2 ⊗ fi/p(x ,Q2),
the sum over all PDF flavors nf of the convolution product between:
d σi
dQ2
the elementary “hard” crosssection which is computed in QCD,depends on the physical process.
⊗
fi/p(x ,Q2)
the PDF of parton i inside a protonp, carrying a momentum fraction xat the energy scale Q2.
Remark: PDFs are essential for theoretical predictions.
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 4 / 14
Motivation - Using PDFs
Where do we need parton distribution functions?
PDFs are necessary to determine theoretical predictions for signal/backgroundof experimental measurements.
Problem: PDF uncertainties on signal range from 4% up to 8%, accordingly tothe channel, of the systematic uncertainties of the measurements.
Solution: Improve PDF extraction methodology and add more data (LHC data).
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 5 / 14
Motivation - Using PDFs
Where do we need parton distribution functions?
PDFs are necessary to determine theoretical predictions for signal/backgroundof experimental measurements.
Problem: PDF uncertainties on signal range from 4% up to 8%, accordingly tothe channel, of the systematic uncertainties of the measurements.
Solution: Improve PDF extraction methodology and add more data (LHC data).
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 5 / 14
Outline
1 IntroductionDefinitionMotivation
2 NNPDF approachOverview on current PDF providersThe NNPDF methodology
3 NNPDF with LHC dataThe new datasetPDF results with LHC dataComparing results between different PDF providersPhenomenology at
√s = 8 TeV
4 Conclusion and outlook
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 5 / 14
PDFs on the market...
CTEQ
MSTW
ABKM
HERAPDF
All available data Limited number of datasets
Mo
nte
Car
loH
essi
an
NNPDF● Polynomials● Neural Networks
Datasets
Ap
pro
ach
The providers use different approaches and datasets.NNPDF uses a high technological approach.
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 6 / 14
PDFs on the market...
CTEQ
MSTW
ABKM
HERAPDF
All available data Limited number of datasets
Mo
nte
Car
loH
essi
an
NNPDF● Polynomials● Neural Networks
Datasets
Ap
pro
ach
The providers use different approaches and datasets.NNPDF uses a high technological approach.
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 6 / 14
The NNPDF methodology (shortly)NNPDF has introduced a new methodology:
I implementation started in 2002, based on Neural Networks,I reduction of all sources of theoretical bias, e.g. the functional form.
PDFs are extracted by usingI Neural Network parametrization,I Minimization driven by a genetic algorithm,I Optimization controlled by training/validation method,I Monte Carlo representation of results.
Expectation values for observables are Monte Carlo integrals:
510 410
310 210 110
2
1
0
1
2
3
4
5
6
7
)2xg(x, Q
NNPDF 2.3 NNLO replicas
NNPDF 2.3 NNLO mean value
error bandσNNPDF 2.3 NNLO 1
NNPDF 2.3 NNLO 68% CL band
)2xg(x, Q MC approach:
〈O[f ]〉 =1N
N∑k=1
O[fk ]
I for observables, errors,correlations, etc.
The NNPDF methodology (shortly)NNPDF has introduced a new methodology:
I implementation started in 2002, based on Neural Networks,I reduction of all sources of theoretical bias, e.g. the functional form.
PDFs are extracted by usingI Neural Network parametrization,I Minimization driven by a genetic algorithm,I Optimization controlled by training/validation method,I Monte Carlo representation of results.
Expectation values for observables are Monte Carlo integrals:
510 410
310 210 110
2
1
0
1
2
3
4
5
6
7
)2xg(x, Q
NNPDF 2.3 NNLO replicas
NNPDF 2.3 NNLO mean value
error bandσNNPDF 2.3 NNLO 1
NNPDF 2.3 NNLO 68% CL band
)2xg(x, Q MC approach:
〈O[f ]〉 =1N
N∑k=1
O[fk ]
I for observables, errors,correlations, etc.
The NNPDF methodology (shortly)NNPDF has introduced a new methodology:
I implementation started in 2002, based on Neural Networks,I reduction of all sources of theoretical bias, e.g. the functional form.
PDFs are extracted by usingI Neural Network parametrization,I Minimization driven by a genetic algorithm,I Optimization controlled by training/validation method,I Monte Carlo representation of results.
Expectation values for observables are Monte Carlo integrals:
510 410
310 210 110
2
1
0
1
2
3
4
5
6
7
)2xg(x, Q
NNPDF 2.3 NNLO replicas
NNPDF 2.3 NNLO mean value
error bandσNNPDF 2.3 NNLO 1
NNPDF 2.3 NNLO 68% CL band
)2xg(x, Q MC approach:
〈O[f ]〉 =1N
N∑k=1
O[fk ]
I for observables, errors,correlations, etc.
Outline
1 IntroductionDefinitionMotivation
2 NNPDF approachOverview on current PDF providersThe NNPDF methodology
3 NNPDF with LHC dataThe new datasetPDF results with LHC dataComparing results between different PDF providersPhenomenology at
√s = 8 TeV
4 Conclusion and outlook
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 7 / 14
NNPDF2.3 - The new dataset
NNPDF2.3 is the first PDF set which includes all the LHC data forwhich the complete experimental information is available ( ).
x5
10 4103
10 210 110 1
]2
[ G
eV
2 T / p
2 / M
2Q
1
10
210
310
410
510
610
710NMCpd
NMC
SLAC
BCDMS
HERAIAV
CHORUS
FLH108
NTVDMN
ZEUSH2
ZEUSF2C
H1F2C
DYE605
DYE886
CDFWASY
CDFZRAP
D0ZRAP
CDFR2KT
D0R2CON
ATLASWZ36pb
CMSWEASY840PB
LHCBW36pb
ATLASJETS10
NNPDF2.3 dataset ATLAS:inclusive jetsW/Z lepton rapiditydistributions
CMS:W leptonasymmetry
LHCb:W rapiditydistributions
3501 data points: 51 LHC W/Z, 90 LHC Jets(ATLAS jets arXiv:1112.6297, ATLAS W/Z arXiv:1109.5141, CMS Weasy arXiv:1206.2598, LHCb W arXiv:1204.1620)
NNPDF2.3 - The new PDF set
x
310
210
110 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
)2 = 10 GeV2xf(x,Q
g/10
u
d
du
ss,
cc,
x
310
210
110 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
)2 GeV4 = 102xf(x,Q
g/10
u
d
du
ss,
cc,
bb,
std. dev.)σNNPDF2.3 NLO PDFs (1
NNPDF2.3 sets are also available:I varying datasets,I varying QCD parameters, e.g. αs ,I with different theoretical frameworks, e.g. perturbative order (NLO/NNLO).
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 9 / 14
Example of NNPDF2.3 PDF
Example of PDFs at Q20 = 2.0 GeV2, with and without LHC data.
x5
10 4103
10 210 110 10
1
2
3
4
5
6
7)
0
2(x, QΣx
NNPDF2.3 NNLO
NNPDF2.3 noLHC NNLO
NNPDF2.3 NNLO
NNPDF2.3 noLHC NNLO
)0
2(x, QΣx
x5
10 4103
10 210 110 1
2
1
0
1
2
3
4
5
6
7)
0
2xg(x, Q
NNPDF2.3 NNLO
NNPDF2.3 noLHC NNLO
NNPDF2.3 NNLO
NNPDF2.3 noLHC NNLO
)0
2xg(x, Q
LHC data reduces PDF uncertainties and improves the χ2/d.o.fbetween data and theoretical predictions produced by the PDFs:
NNPDF2.3 noLHC NNPDF2.3
Total χ2/d.o.f. 1.142 1.139
Improvement about 10 units of χ2.Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 10 / 14
Example of LHC observables
|l
ηLepton Pseudorapidity |0 0.5 1 1.5 2 2.5
| [p
b]
lη
/d|
σd
540
560
580
600
620
640
660
680
700
720
NNPDF2.3 NNLO
CT10 NNLO
MSTW2008 NNLO
Experimental data
lepton pseudorapidity distribution+
ATLAS W
|ηElectron Pseudorapidity |0 0.5 1 1.5 2 2.5
)η
Ele
ctr
on C
ha
rge
Asym
me
try A
(
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24 NNPDF2.3 NNLO
CT10 NNLO
MSTW2008 NNLO
Experimental data
CMS W electron charge asymmetry
NNLO,αs = 0.119
PDF Set NNPDF2.3 MSTW08 CT10
ATLAS W, Z 1.435 3.201 1.160
CMS Weasy 0.813 3.862 1.772
LHCb W 0.831 1.050 0.966
ATLAS jets 0.937 0.935 1.016
|µ
ηMuon Pseudorapidity |2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4
| [p
b]
µη
/d|
σd
0
100
200
300
400
500
600
700
800
NNPDF2.3 NNLO
CT10 NNLO
MSTW2008 NNLO
Experimental data
muon pseudorapidity distribution+
LHCb W
Candle Cross Sections - W± and Z)
[pb
]+
(Wσ
6.6
6.8
7
7.2
7.4
7.6
7.8
= 0.119Sα) VRAP NNLO +
(WσLHC 8 TeV
NNPDF2.3
MSTW08
CT10
ABM11
HERAPDF1.5
CMS 2012
) [p
b]
(W
σ
4.7
4.8
4.9
5
5.1
5.2
5.3
5.4
5.5
5.6
= 0.119Sα) VRAP NNLO
(WσLHC 8 TeV
NNPDF2.3
MSTW08
CT10
ABM11
HERAPDF1.5
CMS 2012
) [p
b]
0(Z
σ
1.06
1.08
1.1
1.12
1.14
1.16
1.18
1.2
1.22
1.24
1.26
= 0.119Sα) VRAP NNLO 0(ZσLHC 8 TeV
NNPDF2.3
MSTW08
CT10
ABM11
HERAPDF1.5
CMS 2012
Sets extracted from all datasetsproduce similar and more preciseresults (NNPDF/CT10/MSTW)
Sets extracted from partial datasetshave large uncertainties and lessprecision (ABM/HERAPDF).
Candle Cross Sections - Higgs and Top(t
t) [
pb
]σ
200
210
220
230
240
250
260
270
= 0.119S
α+NNLL approx
(tt) Top++ v1.2 NNLOσLHC 8 TeV
NNPDF2.3
MSTW08
CT10
ABM11
HERAPDF1.5
CMS 2012
(a) Top inclusive cross section.(H
) [p
b]
σ
17
17.5
18
18.5
19
19.5
20
= 0.119 PDF uncertaintiesS
αLHC 8 TeV iHixs 1.3 NNLO
NNPDF2.3
MSTW08
CT10
ABM11
HERAPDF1.5
(b) Higgs inclusive cross section.
Waiting for Higgs cross section measurements!
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 13 / 14
Outline
1 IntroductionDefinitionMotivation
2 NNPDF approachOverview on current PDF providersThe NNPDF methodology
3 NNPDF with LHC dataThe new datasetPDF results with LHC dataComparing results between different PDF providersPhenomenology at
√s = 8 TeV
4 Conclusion and outlook
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 13 / 14
Conclusion and outlook
1 NNPDF2.3 is the first PDF set including all the LHC data2 The impact of LHC data is small but non-negligible3 The paper will be impressed by Nuclear Physics B.
Outlook:Improvements of the code and the general structure.Near future: Electroweak corrections to PDFs, photon PDF.
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 14 / 14
NNPDF
BACKUP SLIDES
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 15 / 14
Luminosities at√
s = 8 TeV
Luminosity is defined as
Φij(M2X ) =
1s
ˆ 1
τ
dx1
x1fi(x1,M2
X )fj(τ/x1,M2X ), τ =
M2X
s
Preliminary results: gg and qq luminosities at 8 TeV (2012 runs)
XM210
310
Glu
on
G
luo
n L
um
ino
sity
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
= 0.119sαLHC 8 TeV Ratio to NNPDF2.3 NNLO
NNPDF2.3 NNLO
CT10 NNLO
MSTW2008 NNLO
= 0.119sαLHC 8 TeV Ratio to NNPDF2.3 NNLO
XM210
310
Qu
ark
A
ntiq
ua
rk L
um
ino
sity
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
= 0.119sαLHC 8 TeV Ratio to NNPDF2.3 NNLO
NNPDF2.3 NNLO
CT10 NNLO
MSTW2008 NNLO
= 0.119sαLHC 8 TeV Ratio to NNPDF2.3 NNLO
All luminosities are reasonably compatible betweenglobal PDF sets.
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 16 / 14
PDF relative uncertainty
Results: gg and qq luminosities PDF relative uncertainty at 8 TeV.
XM210
310
Glu
on
G
luo
n L
um
ino
sity
0.3
0.2
0.1
0
0.1
0.2
0.3
sαLHC 8 TeV Relative PDF uncertainty default
NNPDF2.3 NNLO
CT10 NNLO
MSTW2008 NNLO
sαLHC 8 TeV Relative PDF uncertainty default
XM210
310
Qu
ark
A
ntiq
ua
rk L
um
ino
sity
0.3
0.2
0.1
0
0.1
0.2
0.3
sαLHC 8 TeV Relative PDF uncertainty default
NNPDF2.3 NNLO
CT10 NNLO
MSTW2008 NNLO
sαLHC 8 TeV Relative PDF uncertainty default
NNPDF2.3 with LHC data has small relative uncertainties=⇒ Improvement of quality in theoretical predictions.
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 17 / 14
Features
Heavy quark mass effects included using the FONLL method up to NNLO,S. Forte et al., arXiv:1001.2312.
FastKernel method for the inclusion of the higher order correctionsThe NNPDF Collaboration, arXiv:1002.4407
I DIS up to NNLOI DY and JET up to NLO
NNLO corrections to DY included by means of K-factors (DYNNLO)
NNLO corrections to inclusive JET implement using FastNLO (hep-ph/0609285)
I approximated NNLO corrections based on threshold resummation.
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 18 / 14
Data sets
NLO/NNLO cutsI W 2 = Q2(1− x)/x > 12.5 GeV2
I Q2 > 3 GeV2 + further cuts on F c2
ATLAS W, Z lepton rapidity distributions cuts
plT ≥ 20 GeV, pνT ≥ 25 GeV, mT < 40 GeV, |ηl | ≤ 2.5
plT ≥ 20 GeV, 66 GeV ≤ ml+l− ≤ 116 GeV, ηl+,l− ≤ 4.9
CMS W electron asymmetry
peT ≥ 35 GeV
LHCb W, Z rapidity distribution
pµT ≥ 20 GeV, 60 GeV ≤ ml+l− ≤ 120 GeV, 2.0 ≤ ηµ1,2 ≤ 4.5
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 19 / 14
NNPDF mechanism
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 20 / 14
Neural Networks
Neural Networks are defined as
ξ(l)i = g
nl−1∑j=1
ω(l−1)ij ξ
(l−1)j − θ(l)i
ω(l−1)ij weights, θ(l)i thresholds, i th neuron, l th layer, where g is the
sigmoid activation function:
g(x) ≡ 11 + e−x
Example: Neural network 1-2-1
ξ(3)1 =
{1 + exp
[θ(3)1 −
ω(2)11
1 + eθ(2)1 −xω(1)
11
−ω(2)12
1 + eθ(2)2 −xω(1)
21
]}−1
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 21 / 14
Genetic algorithm
Stefano Carrazza (Unimi) Parton distributions with LHC data Milano, October 16th, 2012 22 / 14