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Parton distributions with LHC dataThe new generation of PDFs

Stefano Carrazza

Universit 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 QCD)can be written as

ddxdQ2

=

nfi=1

d idQ2

fi/p(x ,Q2),

the sum over all PDF flavors nf of the convolution product between:

d idQ2

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 QCD)can be written as

ddxdQ2

=

nfi=1

d idQ2

fi/p(x ,Q2),

the sum over all PDF flavors nf of the convolution product between:

d idQ2

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

Mon

te C

arlo

Hes

sian

NNPDF Polynomials Neural Networks

Datasets

App

roac

h

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

Mon

te C

arlo

Hes

sian

NNPDF Polynomials Neural Networks

Datasets

App

roac

h

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 bandNNPDF 2.3 NNLO 1

NNPDF 2.3 NNLO 68% CL band

)2xg(x, Q MC approach:

O[f ] = 1N

Nk=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 bandNNPDF 2.3 NNLO 1

NNPDF 2.3 NNLO 68% CL band

)2xg(x, Q MC approach:

O[f ] = 1N

Nk=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 bandNNPDF 2.3 NNLO 1

NNPDF 2.3 NNLO 68% CL band

)2xg(x, Q MC approach:

O[f ] = 1N

Nk=1

O[fk ]

I for observables, errors,correlations, etc.

Outline

1 IntroductionDefinitionMotivation

2 NNPDF approachOverview on current PDF providersThe NNPDF methodology

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 ( ).

x-5

10 -410-3

10 -210 -110 1

]2

[ G

eV

2 T / p

2 / M

2Q

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