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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

    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 ( ).

    x-5

    10 -410-3

    10 -210 -110 1

    ]2

    [ G

    eV

    2 T / p

    2 / M

    2Q

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