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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


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






PDF ≠PDF ≠


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.


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).


Outline




√s = 8 TeV



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.


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




√s = 8 TeV



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).


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!


Outline




√s = 8 TeV



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.


NNPDF

BACKUP SLIDES


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


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


NNPDF2.3 NNLO

CT10 NNLO

MSTW2008 NNLO


All luminosities are reasonably compatible betweenglobal PDF sets.


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


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


NNPDF2.3 NNLO

CT10 NNLO

MSTW2008 NNLO


NNPDF2.3 with LHC data has small relative uncertainties=⇒ Improvement of quality in theoretical predictions.


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.


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


NNPDF mechanism


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


Genetic algorithm


Training/validation method


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