recent developements and open problems in parton distributions · 2011. 3. 1. · pdfs in the lhc...

PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems

ConclusionsExtra Material

Recent Developements and Open Problemsin Parton Distributions

Juan Rojo

Dipartimento di Fisica, Università degli Studi di Milano

Les Rencontres de Physique de la Valle d’Aoste 2011La Thuile, 01/03/2011

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Outline

1 PDFs in the LHC era

2 PDFs: Recent progressBenchmark LHC observablesHeavy quark mass effectsNNPDF@NNLODeviations from fixed order DGLAP

3 PDFs: Open problemsαs , NMC and Higgs productionThe Tevatron W asymmetry data

4 Conclusions

5 Extra Material

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Motivation

The accurate determination of parton distributions (PDFs) is a crucialrequirement for the LHC physics program

PDFs and their uncertainties are relevant for standard candles (W , Z , tt̄),SM backgrounds (inclusive jets, photons) and new physics searches(Higgs, SUSY)

Using accurate PDFs specially relevant for Higgs exclusion bounds (anddiscovery claims?) at Tevatron and LHC

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PARTONS FOR LHC:

THE ACCURATE COMPUTATION OF PHYSICAL PROCESS AT A HADRON COLLIDER

REQUIRES GOOD KNOWLEDGE OF PARTON DISTRIBUTIONS OF THE NUCLEON

FACTORIZATION

⇒

IN ORDER TO EXTRACT THE RELEVANT PHYSICS SIGNAL,

WE NEED TO KNOW THE PARTON DISTRIBUTIONS AND THEIR UNCERTAINTY

IS THIS ASPECT OF LHC PHYSICS UNDER CONTROL?

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An ideal PDF set

S. Forte, Parton Distributions at the Dawn of the LHC, arxiv:1011.5247

1 Use a wide dataset → ensure all relevant experimental information retained

2 Use sufficiently general and unbiased parton parametrization or estimate effect ofparton parametrization variations

3 Provide PDF uncertainty bands checked to provide consistently-sized confidencelevels for individual experiments

4 Include heavy quark mass effects through a GM-VFN scheme, and provideestimate of uncertainties due to subleading terms

5 Use exact computations performed at the highest available perturbative order

6 Provide PDFs for a variety of values of αs (MZ ) and for the heavy quark massesmc and mb

PDF determination was for many years a qualitative artIn the LHC era it must become a quantitative science

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PDFs: Status of the Art

M. Ubiali, Challenges for precision physics at the LHC, Paris 2010

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An ideal PDF set


1 Use a wide dataset → ensure all relevant experimentalinformation retained






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Datasets in PDF analysis

Process Subprocess Partons x range

ℓ± {p, n} → ℓ± X γ∗q → q q, q̄, g x & 0.01ℓ± n/p → ℓ± X γ∗ d/u → d/u d/u x & 0.01pp → µ+µ− X uū, dd̄ → γ∗ q̄ 0.015 . x . 0.35pn/pp → µ+µ− X (ud̄)/(uū) → γ∗ d̄/ū 0.015 . x . 0.35ν(ν̄) N → µ−(µ+) X W∗q → q′ q, q̄ 0.01 . x . 0.5ν N → µ−µ+ X W∗s → c s 0.01 . x . 0.2ν̄ N → µ+µ− X W∗ s̄ → c̄ s̄ 0.01 . x . 0.2

e± p → e± X γ∗q → q g, q, q̄ 0.0001 . x . 0.1e+ p → ν̄ X W + {d, s} → {u, c} d, s x & 0.01e±p → e± cc̄ X γ∗c → c, γ∗g → cc̄ c, g 0.0001 . x . 0.01e±p → jet + X γ∗g → qq̄ g 0.01 . x . 0.1pp̄ → jet + X gg, qg, qq → 2j g, q 0.01 . x . 0.5pp̄ → (W± → ℓ±ν) X ud → W , ūd̄ → W u, d, ū, d̄ x & 0.05pp̄ → (Z → ℓ+ℓ−) X uu, dd → Z d x & 0.05

MSTW08, arXiv:0901.0002

Global PDF sets NNPDF2.1, CT10, MSTW08 include all relevant datasets fromDIS, Drell-Yan, vector-boson production and inclusive jet production

Different data constrain different PDF combinations → Use all available experi-mental information for PDF determinations

PDF sets based on reduced datasets might have some PDFs unconstrained

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An ideal PDF set



2 Use sufficiently general and unbiased parton parametrization orestimate effect of parton parametrization variations





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Simple functional froms vs. NeuralNets

Fit vs H1PDF2000, Q 2 = 4. GeV2

0

1

2

3

4

5

6

7

8

9

10

10-4

10-3

10-2

10-1

1x

xG(x

)

x-410 -310 -210 -110 1

)2 =

4 G

eV02

x g

(x, Q

0

2

4

6

8

10

Simple functional forms q(x) = Axb(1 − x)cP(x) (CT, MSTW, ABKM, HERAPDF)→ systematic underestimation of uncertainties

Artificial Neural Networks as universal interpolants (NNPDF)→ avoid theoretical bias from choice of PDF functional form

Compare O(300) parms in NNPDF with O(10-25) parms in standard PDF sets

also PDFs from Chebichev polynomials, Glazov, Moch, Radescu, arXiv:1009.6170 and Pumplin, arXiv:0909.5176

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An ideal PDF set

S. Forte, Parton Distributions at the Dawn of the LHC, arxiv:





5 Use exact computations performed at the highest availableperturbative order


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Exact NLO/NNLO computations

NLO exact computation of hadronic observablesoften too slow for PDF fits.

MSTW and CT include Drell-Yan and JetsNLO/NNLO as (local) K-factors rescaling theLO cross section

NNPDF uses exact fast NLO calculations

0 0.5 1 1.5 2 2.5

y

0.00001

10ˉ⁴

10ˉ³

10ˉ²

0.1

E605

E886p

E886r

Wasy

Zrap

FastKernel METHOD

Exact fast computations of hadronicobservables now available:

FastNLO: interface for jet inclusivecross-section (hep-ph/0609285)

FastKernel: computation of DYobservables (NNPDF arXiv:1002.4407)

APPLgrid: general purpose interface(arXiv:0911.2985)

APPLGRID, NLO W + → e+ν distribution

Exact NLO/NNLO computations should always be used in global PDF fits

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Benchmark LHC observablesHeavy quark mass effectsNNPDF@NNLODeviations from fixed order DGLAP

Outline




4 Conclusions

5 Extra Material

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Benchmark LHC observables

Study and plots from G. Watt, Les Houches QCD 2011

Good agreement within global PDF setsLarger differences for non-global sets

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Good agreement within global PDF setsLarger differences for non-global sets

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Same trend as for qq̄NNPDF2.1 in good agreement with MSTW08, CT10 lower (also for Higgs)

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Same trend as for qq̄NNPDF2.1 in good agreement with MSTW08, CT10 lower (also for Higgs)

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The PDF4LHC working group

The PDF4LHC group (CERN management mandate) coordinates studies andresearch in PDF determinations from different groups and is responsible forproviding official recommendations for PDF use in LHC experimentsCurrent NLO recommendation for LHC analysis:

http://www.hep.ucl.ac.uk/pdf4lhc/At NNLO: MSTW2008 NNLO central value + NLO envelopeUpdated when new data / PDF sets / theoretical developements require so

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The PDF4LHC recommendation and Higgs searches

PDF4LHC recommendation adopted by ATLAS, CMS and the LHC Higgs cross section workinggroup (CERN Yellow Report, arxiv:1101.0593)

[GeV]HM

100 150 200 250 300 350 400 450 500

R

0.85

0.9

0.95

1

1.05

1.1

1.15

LH

C H

IGG

S X

S W

G 2

010

LHC 7 TeV 68% C.L.sαPDF+

normalized to MSTW2008nlo

)Z

(msαdifferent values of uncertaintiessαexact PDF+

PDF4LHC recipe

NNPDF2.0

CTEQ6.6

MSTW08nlo

[GeV]HM

100 150 200 250 300 350 400 450 500

R1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

LH

C H

IGG

S X

S W

G 2

010

rescaling factorslower curves = upper limit of uncertainty bands

)Z

(msαdifferent values of uncertaintiessαexact PDF+

Tevatron

LHC 7 TeV

LHC 14 TeV

PDF4LHC recipee should be used in all LHC analysis where PDFs are relevant!

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Heavy quark mass effects

Most recent PDF sets all based on aGeneral-Mass VFN scheme for heavyquarks

Precision LHC pheno requires to estimatetheo uncertainties from a) Subleadingterms in the GM-VFN definition and b)choice of mc and mb values

NNPDF (arXiv:1101.1300) and MSTW

(arXiv:1007.2624): detailed studies of

heavy quark mass effects → Important totake into account for:

1 Process sensitive to small-x quarks:W±, Z

2 HQ initiated process: bb̄ → H,single top

Also HERAPDF (arXiv:1006.4471)

Dependence on mh reduced if MSbar massused in the GM-VFN (Alekhin and Moch,arXiv:1011.5790)

x-410 -310 -210 -110

Rat

io to

MS

TW

200

8 N

NLO

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

2Z = M

2Up quark distribution at Q

TevatronLHC7

LHC14

MSTW 2008 NNLO (90% C.L.) = 1.15 GeVcm = 1.65 GeVcm

)Z

(MSα = 1.15 GeV, fix cm)

Z(MSα = 1.65 GeV, fix cm

x-410 -310 -210 -110

Rat

io to

MS

TW

200

8 N

NLO

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

0.8

0.9

1

1.1

1.2

1.3

100 200 300 400 500 600 700

Rel

ativ

e un

cert

aint

y

MH [GeV]

bbar -> H production, NNPDF2.1, mb=4.75 GeV

S = (7 TeV)2

PDFsCombined PDFs+Mb, δmb=0.25 GeVCombined PDFs+Mb, δmb=0.15 GeV

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NNPDF@NNLO

NNPDF2.5: (preliminary) NNLO analysis based on FONLL-C for DIS structure functions

NNLO only shifts central values by 1–1.5–σ at most, PDF uncertainties unchanged

Harder small–x quarks, stable gluon at small-x (larger differences for MSTW)

x-510 -410 -310 -210 -110

0

1

2

3

4

5

6

)0

2 (x, QΣx

NNPDF2.1 NLO

NNPDF2.5 NNLO (prel)

)0

2 (x, QΣx

x-510 -410 -310 -210 -110

0

1

2

3

4

5

6

)0

2 (x, QΣx

MSTW08 NLO

MSTW08 NNLO

)0

2 (x, QΣx

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NNPDF@NNLO

NNPDF2.5: (preliminary) NNLO analysis based on FONLL-C for DIS structure functions

NNLO only shifts central values by 1–1.5–σ at most, PDF uncertainties unchanged

Harder small–x quarks, stable gluon at small-x (larger differences for MSTW)

x-510 -410 -310 -210 -110

-1

0

1

2

3

4

5

)0

2xg (x, Q

NNPDF2.1 NLO

NNPDF2.5 NNLO (prel)

)0

2xg (x, Q

x-510 -410 -310 -210 -110

-1

0

1

2

3

4

5

)0

2xg (x, Q

MSTW08 NLO

MSTW08 NNLO

)0

2xg (x, Q

NNLO NNPDFs soon ready for LHC phenomenology

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A new QCD regime in HERA data

Deviations from NLO DGLAP insmall-x small-Q2 HERA-I data havebeen reported

NNPDF finds that small–x and Q2

data cannot be recovered bybackwards DGLAP evolution whenexcluded from global PDF fit(arXiv:0910.3143,1007.5405)

Prediction: NNLO should be worsethan NLO for small-x HERA

x-410 -310 -210

2Q

1

10

210

datFitted region, N

dat

CCausally connected region, N

dat

DDisconnected region, N

)2 , Qmin

(x

NLO evolution

x-410 -310 -210

)2=3

.5 G

eV2

(x,Q

2F

0.2

0.4

0.6

0.8

1

1.2

1.4 Fit without cuts

= 0.5cutFit with A

= 1.5cutFit with A

Data

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A new QCD regime in HERA data

Deviations from NLO DGLAP insmall-x small-Q2 HERA-I data havebeen reported

NNPDF finds that small–x and Q2

data cannot be recovered bybackwards DGLAP evolution whenexcluded from global PDF fit(arXiv:0910.3143,1007.5405)

Prediction: NNLO should be worsethan NLO for small-x HERA

Independent confirmation fromHERAPDF (H1 prelim-10-044)

New QCD regime: Non–linear dynamics?High–energy resummation?

HERAPDF

NNPDF

x-410 -310 -210

)2=3

.5 G

eV2

(x,Q

2F

0.2

0.4

0.6

0.8

1

1.2

1.4 Fit without cuts

= 0.5cutFit with A

= 1.5cutFit with A

Data

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αs , NMC and Higgs productionThe Tevatron W asymmetry data

Outline




4 Conclusions

5 Extra Material

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PDFs and Higgs production

The Tevatron reports SM Higgs exclusion bounds of 158 ≤ MH ≤ 175 GeV 95% C.L.,theory prediction used MSTW 2008 NNLO

Challenged by Djoaudi et al. (arXiv:1101.1832): ABKM09 and HERAPDF lead to cross

sections smaller by ∼ 20–50% due to both smaller αs (αABKMs = 0.1135,

αMSTWs = 0.1171) and smaller gg lumi

The Tevatron excluded mass range should be reopened?

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Challenged by Djoaudi et al. (arXiv:1101.1832): ABKM09 and HERAPDF lead to cross

sections smaller by ∼ 20–50% due to both smaller αs (αABKMs = 0.1135,

αMSTWs = 0.1171) and smaller gg lumi but ....

... ABKM09 and HERAPDF do not include Tevatron Run II jet data, crucial to pin downlarge-x gluon

χ2 Description of CDF Run-II inclusive jet data

G. Watt, Les Houches QCD 2011

Non-global PDF sets: poor description of jet data

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Challenged by Djoaudi et al. (arXiv:1101.1832): ABKM09 and HERAPDF lead to crosssections smaller by ∼ 20–50%.

Instead, the two NNLO global fits, MSTW08 and NNPDF2.5, that include Tevatron jets, arein very good agreement

[ GeV ]HM100 150 200 250 300 350 400

( H

->

gg )

)σ

R (

0.9

0.95

1

1.05

1.1

1.15

NNLO gg->H production, Ratio to NNPDF2.5 (TMP)

=0.119SαNNPDF2.5 NNLO(TMP)

=0.119SαMSTW08 NNLO

=0.1171SαMSTW08 NNLO


NNPDF2.5/MSTW08 agree forthe NNLO Higgs at ±5%

Tevatron exclusion limits solid!

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NMC data and Higgs production

ABKM report a 3(1)–σ shift at NNLO (NLO) on the Higgs production cross section in gluonfusion at the LHC (and Tevatron) (arXiv:1101.5261)

Claim is different treatment of fixed target DIS NMC data: used as structure functions(MSTW, NNPDF, CT) or cross sections (ABKM) → Origin of ABKM/MSTW discrepancy?

eσ(x, y , Q2) = F2(x, Q

2)

“

2 − 2y + y2/h

1 + R“

x, Q2”i”

NNPDF finds negligible impact of the treatment of NMC data for Higgs production, both atNLO and at NNLO

5.4

5.5

5.6

5.7

5.8

5.9

σ( H

) [p

b]

LHC 7 TeV - mH = 165 GeV, MCFM NLO

NNPDF2.1 NNPDF2.1 NNPDF2.1reference NMC xsecs wo NMC data

5.5

5.6

5.7

5.8

5.9

6

6.1

6.2

6.3

6.4

σ( H

) [p

b]

LHC 7 TeV - mH = 165 GeV, MCFM NLO

ABKM09 ABKM09NMC xsec NMC F2

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NMC data and Higgs production

ABKM report a 3(1)–σ shift at NNLO (NLO) on the Higgs production cross section in gluonfusion at the LHC (and Tevatron) (arXiv:1101.5261)

Claim is different treatment of fixed target DIS NMC data: used as structure functions(MSTW, NNPDF, CT) or cross sections (ABKM) → Origin of ABKM/MSTW discrepancy?

eσ(x, y , Q2) = F2(x, Q

2)

“

2 − 2y + y2/h

1 + R“

x, Q2”i”

NNPDF finds negligible impact of the treatment of NMC data for Higgs production, both atNLO and at NNLO

[ GeV ]HM100 120 140 160 180 200 220 240 260 280 300 320

( H

->

gg )

)σ

R (

0.9

0.95

1

1.05

1.1

1.15


NNPDF2.5 NNLO(TMP) NMC-XSEC

NNPDF2.5 NNLO(TMP) NMC SF


6.5

7

7.5

8

8.5

σ( H

) [p

b]

LHC 7 TeV - mH = 165 GeV, BDV NNLO

ABKM09 ABKM09NMC xsec NMC F2

The treatment of NMC data has negligible impact on collider Higgs productionAgain, the Tevatron exclusion bounds are solid!

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αs(MZ ) from PDF analysis

Good: Small statistical errors from large dataset

Bad: Bias from PDF parametrization? Dependence on dataset?

NLO: reasonable agreement, NNPDF2.1 smallest statistical uncertainties withoutany theoretical bias

Compare with current PDF average αPDGs (MZ ) = 0.1184 ± 0.0007

0.115

0.116

0.117

0.118

0.119

0.12

0.121

0.122

0.123

αs

( M

Z )

NLO determinations of αs ( MZ ) from PDF Analyses

NNPDF 2.1MSTW08

CTEQ6.6ABKM09

Only statistical errors

PDG10

3860

3880

3900

3920

3940

3960

3980

0.113 0.115 0.117 0.119 0.121 0.123 0.125

χ2

αs(MZ)

NNPDF2.1 Total Dataset

DataParabolic Fit

N.B.: CT, NNPDF and MSTW provide PDF sets for a wide range of αs (MZ ) values

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αs(MZ ) from PDF analysis

Good: Small statistical errors from large dataset

Bad: Bias from PDF parametrization? Dependence on dataset?

NNLO: larger discrepancies, αs lower than αPDGs

Is it meaningful to use αs (MZ ) = 0.1135 in LHC phenomenology?

G. Watt 2011

Crucial to provide PDF sets with varying αs (MZ )

This includes αPDGs (MZ ) for reliable LHC phe-nomenology

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The Tevatron W lepton asymmetry

Accurate Run-II Tevatron data on thepp̄ → W± → l±ν asymmetry available

Aℓ(yℓ) =dσ(W +)/dyℓ − dσ(W

−)/dyℓ

dσ(W +)/dyℓ + dσ(W−)/dyℓ

Some groups (CT10, MSTW) reporttension with other datasets, specially DISdeuteron data. Problem with deuteronnuclear corrections?

CT10 produced two sets, CT10 andCT10W, with and without D0 W asy data(arXiv:1007.2241)

ℓ Cut (GeV) Points χ2 CT10 CT10W

e pℓT > 25 12 79.5 25.3

e 25 < pℓT < 35 12 20.7 25.5

e pℓT > 35 12 91.4 26.5

µ pℓT > 20 9 8.3 13.5

What do we do with Tevatron Wasy data?

ey

0 0.5 1 1.5 2 2.5 3

) e (

ye

A

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

> 35 GeVeT

p

=1.96 TeVS+X ν ± e→ ± W→pp

> 25 GeVνTE

)-1D0 electron data (0.75 fbCT10 (Solid band)CTEQ6.6 (Hatched band)

ey

0 0.5 1 1.5 2 2.5 3

) e (

ye

A

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

> 35 GeVeT

p

=1.96 TeVS+X ν ± e→ ± W→pp

> 25 GeVνTE

)-1D0 electron data (0.75 fbCT10W (Solid band)CTEQ6.6 (Hatched band)

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The Tevatron W lepton asymmetry

Accurate Run-II Tevatron data on thepp̄ → W± → l±ν asymmetry available

Some groups report tension with otherdatasets, specially DIS deuteron data.Problem with deuteron nuclearcorrections?

NNPDF (arXiv:1012.0836): D0 µ + e

inclusive data (not binned in plt) perfectlyconsistent with global fit, reduction invalence PDF uncertainty + no tensionexclusive to deuteron data found

Set χ2 χ2rw χ2tot

D0 µ (ET > 20 GeV) 0.62 0.51 1.14D0 e bin A (ET > 25 GeV) 2.12 1.55 1.13

D0 µ + e bin A 1.44 1.11 1.13D0 e bin B (25< ET < 35 GeV) 4.75 1.12 1.16

D0 e bin C (ET > 35 GeV) 5.06 2.51 1.16

TeV W asy data: useful constrains on PDFsNo issues with DIS deuteron data, but care with

systematics for binned peT data

x0.1 0.2 0.3 0.4 0.5 0.6 0.7

) ]

2 0R

elE

rr [

d / u

( x

, Q

0

0.02

0.04

0.06

0.08

0.1

0.12NNPDF2.0

NNPDF2.0 + eBinA + mu

NNPDF2.0 + mu

NNPDF2.0 + eBinA

NNPDF2.0 + eBinB

NNPDF2.0 + eBinC

η0 0.5 1 1.5 2 2.5 3

)ηA

(

-80

-60

-40

-20

0

20

binB

NNPDF20

NNPDF20+Rwgt(binB)

D0(e,binB)

binB

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Outline




4 Conclusions

5 Extra Material

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Conclusions

Very intense progress in PDF determinations in the last years

Systematic benchmarking, heavy quark mass effects, many new datasets,unbiased NNPDFs, among many other theoretical and computationaldevelopements

The LHC is performing extremely well → Precision measurements aroundthe corner → Need precision PDFs to match the data accuracy

Global PDF sets in reasonable agreement → PDF4LHC recipeeDangerous to use non-global PDF sets for LHC phenomenology

Not discussed here, but very relevant: Impact of PDFs for precisiondetermination of ElectroWeak parameters at the LHC

Thanks for your attention!

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Conclusions

Very intense progress in PDF determinations in the last years

Systematic benchmarking, heavy quark mass effects, many new datasets,unbiased NNPDFs, among many other theoretical and computationaldevelopements

The LHC is performing extremely well → Precision measurements aroundthe corner → Need precision PDFs to match the data accuracy

Global PDF sets in reasonable agreement → PDF4LHC recipeeDangerous to use non-global PDF sets for LHC phenomenology

Not discussed here, but very relevant: Impact of PDFs for precisiondetermination of ElectroWeak parameters at the LHC

Thanks for your attention!

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Outline




4 Conclusions

5 Extra Material

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Bayesian reweighting

Given the probability distribution of the PDFs represented by Nrep instances,{PDFi}, i = 1, Nrep

Given a set of new experimental data (or simulated pseudo-data) y = {y1, y2, · · · , yn}

Given a general functional of the PDFs, O [{PDF}]

The impact of the new data y on the PDFs can be determined using Bayesian inference withoutrefitting : PDF reweighting

〈O〉old =

NrepX

k=1

1

NrepO[fk ] → 〈O〉new =

NX

k=1

wk O[fk ]

wk ≡ Nχ(χ2(y , fk ))

n/2−1e− 1

2χ2(y,fk ),

χ2(y , fk ) → χ2 of new data for the prediction of PDFk

No need of any refitting!

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Bayesian reweighting

Given the probability distribution of the PDFs represented by Nrep instances,{PDFi}, i = 1, Nrep

Given a set of new experimental data (or simulated pseudo-data) y = {y1, y2, · · · , yn}

Given a general functional of the PDFs, O [{PDF}]

The impact of the new data y on the PDFs can be determined using Bayesian inference withoutrefitting : PDF reweighting

〈O〉old =

NrepX

k=1

1

NrepO[fk ] → 〈O〉new =

NX

k=1

wk O[fk ]

wk ≡ Nχ(χ2(y , fk ))

n/2−1e− 1

2χ2(y,fk ),

χ2(y , fk ) → χ2 of new data for the prediction of PDFk

No need of any refitting!

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Validation: Tevatron inclusive jets

Tevatron inclusive jets constrain large-x gluon

Compare refitting with reweighting → Statistically identical results

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

) 02xg

(x, Q

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7NNPDF2.0 (DIS+DYP)

NNPDF2.0 (DIS+DYP) + rw JET

NNPDF2.0

x0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

) 02A

bs.e

r.(x

g) (

x, Q

0

0.05

0.1

0.15

0.2

0.25NNPDF2.0 (DIS+DYP)

NNPDF2.0 (DIS+DYP) + rw JET

NNPDF2.0

NNPDFs provides a bona-fide, statistically solid representation of the PDF uncertaintiesNNPDF uncertainties behave as required by Bayes Theorem

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An ideal PDF set




3 Provide PDF uncertainty bands checked to provideconsistently-sized confidence levels for individual experiments




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PDF sets from reduced datasets

xg(x,Q20) xV(x,Q20)

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

0.6NNPDF2.1 global

NNPDF2.1 DIS-only

NNPDF2.1 HERA-only

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 NNPDF2.1 global

NNPDF2.1 DIS-only

NNPDF2.1 HERA-only

If PDF errors are reliably estimated, PDF uncertainties consistently grow when datasets areremoved

When PDF parametrizations not flexible enough, adding new data → larger PDF errors

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PDF sets from reduced datasets

If PDF errors are reliably estimated, PDF uncertainties consistently grow when datasets areremoved

When PDF parametrizations not flexible enough, adding new data → larger PDF errorsexample CT10 (26 params) vs. CTEQ6.6 (22 params)

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Distances between NNPDF NLO and NNLO

0

2

4

6

8

10

12

14

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 current fit vs NNPDF 2.1Σg

T3V

∆Ss+s-

0

2

4

6

8

10

12

14

1e-05 0.0001 0.001 0.01 0.1 1

d[ q

(x,Q

02)

]

x



T3V

∆Ss+s-

0

2

4

6

8

10

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


T3V

∆Ss+s-

0

2

4

6

8

10

1e-05 0.0001 0.001 0.01 0.1 1

d[ σ

q(x,

Q02

) ]

x



T3V

∆Ss+s-

45 / 62



Towards PDF convergence

Global PDF sets have improved convergence in recent releases

But still some important disagreements to be understood

LOW-X GLUON

x-510 -410 -310 -210 -110

) 02xg

(x,

Q

-2

-1

0

1

2

3

4

5

6

Small-x gluon - Status prior to NNPDF1.0

CTEQ6.6

MRST2001E

Small-x gluon - Status prior to NNPDF1.0

46 / 62






LOW-X GLUON

x-510 -410 -310 -210 -110

) 02xg

(x,

Q

-2

-1

0

1

2

3

4

5

6

Small-x gluon - NNPDF1.0 released

NNPDF1.0

CTEQ6.6

MRST2001E

Small-x gluon - NNPDF1.0 released

47 / 62






LOW-X GLUON

x-510 -410 -310 -210 -110

) 02xg

(x,

Q

-2

-1

0

1

2

3

4

5

6

Small-x gluon - Status 2010

NNPDF2.0

CT10

MSTW2008

Small-x gluon - Status 2010

GOOD!48 / 62






STRANGENESS

x-310 -210 -110

) 02 (

x, Q

+xs

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

NNPDF2.1

CT10

MSTW08

BAD! To be understood!49 / 62



PDF uncertainties in Hessian approach

PDF parametrization bias are an important (often dominant) source ofuncertainty:

... parametrization error is in many places as large as the uncertainty estimated, via∆χ2 = 10, on the basis of conflicts observed between the different data sets usedin the analysis. At very large x, ..., the parametrization error even becomes largecompared to the modified ∆χ2 = 100 uncertainty estimate used in CT10 ... Theseparametrization effects persist up to scales of Q = 100 GeV and beyond, so theyare significant for predictions of important background and discovery processes atthe Tevatron and LHC. (J. Pumplin, arXiv:0909.5176)

50 / 62



PDF uncertainties in Hessian approach

PDF parametrization bias are an important (often dominant) source ofuncertainty:Hessian PDF sets need to account for this effect. Two options:

1 Effective larger tolerances ∆χ2 ≫ 1 (CT10, MSTW, JR)2 Explicit parametrization uncertainties (HERAPDF1.0)

Without accounting for parametrization bias → substantialunderestimation of PDF uncertainties

0.2

0.4

0.6

0.8

1

-410 -310 -210 -110 1

0.2

0.4

0.6

0.8

1

HERAPDF1.0

exp. uncert.

model uncert.

parametrization uncert.

x

xf 2 = 1.9 GeV2Q

vxu

vxd

0.05)×xS ( 0.05)×xg (

H1 and ZEUS

0.2

0.4

0.6

0.8

1

-310

-210

-110

1

10

-410 -310 -210 -110 1-310

-210

-110

1

10

HERAPDF1.0

exp. uncert.

model uncert.

parametrization uncert.

x

xf 2 = 1.9 GeV2Q

vxu

vxd

xS

xg

H1 and ZEUS

-310

-210

-110

1

10

51 / 62



Heavy quark schemes for F c2 (x , Q2)

NNPDF based on FONLL-A (at NLO) and FONLL-C (at NNLO) GM-VFNForte, Nason, Laenen and Rojo, arxiv:1001.2312GM-VFN interpolate between FFN at low Q2 and ZM–VFN at high-Q2

Benchmark comparison of GM-VFN schemes: J. Rojo et al., arXiv:1003.1241

FONLL originally for hadronic collisions: Cacciari, Greco and Nason, hep-ph/9803400

52 / 62



Parametrization independence

Compute distances between NNPDF2.1 with varying NN architectureFrom arch. 2-5-3-1 to arch. 2-4-3-1 → From 289 to 230 parameters

d2“

〈q(1)〉, 〈q(2)〉”

=

`

〈q(1)〉(1) − 〈q(2)〉(2)

´2

σ2(1)

[〈q(1)〉] + σ2(2)

[〈q(2)〉]

All distances d ∼ 1 → The two PDF sets are statistically identical(S. Forte, PHYSTAT 2011)

0.8

1

1.2

1.4

1.6

1.8

2

1e-05 0.0001 0.001 0.01 0.1 1

d[ q

(x,Q

02)

]

x


NNPDF 2.1, arch 2-5-3-1 vs 2-4-3-1, Nrep=100Σg

T3V

∆Ss+s-

0.8

1

1.2

1.4

1.6

1.8

2

1e-05 0.0001 0.001 0.01 0.1 1

d[ σ

q(x,

Q02

) ]

x


NNPDF 2.1, arch 2-5-3-1 vs 2-4-3-1, Nrep=100Σg

T3V

∆Ss+s-

53 / 62



Impact on NuTeV anomaly

Accurate determination of xs− → Important phenomenological implications:NuTeV anomaly: Discrepancy (≥ 3σ) between indirect (global fit)and direct (NuTeVneutrino scattering) determinations of sin2 θW

EW fit

sin2 θW = 0.2223 ± 0.0003

NuTeV (assumes [S−] = 0)

sin2 θW = 0.2277 ± 0.0017

54 / 62



Impact on NuTeV anomaly

Accurate determination of xs− → Important phenomenological implications:NuTeV anomaly: Discrepancy (≥ 3σ) between indirect (global fit)and direct (NuTeVneutrino scattering) determinations of sin2 θW

EW fit

sin2 θW = 0.2223 ± 0.0003

NuTeV (assumes [S−] = 0)

sin2 θW = 0.2277 ± 0.0017

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

NuTeV01+ NNPDF2.0/2.1 Once NNPDF

ˆ

S−˜

accountedfor the NuTeV anomalydisappears

NuTeV + [S−]nnpdf2.1

sin2 θW = 0.2244 ± 0.0025

55 / 62



Direct |Vcs| determination

The CKM matrix element |Vcs | is afundamental SM parameter

Its precision determination relevant for BSMindirect searches via CKM unitarity violations

|Vcs | in neutrino DIS affected by large PDFuncertainties in s(x , Q2)

σν,c ∼ |Vcs |

2s(x , Q2)

PDF determinations useless for |Vcs |2?

CKM global fit

Vcs = 0.97334±0.00023, ∆Vcs ∼ 0.02%

Direct determination-D and B decays

Vcs = 1.04 ± 0.06, ∆Vcs ∼ 6%

Direct det from ν−DIS (CCFR)

Vcs ≥ 0.74 (90%CL)

[PDG, Amsler et al, Phys. Lett. B67(2008) 1.]

56 / 62



Direct |Vcs| determination

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)

Direct det from ν−DIS (CCFR)

Vcs ≥ 0.74 (90%CL)

Direct determination-D and B decays

Vcs = 1.04 ± 0.06, ∆Vcs ∼ 6%

Direct det NNPDF1.2

Vcs = 0.96 ± 0.07, ∆Vcd ∼ 7%

[PDG, Amsler et al, Phys. Lett. B67(2008) 1.]

Unbiased parametrizations for PDFs allow to discriminate variations in s+(x)from variations in CKM matrix elements

NNPDF |Vcs| determination to be included in next PDG global average

57 / 62



Combined PDF+αs uncertainties

10.5

11

11.5

12

12.5

13

σ(H

( 12

0 G

eV )

) [p

b]

PDF4LHC benchmarks - NNPDF2.0 - LHC 7 TeV

αs=0.115

αs=0.117

αs=0.119

αs=0.121

αs=0.123

PDF+αs(Quad)

PDF+αs(Exact)

150

160

170

180

190

200

σ(tt)

[pb]

PDF4LHC benchmarks - NNPDF2.0 - LHC 14 TeV

αs=0.115

αs=0.117

αs=0.119

αs=0.121

αs=0.123

PDF+αs(Quad)

PDF+αs(Exact)

Combined PDF+αs uncertainties important for processes sensitive to αs atBorn level (gg → H, tt̄)

58 / 62



Impact of future LHC data

NNPDF allows to optimize and design dedicated LHC measurements to achieve best performanceExample: Proposal to measure machine lumi with 2% accuracy → Within the NNPDF approach wecan quantify impact for precision EWK measurements ....

x-410 -310 -210 -110

xuba

r

0.9

0.95

1

1.05

1.1

1.15

1.2

, ratio to NNPDF2.12 GeV4 = 102Q

NNPDF2.1

NNPDF2.1 + LHC7 Wasy

(Z)/dyσNNPDF2.1 + LHC7 Wasy + d

, ratio to NNPDF2.12 GeV4 = 102Q

Precision Physics at the LHC, LPNHE Paris 2010

59 / 62



Deviations from NLO DGLAP

x-510 -410 -310 -210 -110 1

]2 [

GeV

2 T /

p2

/ M

2Q

1

10

210

310

410

510

610 NMC-pdNMCSLACBCDMSHERAI-AVCHORUSFLH108NTVDMNZEUS-H2DYE886CDFWASYCDFZRAPD0ZRAPCDFR2KT

= 0.5cutA = 1.0cutA = 1.5cutA = 3.0cutA = 6.0cutA

NNPDF2.0 dataset

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Deviations from NLO DGLAP [n

b]lν + l

B +Wσ

11.4

11.6

11.8

12

12.2

12.4

12.6

61 / 62



Deviations from NLO DGLAPH

→ggσ

36.5

37

37.5

38

38.5

39

62 / 62

PDFs in the LHC eraPDFs: Recent progressBenchmark LHC observablesHeavy quark mass effectsNNPDF@NNLODeviations from fixed order DGLAP

PDFs: Open problemss, NMC and Higgs productionThe Tevatron W asymmetry data


recent developements and open problems in parton distributions · 2011. 3. 1. · pdfs in the lhc...

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