recent developements and open problems in parton distributions · 2011. 3. 1. · pdfs in the lhc...
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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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
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 in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
PDFs: Status of the Art
M. Ubiali, Challenges for precision physics at the LHC, Paris 2010
6 / 62
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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
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 experimentalinformation 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
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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
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 orestimate effect of parton 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
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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
An ideal PDF set
S. Forte, Parton Distributions at the Dawn of the LHC, arxiv:
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 availableperturbative order
6 Provide PDFs for a variety of values of αs (MZ ) and for the heavy quark massesmc and mb
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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
Benchmark LHC observablesHeavy quark mass effectsNNPDF@NNLODeviations from fixed order DGLAP
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
Benchmark LHC observablesHeavy quark mass effectsNNPDF@NNLODeviations from fixed order DGLAP
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
Benchmark LHC observablesHeavy quark mass effectsNNPDF@NNLODeviations from fixed order DGLAP
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
Benchmark LHC observablesHeavy quark mass effectsNNPDF@NNLODeviations from fixed order DGLAP
Benchmark LHC observables
Study and plots from G. Watt, Les Houches QCD 2011
Same trend as for qq̄NNPDF2.1 in good agreement with MSTW08, CT10 lower (also for Higgs)
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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
Benchmark LHC observablesHeavy quark mass effectsNNPDF@NNLODeviations from fixed order DGLAP
Benchmark LHC observables
Study and plots from G. Watt, Les Houches QCD 2011
Same trend as for qq̄NNPDF2.1 in good agreement with MSTW08, CT10 lower (also for Higgs)
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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
Benchmark LHC observablesHeavy quark mass effectsNNPDF@NNLODeviations from fixed order DGLAP
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
Benchmark LHC observablesHeavy quark mass effectsNNPDF@NNLODeviations from fixed order DGLAP
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
Benchmark LHC observablesHeavy quark mass effectsNNPDF@NNLODeviations from fixed order DGLAP
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
Benchmark LHC observablesHeavy quark mass effectsNNPDF@NNLODeviations from fixed order DGLAP
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
Benchmark LHC observablesHeavy quark mass effectsNNPDF@NNLODeviations from fixed order DGLAP
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
Benchmark LHC observablesHeavy quark mass effectsNNPDF@NNLODeviations from fixed order DGLAP
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
Benchmark LHC observablesHeavy quark mass effectsNNPDF@NNLODeviations from fixed order DGLAP
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
24 / 62
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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
αs , NMC and Higgs productionThe Tevatron W asymmetry data
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
25 / 62
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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
αs , NMC and Higgs productionThe Tevatron W asymmetry data
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
αs , NMC and Higgs productionThe Tevatron W asymmetry data
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 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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
αs , NMC and Higgs productionThe Tevatron W asymmetry data
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 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
NNLO gg->H production, Ratio to NNPDF2.5 (TMP)
NNPDF2.5/MSTW08 agree forthe NNLO Higgs at ±5%
Tevatron exclusion limits solid!
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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
αs , NMC and Higgs productionThe Tevatron W asymmetry data
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
αs , NMC and Higgs productionThe Tevatron W asymmetry data
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
NNLO gg->H production, Ratio to NNPDF2.5 (TMP)
NNPDF2.5 NNLO(TMP) NMC-XSEC
NNPDF2.5 NNLO(TMP) NMC SF
NNLO gg->H production, Ratio to NNPDF2.5 (TMP)
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
αs , NMC and Higgs productionThe Tevatron W asymmetry data
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
αs , NMC and Higgs productionThe Tevatron W asymmetry data
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
αs , NMC and Higgs productionThe Tevatron W asymmetry data
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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ConclusionsExtra Material
αs , NMC and Higgs productionThe Tevatron W asymmetry data
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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ConclusionsExtra Material
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
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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ConclusionsExtra Material
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
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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ConclusionsExtra Material
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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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
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 provideconsistently-sized confidence levels 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
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ConclusionsExtra Material
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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ConclusionsExtra Material
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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ConclusionsExtra Material
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
Distance between central values
NNPDF current fit vs NNPDF 2.1Σg
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
NNPDF current fit vs NNPDF 2.1Σg
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
Distance between PDF uncertainties
NNPDF current fit vs NNPDF 2.1Σg
T3V
∆Ss+s-
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ConclusionsExtra Material
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
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ConclusionsExtra Material
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 - NNPDF1.0 released
NNPDF1.0
CTEQ6.6
MRST2001E
Small-x gluon - NNPDF1.0 released
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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
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 2010
NNPDF2.0
CT10
MSTW2008
Small-x gluon - Status 2010
GOOD!48 / 62
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ConclusionsExtra Material
Towards PDF convergence
Global PDF sets have improved convergence in recent releases
But still some important disagreements to be understood
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
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ConclusionsExtra Material
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)
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ConclusionsExtra Material
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
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ConclusionsExtra Material
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
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ConclusionsExtra Material
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
Distance between central values
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
Distance between PDF uncertainties
NNPDF 2.1, arch 2-5-3-1 vs 2-4-3-1, Nrep=100Σg
T3V
∆Ss+s-
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ConclusionsExtra Material
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
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ConclusionsExtra Material
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
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ConclusionsExtra Material
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.]
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ConclusionsExtra Material
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
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ConclusionsExtra Material
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)
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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
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
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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
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
60 / 62
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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
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
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PDFs in the LHC eraPDFs: Recent progressPDFs: Open problems
ConclusionsExtra Material
Deviations from NLO DGLAPH
→ggσ
36.5
37
37.5
38
38.5
39
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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
ConclusionsExtra Material
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