Parton Distributions and the Relation to LHC and Higgs Physics · 2012. 2. 17. · Parton...

Parton Distributions and the Relation to LHC and

Higgs Physics

Robert Thorne

February 15th, 2012

University College London

Thanks to Alan Martin, James Stirling and Graeme Watt

Birmingham – February 2012

e e

γ⋆ Q2

x

P

perturbativecalculable

coefficient function

CPi (x, αs(Q2))

nonperturbativeincalculable

parton distribution

fi(x, Q2, αs(Q

2))

Strong force makes it difficultto perform analytic calculationsof scattering processes involvinghadronic particles.

The weakening of αS(µ2) at

higher scales → the FactorizationTheorem.

Hadron scattering with anelectron factorizes.

Q2 – Scale of scattering

x = Q2

2mν – Momentum fraction ofParton (ν=energy transfer)

Birmingham – February 2012 1

P

P

fi(xi, Q2, αs(Q

2))

CPij(xi, xj, αs(Q2))

fj(xj, Q2, αs(Q

2))

The coefficient functionsCPi (x, αs(Q

2)) are processdependent (new physics) butare calculable as a power-seriesin αs(Q

2).

CPi (x, αs(Q2)) =

∑

k

CP,ki (x)αks(Q

2).

Since the parton distributionsfi(x,Q

2, αs(Q2)) are process-

independent, i.e. universal,and evolution with scaleis calculable, once theyhave been measured atone experiment, one canpredict many other scatteringprocesses.


Obtaining PDF sets – General procedure.

Start parton evolution at low scale Q20 ∼ 1GeV2. In principle 11 different partons to

consider.

u, ū, d, d̄, s, s̄, c, c̄, b, b̄, g

mc, mb ≫ ΛQCD so heavy parton distributions determined perturbatively. Leaves 7independent combinations, or 6 if we assume s = s̄ (just started not to).

uV = u − ū, dV = d − d̄, sea = 2 ∗ (ū + d̄ + s̄), s + s̄ d̄ − ū, g.

Input partons parameterised as, e.g. MSTW,

xf(x, Q20) = (1 − x)η(1 + ǫx0.5 + γx)xδ.

Evolve partons upwards using LO, NLO (or increasingly NNLO) DGLAP equations.

dfi(x,Q2, αs(Q

2))

d lnQ2=

∑

j

Pij(x, αs(Q2)) ⊗ fj(x,Q

2, αs(Q2))


Fit data for scales above 2−5GeV2. Need many different types for full determination.

● Lepton-proton collider HERA – (DIS) → small-x quarks (best below x ∼ 0.05).Also gluons from evolution (same x), and now FL(x, Q

2). Also, jets → moderate-xgluon.Charged current data some limited info on flavour separation. Heavy flavourstructure functions – gluon and charm, bottom distributions and masses.

● Fixed target DIS – higher x – leptons (BCDMS, NMC, . . .) → up quark (proton)or down quark (deuterium) and neutrinos (CHORUS, NuTeV, CCFR) → valenceor singlet combinations.

● Di-muon production in neutrino DIS – strange quarks and neutrino-antineutrinocomparison → asymmetry . Only for x > 0.01.

● Drell-Yan production of dileptons – quark-antiquark annihilation (E605, E866) –high-x sea quarks. Deuterium target – ū/d̄ asymmetry.

● High-pT jets at colliders (Tevatron) – high-x gluon distribution – x > 0.01 .

● W and Z production at colliders (Tevatron/LHC) – different quark contributionsto DIS.


This procedure is generally successful and is part of a large-scale, ongoing project.Results in partons of the form shown.

x-410 -310 -210 -110 1

)2xf

(x,Q

0

0.2

0.4

0.6

0.8

1

1.2

g/10

d

d

u

uss,

cc,

2 = 10 GeV2Q

x-410 -310 -210 -110 1

)2xf

(x,Q

0

0.2

0.4

0.6

0.8

1

1.2

x-410 -310 -210 -110 1

)2xf

(x,Q

0

0.2

0.4

0.6

0.8

1

1.2

g/10

d

d

u

u

ss,

cc,

bb,

2 GeV4 = 102Q

x-410 -310 -210 -110 1

)2xf

(x,Q

0

0.2

0.4

0.6

0.8

1

1.2

MSTW 2008 NLO PDFs (68% C.L.)

Various choices of PDF – MSTW, CTEQ, NNPDF, AB(K)M, HERA, Jimenez-Delgadoet al etc.. All LHC cross-sections rely on our understanding of these partons.


|y|0 0.5 1 1.5 2 2.5 3

/dy

σ dσ

1/

0

0.1

0.2

0.3

Run II∅* rapidity shape distribution from DγZ/

MRST2006 NNLO PDFs

LO Vrap

NLO Vrap

NNLO Vrap

Run II∅* rapidity shape distribution from DγZ/Leads to very accurate andprecise predictions.

Comparison of MSTW predictionfor Z rapidity distribution withdata.


Interplay of LHC and pdfs/QCD

Make predictions for all processes, both SM and BSM, as accurately as possible givencurrent experimental input and theoretical accuracy.

Check against well-understood processes, e.g. central rapidity W, Z production(luminosity monitor), lowish-ET jets, .....

Compare with predictions with more uncertainty and lower confidence, e.g. high-ETjets, high rapidity bosons or heavy quarks .....

Improve uncertainty on parton distributions by improved constraints, and checkunderstanding of theoretical uncertainties, and determine where NNLO, electroweakcorrections, resummations etc. needed.

Make improved predictions for both background and signals with improved partonsand surrounding theory.

Spot new physics from deviations in these predictions. As a nice by-product improveour understanding of the strong sector of the Standard Model considerably.

Remainder of talk describes this process in more detail.


LHC Physics

10-7

10-6

10-5

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10-3

10-2

10-1

100

100

101

102

103

104

105

106

107

108

109

fixedtarget

HERA

x1,2

= (M/14 TeV) exp(±y)Q = M

LHC parton kinematics

M = 10 GeV

M = 100 GeV

M = 1 TeV

M = 10 TeV

66y = 40 224

Q2

(G

eV2 )

x

LHCb LHCb

The kinematic range forparticle production at the LHCis shown.

x1,2=x0 exp(±y), x0=M√

s.

Smallish x ∼ 0.001 − 0.01parton distributions thereforevital for understanding thestandard production processesat the LHC.

However, even smaller (andhigher) x required when onemoves away from zero rapidity,e.g. when calculating totalcross-sections.


0 1 2 3 4 5

1

10

100

24 GeV

pdf uncertainty ondσ(W+)/dy

W, dσ(W-)/dy

W,

dσ(Z)/dyZ, dσ(DY)/dMdy

at LHC using MSTW2007NLO

% p

df u

ncer

tain

ty

y

8 GeV

Uncertainty on σ(Z) and σ(W+)grows at high rapidity. Converges– both dominated by u(x1)ū(x2) atvery high y.

Uncertainty on σ(W−) grows morequickly at very high y.

Uncertainty on σ(γ⋆) is greatest as yincreases.


) (nb)ν± l→ ± B(W⋅ ±Wσ

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11

) (

nb)

- l+ l→ 0

B(Z

⋅ 0Zσ

0.8

0.85

0.9

0.95

1

= 7 TeV)sNLO W and Z cross sections at the LHC (

SαOuter error bars: PDF+Inner error bars: PDF only

R(W/Z) = 10.8

10.911.0

G. W

att

(A

pril

2011

)

68% C.L. PDFMSTW08CTEQ6.6

CT10

CT10W

NNPDF2.1HERAPDF1.0HERAPDF1.5

ABKM09GJR08

) (nb)ν± l→ ± B(W⋅ ±Wσ

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11

) (

nb)

- l+ l→ 0

B(Z

⋅ 0Zσ

0.8

0.85

0.9

0.95

1

Predictions (Watt) for W andZ cross-sections for LHC withcommon NLO QCD and vectorboson width effects, and commonbranching ratios, and at 7TeV.

Good agreement at NLO forvariety of PDFs.

In fact comparing all groups getsignificant discrepancies betweenthem even for this benchmarkprocess.

Can understand some of thesystematic differences.

Total W, Z total cross-sectionsbest-case scenario – rapiditiesshow more variation.


More discrepancy.

)2Z

(MSα0.114 0.116 0.118 0.12 0.122 0.124

-Wσ

/ +Wσ ≡ ±

R

1.4

1.42

1.44

1.46

1.48

1.5

68% C.L. PDFMSTW08

CTEQ6.6

NNPDF2.0HERAPDF1.0

ABKM09GJR08

= 7 TeV)s ratio at the LHC (-/W+NLO W

SαOuter: PDF+Inner: PDF onlyVertical error bars

)2Z

(MSα0.114 0.116 0.118 0.12 0.122 0.124

-Wσ

/ +Wσ ≡ ±

R

1.4

1.42

1.44

1.46

1.48

1.5

More variation also in W+/W− ratio. Shows variations in flavour and quark-antiquarkdecompositions.


Variations in Higgs Cross-Section Predictions – NLO

Much more dependent on gluon distributions.

)2Z

(MSα0.114 0.116 0.118 0.12 0.122 0.124

(pb

)Hσ

10.5

11

11.5

12

12.5

13

68% C.L. PDFMSTW08

CTEQ6.6

NNPDF2.0HERAPDF1.0

ABKM09GJR08

= 120 GeVH

= 7 TeV) for MsH at the LHC (→NLO gg


)2Z

(MSα0.114 0.116 0.118 0.12 0.122 0.124

(pb

)Hσ

10.5

11

11.5

12

12.5

13

)2Z

(MSα0.114 0.116 0.118 0.12 0.122 0.124

(pb

)Hσ

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3

68% C.L. PDFMSTW08

CTEQ6.6

NNPDF2.0HERAPDF1.0

ABKM09GJR08

= 240 GeVH



)2Z

(MSα0.114 0.116 0.118 0.12 0.122 0.124

(pb

)Hσ

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3

Dotted lines show how central PDF predictions vary with αS(M2Z). (Again plots by G

Watt.)


Sources of Variations/Uncertainty

It is vital to consider theoretical/assumption-dependent uncertainties:

● Methods of determining “best fit” and uncertainties.

● Underlying assumptions in procedure, e.g. parameterisations and data used.

● Treatment of heavy flavours.

● PDF and αS correlations.

Responsible for differences between groups for extraction of fixed-order PDFs.


Variety of PDFs

MSTW make available PDFs in a very wide variety of forms.

● At , LO, NLO and NNLO, with some minor approximations at NNLO.

● Also a variety of extensions such as different αS values, heavy quark masses,different flavour numbers. Latter covered tomorrow.

● Older MRST versions of modified LO* and LO** PDFs and of PDFs includingQED evolution.

Fit data for scales above 2GeV2. (most) DIS data for W 2 > 15GeV2. Will mentioneffect of cuts later.

Don’t yet include combined HERA cross-section data. Have checked effects of this.In some cases predictions change by a little over 1σ, in many cases less.

Major problems with high-luminosity D0 lepton asymmetry in some binnings. Samefor other groups.


0

20

40

60

80

100

10-5

10-4

10-3

10-2

10-1

1x

xg(x,Q2=10000GeV2)

-10

-5

0

5

10

15

10-5

10-4

10-3

10-2

10-1x

percentage difference at Q2=10000GeV2

Comparison of gluon from fitusing combined HERA data toMSTW2008 NNLO versions with 1−σ, uncertainty shown.

Slight difference in details ofnormalisation treatment compared toprevious versions, still preliminary.First times showed uncertainty.

Value of αS(M2Z) moves slightly,

0.1171 → 0.1178.

Changes always within 1 − σ, andreally less due to correlations withαS.

Uncertainty slightly smaller, especiallyat very small x.


0

2

4

6

10-5

10-4

10-3

10-2

10-1

1x

xu(x,Q2=10000GeV2)

-10

-5

0

5

10

15

10-5

10-4

10-3

10-2

10-1x


0

2

4

6

10-5

10-4

10-3

10-2

10-1

1x

xd(x,Q2=10000GeV2)

-10

-5

0

5

10

15

10-5

10-4

10-3

10-2

10-1x


Most dramatic change for up quark at about x = 0.01.


Impact on Cross Sections.

The values of the predicted cross-sections at NNLO for Z and a 120 GeV Higgs bosonat the Tevatron and the LHC (latter for 14 TeV centre of mass energy).

PDF set Bl+l−·σZ(nb)TeV σH(pb)TeV Bl+l−·σZ(nb)LHC σH(pb)LHCMSTW08 0.2507 0.9549 2.051 50.51

Comb HERA +2.1% +1.2% +0.9% +0.7%

For new global fits 2% effect on Z (and W ) cross sections at Tevatron, but smallchange at LHC. Similar to, or less than 1 − σ uncertainty in former case.

Maximum of ∼ 1% for Higgs. Small effect.


Parton Fits and Uncertainties. Two main approaches.

Parton parameterization and Hessian (Error Matrix) approach first used by H1 andZEUS, and extended by CTEQ.

χ2 − χ2min ≡ ∆χ2 =

∑

i,j

Hij(ai − a(0)i )(aj − a

(0)j )

The Hessian matrix H is related to the covariance matrix of the parameters by

Cij(a) = ∆χ2(H−1)ij.

We can then use the standard formula for linear error propagation.

(∆F )2 = ∆χ2∑

i,j

∂F

∂ai(H)−1ij

∂F

∂aj,

This is now the most common approach.


Can find and rescale eigenvectors of H leading to diagonal form

∆χ2 =∑

i

z2i

Implemented by CTEQ, then MRST/MSTW, HERAPDF. Uncertainty on physicalquantity then given by

(∆F )2 =∑

i

(

F (S(+)i ) − F (S

(−)i )

)2,

where S(+)i and S

(−)i are PDF sets displaced along eigenvector direction.

Must choose “correct” ∆χ2 given complication of errors in full fit and sometimesconflicting data sets.


Determination of best fit and uncertainties

All but NNPDF minimise χ2 and expand about best fit.

● MSTW08 – 20 eigenvectors. Due to incompatibility of different sets and (perhapsto some extent) parameterisation inflexibility (little direct evidence for this) haveinflated ∆χ2 of 5 − 20 for eigenvectors.

● CT10 – 26 eigenvectors. Inflated ∆χ2 of ∼ 50 for 1 sigma for eigenvectors.

● HERAPDF2.0 – 10 eigenvectors. Use “∆χ2 = 1′′. Additional model andparameterisation uncertainties.

● ABKM09 – 21 parton parameters. Use ∆χ2 = 1. Also αS, mc, mb.

● GJR08 – 20 parton parameters (8 fixed for uncertainty) and αS. Use ∆χ2 ≈ 20.

Impose strong theory constraint on input form of PDFs.

Perhaps surprisingly all get rather similar uncertainties for PDFs cross-sections, thoughdon’t all mean the same.


Neural Network group (Ball et al.) limit parameterization dependence. Leads toalternative approach to “best fit” and uncertainties.

First part of approach, no longer perturb about best fit. Construct a set of Monte

Carlo replicas F art,ki,p of the original data set Fexp,(k)i,p .

Where r(k)p are random numbers following Gaussian distribution, and S

(k)p,N is the

analogous normalization shift of the of the replica depending on 1 + r(k)p,nσnormp .

Hence, include information about measurements and errors in distribution of Fart,(k)i,p .

Fit to the data replicas obtaining PDF replicas q(net)(k)i (follows Giele et al.)

Mean µO and deviation σO of observable O then given by

µO =1

Nrep

Nrep∑

1

O[q(net)(k)i ], σ

2O =

1

Nrep

Nrep∑

1

(O[q(net)(k)i ] − µO)

2.

Eliminates parameterisation dependence by using a neural net which undergoes aseries of (mutations via genetic algorithm) to find the best fit. In effect is a muchlarger sets of parameters – ∼ 37 per distribution.


Parameterisations - for the gluon at small x different parameterisations lead to verydifferent uncertainty for small x gluon.

x-510 -410 -310 -210 -110

Fra

ctio

nal u

ncer

tain

ty

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

2 = 5 GeV2Gluon distribution at Q

MSTW 2008 NLO (90% C.L.)

CTEQ6.6 NLO

Alekhin 2002 NLONNPDF1.0 (1000 replicas)

x-510 -410 -310 -210 -110

Fra

ctio

nal u

ncer

tain

ty

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Most assume single power xλ at input → limited uncertainty. If input at low Q2 λpositive and small-x input gluon fine-tuned to ∼ 0. Artificially small uncertainty.

If g(x) ∝ xλ±∆λ then ∆g(x) = ∆λ ln(1/x) ∗ g(x).

MRST/MSTW and NNPDF more flexible (can be negative) → rapid expansion ofuncertainty where data runs out. CT10 more flexible than previous versions.


Generally high-x PDFs parameterisedso will behave like (1 − x)η asx → 1. More flexibility in CTEQ.

Very hard high-x gluon distribution(more-so even than NNPDFuncertainties).

However, is gluon, which isradiated from quarks, harder thanthe up valence distribution forx → 1?


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

MSTW has theory assumption on strange at small x, CT10 less strong and NNPDFfully flexible.

Variation near x = 0.05 where data exists likely due to heavy flavour definitions/nuclearcorrections.


Heavy Quarks – Essential to treat these correctly. Two distinct regimes:

Near threshold Q2 ∼ m2H massive quarks not partons. Created in final state. Describedusing Fixed Flavour Number Scheme (FFNS).

F (x,Q2) = CFFk (Q2/m2H) ⊗ f

nfk (Q

2)

Does not sum lnn(Q2/m2H) terms, and not calculated for many processes beyond LO.Used by AB(K)M and (G)JR. Sometimes final state details in this scheme only.

Alternative, at high scales Q2 ≫ m2H heavy quarks like massless partons. Behavelike up, down, strange. Sum ln(Q2/m2H) terms via evolution. Zero Mass VariableFlavour Number Scheme (ZM-VFNS). Normal assumption in calculations. IgnoresO(m2H/Q

2) corrections. No longer used.

F (x,Q2) = CZMV Fj ⊗ fnf+1

j (Q2).

Advocate a General Mass Variable Flavour Number Scheme (GM-VFNS)interpolating between the two well-defined limits of Q2 ≤ m2H and Q

2 ≫ m2H.Used by MRST/MSTW and more recently (as default) by CTEQ, and now also byHERAPDF and NNPDF.


H1 Fb2b_

(x,Q2)

10-2

10-1

1

10

10 102

103

x=0.0002i=5

x=0.0005i=4

x=0.0013i=3

x=0.005i=2

x=0.013i=1

x=0.032i=0

H1

Q2 / GeV2

Fb 2

b_

× 6

i

H1 DataMSTW08 NNLOMSTW08CTEQ6.6

Various definitions possible. Versionsused by MSTW (RT) and CTEQ(ACOT) have converged somewhat.

Various significant differences stillexist as illustrated by comparisonto most recent H1 data on bottomproduction.


0.9

0.95

1

1.05

1.1

10-5

10-4

10-3

10-2

10-1

MSTW08GMVFNS1GMVFNS2GMVFNS3

GMVFNS4GMVFNS5GMVFNS6ZMVFNS

GMVFNSopt

GM

VFN

Sa/2

008

at N

LO

for

g(x

,Q2 )

0.9

0.95

1

1.05

1.1

10-5

10-4

10-3

10-2

10-1

MSTW08GMVFNS1GMVFNS2GMVFNS3

GMVFNS4GMVFNS5GMVFNS6ZMVFNS

GMVFNSopt

GM

VFN

Sa/2

008

at N

LO

for

u(x

,Q2 )

0.9

0.95

1

1.05

1.1

10-5

10-4

10-3

10-2

10-1

MSTW08NNLOGMVFNS1GMVFNS2GMVFNS3

GMVFNS4GMVFNS5GMVFNS6GMVFNSopt

GM

VFN

Sa/2

008

at N

NL

O f

or g

(x,Q

2 )0.9

0.95

1

1.05

1.1

10-5

10-4

10-3

10-2

10-1

MSTW08NNLOGMVFNS1GMVFNS2GMVFNS3

GMVFNS4GMVFNS5GMVFNS6GMVFNSopt

GM

VFN

Sa/2

008

at N

NL

O f

or u

(x,Q

2 )

Variations in partons extracted from global fit due to different choices of GM-VFNSat NLO and at NNLO.


PDF correlation with αS.

Can also look at PDF changes and uncertainties at different αS(M2Z). Fully included

(difficult to disentangle) in ABKM, (G)JR), but often only for one fixed αS(M2Z).

MSTW produce sets for limits of αS uncertainty – PDF uncertainties reduced sincequality of fit already worse than best fit.

x-410 -310 -210 -110

Rat

io to

MS

TW

200

8 N

NLO

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

1.04

1.05

2 = (120 GeV)2H = M 2Gluon at Q

at Tevatron y = 0

at LHCy = 0

MSTW 2008 NNLO (68% C.L.)

at +68% C.L. limitS

αFix

at - 68% C.L. limitS

αFix

x-410 -310 -210 -110

Rat

io to

MS

TW

200

8 N

NLO

0.95

0.96

0.97

0.98

0.99

1

1.01

1.02

1.03

1.04

1.05

Expected gluon–αS(M2Z) small–x anti-correlation → high-x correlation from sum rule.


NNLO predictions for Higgs (120GeV) production for different allowed αS(M2Z) values

and their uncertainties.

= 120 GeV) with MSTW 2008 NNLO PDFsH

Higgs (M

)2Z

(MSα∆σ−1 /2σ− 0 /2σ+ σ+1σ−1 /2σ− 0 /2σ+ σ+1

(%

)N

NLO

Hσ∆

−6

−4

−2

0

2

4

6 = 1.96 TeVsTevatron,

)2Z

(MSα∆σ−1 /2σ− 0 /2σ+ σ+1σ−1 /2σ− 0 /2σ+ σ+1

(%

)N

NLO

Hσ∆−6

−4

−2

0

2

4

6 = 14 TeVsLHC,

68% C.L. uncertainties

)2H

(M2S

α

gg luminosity

Increases by a factor of 2−3 (up more than down) at LHC. Direct αS(M2Z) dependence

mitigated somewhat by anti-correlated small-x gluon (asymmetry feature of minorproblems in fit to HERA data). At Tevatron intrinsic gluon uncertainty dominates.


Other sources of Uncertainty.

Also other sources which (mainly) lead to inaccuracies common to all fixed-orderextractions.

● Standard higher orders NNLO. Many sets available here, soon all of them.

● QED and Weak (comparable to NNLO ?) (α3s ∼ α). Sometime enhancements.

● Nuclear/deuterium corrections to structure functions.

● Resummations, e.g. small x (αns lnn−1(1/x)), or large x (αns ln

2n−1(1 − x)).

● low Q2 (higher twist), saturation.


Deuterium corrections.

0 0.2 0.4 0.6 0.8 1x

0.95

1

1.05

1.1

1.15

F2d

/ F

2N

on-shell convolution+ off-shell (mKP)density

Variation in W+/W− ratio probably partially related to the issue of deuteriumcorrections.

Recent study (Accardi et al) suggests these may be large.

Uncertainty in correction as large as PDF uncertainty, but size of corrections can belarger.


0.9

0.95

1

1.05

10-2

10-1

constrained model

Simple model

D0II electron combined ET weighted

D0II electron combined ET

x

corr

ectio

n fa

ctor

MSTW found improvement in fitto both global data set andlepton asymmetry with deuteriumcorrections, but < 1 for all but veryhigh x.

Also find significant improvementwith rather more plausible deuteriumcorrections.

Ongoing study for MSTW.


PDFs at NNLO

NNLO splitting functions (Moch, Vermaseren and Vogt) allow essentially full NNLOdetermination of partons now being performed, though heavy flavour not fully workedout in the fixed-flavour number scheme (FFNS) and jet cross-sections are onlyapproximate. Improves consistency of fit very slightly, and reduces αS.

Surely this is best, i.e. most accurate.

Yes, but ...... only know some hard cross-sections at NNLO.

Processes with two strongly interacting particles largely completed

DIS coefficient functions and sum rules

pp(p̄) → γ⋆, W, Z (including rapidity dist.), H, A0, WH, ZH.

But for many other final states NNLO not known. NLO still more appropriate.


How do NNLO PDFs compare to NLO?

-5

0

5

10-5

10-4

10-3

10-2

10-1

1x

xg a

t Q2 =

2GeV

2

0

10

20

30

10-4

10-3

10-2

10-1

x

MSTW08 NNLO

MSTW08 NLO

xg(x,Q2=100GeV2)

-10

-5

0

5

10

15

10-4

10-3

10-2

10-1x

MSTW08 NNLO

MSTW08 NLO


Gluons different at NLO and NNLO at low Q2. Largely washed out by evolution, butonly because of different αS.


0

0.5

1

1.5

10-4

10-3

10-2

10-1

x

MSTW08 NNLO

MSTW08 NLO

xu(x,Q2=100GeV2)

-10

-5

0

5

10

15

10-4

10-3

10-2

10-1x

MSTW08 NNLO

MSTW08 NLO


Sometimes vital to use NNLOPDFs if calculating at NNLO.

Systematic difference betweenPDF defined at NLO and atNNLO.

Due to large (negative) gluoncoefficient function at not toosmall x.

Systematic difference betweenPDF defined at NLO and atNNLO.


Considerations of differences and of NNLO

0

0.5

1

1.5

2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8xF

K-factor for Drell-Yan Cross-section

LO

NLO

NNLOM=4GeV

0

0.5

1

1.5

2

1 10 102

103

σ~(x,Q2)HERA (F2(x,Q

2)FixedTarget) + c

x=0.00016 (c=0.4)

x=0.0005 (c=0.35)

x=0.0013 (c=0.3)

x=0.0032 (c=0.25)

x=0.008 (c=0.2)

x=0.013 (c=0.15)

x=0.05 (c=0.1)

x=0.18 (c=0.05)

x=0.35 (c=0.0)

Q2(GeV2)

H1ZEUSNMCBCDMSSLAC

NNLO NLO LO

MSTW 2008

In general NNLO corrections either positive for cross sections, e.g. Drell Yan, or forevolution in structure functions.

Automatically leads to lower αS(M2Z) at NNLO than at NLO, i.e. 0.1171 rather than

0.1202. Difference between two quite stable.


Converging on general agreement that the NNLO values of αS are 0.0002 − 0.0003smaller than the NLO values of αS?

MSTW08 – αS(M2Z) = 0.1202 → 0.1171.

ABKM09 – αS(M2Z) = 0.1179 → 0.1135.

GJR/JR – αS(M2Z) = 0.1145 → 0.1124.

NNPDF2.1 – αS(M2Z) = 0.1191 → 0.1174.

CT10.1 – αS(M2Z) = 0.1196 → 0.1180(both prelim – PDF4LHC, DESY July).

HERAPDF1.6 – αS(M2Z) = 0.1202 at NLO and general preference for ∼ 0.1176 at

NNLO.

Central values differ far more than NLO → NNLO trend.


NLO → NNLO PDF differences

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2 = 7 TeV)s) luminosity at LHC (q(qqΣ

W Z

MSTW08 NLO

HERAPDF1.0

HERAPDF1.5

ABKM09

GJR08

G. W

att

(S

epte

mbe

r 20

11)

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

NLO

(68

% C

.L.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15


W Z

MSTW08 NNLO

HERAPDF1.0

HERAPDF1.5ABKM09

JR09

NNPDF2.1

G. W

att

(S

epte

mbe

r 20

11)

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

NLO

(68

% C

.L.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Luminosity differences for quarks largely the same at NNLO as at NLO, except forHERAPDF1.5 at large x.

Differences between different sets not likely to be due to theory choices which woulddiminish at higher orders, or approx. at NNLO which would change relative NLO andNNLO differences.


/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2 = 7 TeV)sgg luminosity at LHC (

tt120 180 240

(GeV)HM

MSTW08 NLO

HERAPDF1.0

HERAPDF1.5

ABKM09

GJR08

G. W

att

(S

epte

mbe

r 20

11)

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

NLO

(68

% C

.L.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15


tt120 180 240

(GeV)HM

MSTW08 NNLO

HERAPDF1.0

HERAPDF1.5ABKM09

JR09

NNPDF2.1

G. W

att

(S

epte

mbe

r 20

11)

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

NLO

(68

% C

.L.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Luminosity differences for the gluon also largely the same at NNLO as at NLO, exceptfor HERAPDF1.5 again.


Investigation to stability under changes in cuts.

0.9

0.95

1

1.05

1.1

10-5

10-4

10-3

10-2

10-1

MSTW08 NLOQ2=5GeV2, W2=20GeV2

Q2=10GeV2, W2=20GeV2

Preliminary

Q2=10,000GeV2

part

ons/

MST

W20

08 a

t NL

O f

or g

(x,Q

2 )

0.9

0.95

1

1.05

1.1

10-5

10-4

10-3

10-2

10-1

MSTW08 NLOQ2=5GeV2, W2=20GeV2


Preliminary

Q2=10,000GeV2

part

ons/

MST

W20

08 a

t NL

O f

or u

(x,Q

2 )

Raise W 2cut to 20GeV2, but no real

changes.

Also raise Q2cut to 5GeV2 and then

10GeV2.

At NLO some movement just outsidedefault error bands at general x.

Find αS(M2Z) = 0.1202 → 0.1193 →

0.1175, though for Q2 = 10GeV2 cuterror has roughly doubled to about0.0025.


0.9

0.95

1

1.05

1.1

10-5

10-4

10-3

10-2

10-1

MSTW08 NNLOQ2=5GeV2, W2=20GeV2


Preliminary

part

ons/

MST

W20

08 a

t NN

LO

for

g(x

,Q2 )

0.9

0.95

1

1.05

1.1

10-5

10-4

10-3

10-2

10-1

MSTW08 NNLOQ2=5GeV2, W2=20GeV2


Preliminarypa

rton

s/M

STW

2008

at N

NL

O f

or u

(x,Q

2 )

At NNLO most movement outsidedefault error bands at low x, whereconstraint vanishes as Q2 cut raises.

For Q2cut = 10GeV2 no points below x =

0.0001, and little lever arm for evolutionconstraint for a bit higher.

Find αS(M2Z) = 0.1171 → 0.1171 →

0.1164, i.e. no change of significance.


The % change in the cross sections after cuts (MH = 165GeV).

NLO NNLOQ2cut 5GeV

2 10GeV2 5GeV2 10GeV2

W Tev 0.0 -2.4 -0.7 -0.4Z Tev 0.0 -0.8 -0.4 0.0W LHC (7TeV) -0.2 -0.1 -0.2 -0.2Z LHC (7TeV) -0.2 -0.3 -0.4 -0.5W LHC (14TeV) -0.6 -1.1 0.3 0.8Z LHC (14TeV) -0.6 -1.5 0.2 0.4Higgs TeV -1.1 -1.5 -1.2 -3.2Higgs LHC (7TeV) -0.8 -2.5 0.4 -1.8Higgs LHC (14TeV) -0.9 -1.9 1.0 -0.8

More variation at NLO than at NNLO, i.e. 7 changes of > 1% compared to 4.

However, both small, and changes with change in Q2cut slow. Does not suggestsignificant higher twist or problem with default cuts.


Small-x Theory

At each order in αS each splitting function and coefficient function obtains an extrapower of ln(1/x) (some accidental zeros in Pgg), i.e. Pij(x, αs(Q

2)), CPi (x, αs(Q2)) ∼

αms (Q2) lnm−1(1/x).

Summed using BFKL equation (and a lot of work – Altarelli-Ball-Forte, Ciafaloni-Colferai-Salam-Stasto and White-RT)

0

0.5

1

= 460, 575, 920 GeVpE

0.00

0059

0.00

0087

0.00

013

0.00

017

0.00

021

0.00

029

0.00

040

0.00

052

0.00

067

0.00

090

0.00

11

0.00

15

0.00

23x

H1 (Prelim.) MSTW NLO MSTW NNLO WT NLO + NLL(1/x)

LH1 Preliminary F

2 / GeV 2Q

)2 (

x, Q

LF

0

0.5

1

10 210

Comparison to H1 prelim data onFL(x,Q

2) at low Q2, only withinWhite-RT approach, suggestsresummations may be important.

Could possibly give a few percenteffect on Higgs cross sections.


-0.2

0

0.2

0.4

2 10 50

0.28

0.43

0.59

0.88

1.29

1.69

2.24

3.19

4.02

5.40

6.86

10.3

14.6

x 10

4

H1 DataHERAPDF1.0 NLOCT10 NLO GJR08 NNLO

ABKM09 NNLONNPDF2.1 NLO

MSTW08 NNLO

H1 Collaboration

Q2 / GeV2

FL

However, quite a large PDF uncertainty (in general) and even larger spread, at fixedorder.


(GeV)JETT

p210

T =

pµ

with

σ

Rat

io w

.r.t

NLO

0.6

0.7

0.8

0.9

1

1.1

1.2

1.31.4

| < 0.4JET0.0 < |y

Tp× = 0.5Fµ = Rµ

Tp× = 1.0Fµ = Rµ

Tp× = 2.0Fµ = Rµ

(GeV)JETT

p210

T =

pµ

with

σ

Rat

io w

.r.t

NLO

0.6

0.7

0.8

0.9

1

1.1

1.2

1.31.4

+ 2-loop thresholdσDashed lines: NLO σSolid lines: NLO

| < 0.8JET0.4 < |y

(GeV)JETT

p210

T =

pµ

with

σ

Rat

io w

.r.t

NLO

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

| < 1.2JET0.8 < |y

(GeV)JETT

p210

T =

pµ

with

σ

Rat

io w

.r.t

NLO

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

| < 1.6JET1.2 < |y

(GeV)JETT

p210

T =

pµ

with

σ

Rat

io w

.r.t

NLO

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

| < 2.0JET1.6 < |y

(GeV)JETT

p210

T =

pµ

with

σ

Rat

io w

.r.t

NLO

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

| < 2.4JET2.0 < |y

Run II inclusive jet data (cone, R = 0.7)∅D using MSTW08 NNLO PDFs)

T = pµ with σ(Ratio w.r.t. NLO

Fits to Jet Data and relationto NNLO

NNLO approx. jet corrections.

Shape of corrections as functionof pT at NLO and also at approx.NNLO in inclusive case.

NNLO uses threshold (Kidonakisand Owens) approx. for Tevatronjets.

NNLO approximation not largeand aids stability – always worstat high-pT i.e. high-x. Includeslarge ln(pT/µ) terms predicted byrenormalisation group.


de Florian and Vogelsang result forinclusive jet K-factor for dσ/dpTat order α2+nS compared to NLO.


Impact on Higgs at Tevatron.

Plots (Watt) show the gluon luminosities at the Tevatron NLO and NNLO

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4 = 1.96 TeV)sgg luminosity at Tevatron (

120 180 240 (GeV)HM

MSTW08 NLOCTEQ6.6

CT10

NNPDF2.1

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

NLO

(68

% C

.L.)

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4 = 1.96 TeV)sgg luminosity at Tevatron (

120 180 240 (GeV)HM

MSTW08 NNLO

HERAPDF1.0

ABKM09

JR09

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

NLO

(68

% C

.L.)

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

Similar to the LHC, but deviations with high-x PDF origin persist to lower ŝ.

Differences in αS(M2Z) generally increase effect of discrepancy.


Higgs production via gluon fusion at the Tevatron and LHC at NLO and NNLO.

)2Z

(MSα0.11 0.115 0.12 0.125 0.13

(pb

)Hσ

9

10

11

12

13

14

15

16

17

68% C.L. PDF

MSTW08

HERAPDF1.0

ABKM09

GJR08/JR09

= 120 GeVH

= 7 TeV) for MsH at the LHC (→NNLO gg

Open symbols: NLOClosed symbols: NNLO


G. W

att

(A

pril

2011

)

)2Z

(MSα0.11 0.115 0.12 0.125 0.13

(pb

)Hσ

9

10

11

12

13

14

15

16

17

)2Z

(MSα0.11 0.115 0.12 0.125 0.13

(pb

)Hσ

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

68% C.L. PDF

MSTW08

HERAPDF1.0

ABKM09

GJR08/JR09

= 120 GeVH

= 1.96 TeV) for MsH at the Tevatron (→NNLO gg



)2Z

(MSα0.11 0.115 0.12 0.125 0.13

(pb

)Hσ

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

)2Z

(MSα0.11 0.115 0.12 0.125 0.13

(pb

)Hσ

2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

68% C.L. PDF

MSTW08

HERAPDF1.0

ABKM09

GJR08/JR09

= 240 GeVH

= 7 TeV) for MsH at the LHC (→NNLO gg



G. W

att

(A

pril

2011

)

)2Z

(MSα0.11 0.115 0.12 0.125 0.13

(pb

)Hσ

2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

)2Z

(MSα0.11 0.115 0.12 0.125 0.13

(pb

)Hσ

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

68% C.L. PDF

MSTW08

HERAPDF1.0

ABKM09

GJR08/JR09

= 240 GeVH

= 1.96 TeV) for MsH at the Tevatron (→NNLO gg



)2Z

(MSα0.11 0.115 0.12 0.125 0.13

(pb

)Hσ

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

Larger deviation at the Tevatron. NNLO pattern very similar to NLO.


High-x gluon, at least to some extent, constrained by comparison to Tevatron jetdata.

However, important point, CDF Z-rapidity data, or cross sections, sets Tevatronnormalisation in a fit.

Only allows a few percent variation in normalisation.

Different PDF predictions for W and Z cross sections at the Tevatron compared todata.

)2Z

(MSα0.11 0.115 0.12 0.125 0.13

) (

nb)

ν± l→ ±

B(W

⋅ ±Wσ

2.5

2.55

2.6

2.65

2.7

2.75

2.8

2.85

2.9

2.95

3-1CDF, L = 72 pb

Shaded bands: stat.+syst.+lumi.Thinner lines: stat.+syst.Thicker lines: central value

68% C.L. PDF

MSTW08

HERAPDF1.0

ABKM09

JR09

= 1.96 TeV)s at the Tevatron (ν± l→ ±NNLO W


)2Z

(MSα0.11 0.115 0.12 0.125 0.13

) (

nb)

ν± l→ ±

B(W

⋅ ±Wσ

2.5

2.55

2.6

2.65

2.7

2.75

2.8

2.85

2.9

2.95

3

)2Z

(MSα0.11 0.115 0.12 0.125 0.13

) (

nb)

- l+ l→ 0

B(Z

⋅ 0Zσ

0.2

0.21

0.22

0.23

0.24

0.25

0.26

0.27

0.28

0.29

0.3-1CDF, L = 2.1 fb

-1, L = 1 fb∅DShaded bands: stat.+syst.+lumi.Thinner lines: stat.+syst.Thicker lines: central value

68% C.L. PDF

MSTW08

HERAPDF1.0

ABKM09

JR09

= 1.96 TeV)s at the Tevatron (-l+ l→ 0NNLO Z


)2Z

(MSα0.11 0.115 0.12 0.125 0.13

) (

nb)

- l+ l→ 0

B(Z

⋅ 0Zσ

0.2

0.21

0.22

0.23

0.24

0.25

0.26

0.27

0.28

0.29

0.3

Everyone ok or a bit high. Normalisation no room to move down.


NLO PDF (with NLO σ̂) µ = pT/2 µ = pT µ = 2pTMSTW08 0.75 (0.30) 0.68 (0.28) 0.91 (0.84)CTEQ6.6 1.25 (0.14) 1.66 (0.20) 2.38 (0.84)CT10 1.03 (0.13) 1.20 (0.19) 1.81 (0.84)NNPDF2.1 0.74 (0.29) 0.82 (0.25) 1.23 (0.69)HERAPDF1.0 2.43 (0.39) 3.26 (0.66) 4.03 (1.67)HERAPDF1.5 2.26 (0.40) 3.05 (0.66) 3.80 (1.66)ABKM09 1.62 (0.52) 2.21 (0.85) 3.26 (2.10)GJR08 1.36 (0.23) 0.94 (0.13) 0.79 (0.36)

NNLO PDF (with NLO+2-loop σ̂) µ = pT/2 µ = pT µ = 2pTMSTW08 1.39 (0.42) 0.69 (0.44) 0.97 (0.48)HERAPDF1.0, αS(M

2Z) = 0.1145 2.64 (0.36) 2.15 (0.36) 2.20 (0.46)

HERAPDF1.0, αS(M2Z) = 0.1176 2.24 (0.35) 1.17 (0.32) 1.23 (0.31)

ABKM09 2.55 (0.82) 2.76 (0.89) 3.41 (1.17)JR09 0.75 (0.37) 1.26 (0.41) 2.21 (0.49)

Table 1: Values of χ2/Npts. for the CDF Run II inclusive jet data using the kT jetalgorithm with Npts. = 76 and Ncorr. = 17, for different PDF sets and different scalechoices At most a 1-σ shift in normalisation is allowed.


NLO PDF (with NLO σ̂) µ = pT/2 µ = pT µ = 2pTMSTW08 0.75 (+0.32) 0.68 (−0.88) 0.63 (−2.69)CTEQ6.6 1.03 (−2.47) 1.04 (−3.49) 0.99 (−4.75)CT10 0.99 (−1.64) 0.92 (−2.69) 0.86 (−4.10)NNPDF2.1 0.74 (−0.33) 0.79 (−1.60) 0.80 (−3.12)HERAPDF1.0 1.52 (−4.07) 1.57 (−5.21) 1.43 (−6.22)HERAPDF1.5 1.48 (−3.85) 1.52 (−5.00) 1.39 (−6.03)ABKM09 1.03 (−3.49) 1.01 (−4.53) 1.05 (−5.80)GJR08 1.14 (+2.47) 0.93 (+1.25) 0.79 (−0.50)

NNLO PDF (with NLO+2-loop σ̂) µ = pT/2 µ = pT µ = 2pTMSTW08 1.39 (+0.35) 0.69 (−0.45) 0.97 (−1.30)HERAPDF1.0, αS(M

2Z) = 0.1145 2.37 (−2.65) 1.48 (−3.64) 1.29 (−4.12)

HERAPDF1.0, αS(M2Z) = 0.1176 2.24 (−0.48) 1.13 (−1.60) 1.09 (−2.23)

ABKM09 1.53 (−4.27) 1.23 (−5.05) 1.44 (−5.65)JR09 0.75 (+0.13) 1.26 (−0.61) 2.20 (−1.22)

Table 2: Values of χ2/Npts. for the CDF Run II inclusive jet data using the kT jetalgorithm No restriction is imposed on the shift in normalisation and the optimal valueof “−rlumi.” is shown in brackets.


Comparisons to LHC data

CMS results very similar.


) (nb)ν± l→ ± B(W⋅ ±Wσ

9.8 10 10.2 10.4 10.6 10.8 11

) (

nb)

- l+ l→ 0

B(Z

⋅ 0Zσ

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

= 7 TeV)sNNLO W and Z cross sections at the LHC (

SαOuter error bars: PDF+Inner error bars: PDF only

-1CMS, L = 36 pb

-1ATLAS, L = 33-36 pb

R(W/Z) =

10.810.9

11.0

G. W

att

(S

epte

mbe

r 20

11)

68% C.L. PDF

MSTW08

NNPDF2.1

HERAPDF1.0

HERAPDF1.5

ABKM09

JR09

) (nb)ν± l→ ± B(W⋅ ±Wσ

9.8 10 10.2 10.4 10.6 10.8 11

) (

nb)

- l+ l→ 0

B(Z

⋅ 0Zσ

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

Differences in predictions atNNLO compared to NLO (Watt).

Differences very much the sameas they are comparing at NLO.


Differential data on rapidity is becoming very constraining – on both shapes and onnormalisations of predictions.

Would be particularly interesting to see for γ⋆ at low masses (LHCb).


Clearly some of this information lost in ratios and asymmetries.

Ideally want individual distributions, with full correlations.


Details from single charged-lepton cross sections and asymmetries – Stirling

0 1 2 3 4 5-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

35

W asymmetry lepton asymmetry,

variable pTlep

(min)

02010 30

A+

-(y)

ylep

or yW

LHC 7 TeVMSTW2008 NLO

for low pT main boost from W decayto leptons.

Dip towards −1 for lower pT cutsfrom preferential forward productionfrom dV (x1)ū(x2) due to axial vectornature of coupling.

Eventual turn-up when/if uV (x1)d̄(x2) ≫dV (x1)ū(x2)

The larger the lepton pT the earlier(in terms of increasing yℓ) this willhappen, and for pT → mW/2 thereis no V ± A dominance at all.

So asymmetry at large yℓ in terms ofpT tells us about d/u at large x.


MSTW comparison better if pT cut at 20GeV2.


LHCb (with pT (min) = 20GeV) already testing dip.

With higher pT (min) could potentially see upturn.


Inclusive Jets at the LHC

ATLAS data compared to various PDF set predictions. Each fit well so far with sizeof correlated uncertainties limiting discriminative power.

Interesting to see jets from LHCb as well.


Top-antitop Cross-section Inclusive cross-section known approximately to NNLO

Intrinsic theory uncertainty not verylarge – for example, recent NNLLcalculation by Beneke et al.

Data getting precise. Main uncertaintyin choice of PDFs, not in individualuncertainty but choice of set.Correlated to Higgs predictions.

)2Z

(MSα0.114 0.116 0.118 0.12 0.122 0.124

(pb

)ttσ

120

130

140

150

160

170

180

190

200

210 = 171.3 GeVpoletm-1CMS, L = 0.8-1.09 fb

-1ATLAS, L = 0.7 fb

68% C.L. PDF

MSTW08

CTEQ6.6

CT10

NNPDF2.1

HERAPDF1.0

HERAPDF1.5

ABKM09

GJR08

= 7 TeV)s cross sections at the LHC (tNLO t


G. W

att

(S

epte

mbe

r 20

11)

)2Z

(MSα0.114 0.116 0.118 0.12 0.122 0.124

(pb

)ttσ

120

130

140

150

160

170

180

190

200

210

)2Z

(MSα0.111 0.112 0.113 0.114 0.115 0.116 0.117 0.118 0.119 0.12 0.121

(pb

)ttσ

120

140

160

180

200

220 = 171.3 GeVpoletm-1CMS, L = 0.8-1.09 fb

-1ATLAS, L = 0.7 fb

68% C.L. PDF

MSTW08

NNPDF2.1

HERAPDF1.0

HERAPDF1.5

ABKM09

JR09

= 7 TeV)s cross sections at the LHC (tNNLO (approx.) t


G. W

att

(S

epte

mbe

r 20

11)

)2Z

(MSα0.111 0.112 0.113 0.114 0.115 0.116 0.117 0.118 0.119 0.12 0.121

(pb

)ttσ

120

140

160

180

200

220

Plots by G. Watt. Differences between groups significant at NLO, and at NNLO.


Uncertainty in tt̄, Higgs via gluonfusion and ratios. PDF onlyuncertainty, but αS uncertaintycancels in ratios.

Very strong correlation of top withHiggs production for mH ∼ 400GeVat the LHC.

Similar correlation for mH ∼ 400 ×1.96/7 ∼ 130GeV at the Tevatron.

Particularly important at themoment.


10 100 10001

2

3

4

5

8/7

gg Σqq (Σq)(Σq)

WJS 2010

ratios of LHC parton luminosities:8 TeV / 7 TeV and 9 TeV / 7 TeV

lum

inos

ity r

atio

MX (GeV)

MSTW2008NLO

9/7

What will be the advantages of runningat 8TeV?

Limited for quark dominated processesup to mX > 1TeV, but more for gluondominated processes for MX > 200 −300GeV.


Conclusions

One can determine the parton distributions and predict cross-sections at the LHC, andthe fit quality using NLO or NNLO QCD is fairly good. Nearly full range of NNLOPDFs now. Comparison between different PDF sets at NLO and NNLO very similar.

Various ways of looking at experimental uncertainties. Uncertainties ∼ 1 − 5% formost LHC quantities. Ratios, e.g. W+/W− tight constraint on partons, but don’twant to lose information when taking ratios.

Effects from input assumptions e.g. selection of data fitted, cuts and inputparameterisation can shift central values of predictions significantly. Also affectsize of uncertainties. Want balance between freedom and sensible constraints.

Data from the LHC just starting to have some effect on improving the precision ofPDFs. Might start to discriminate between PDFs first.

Extraction of PDFs from existing data and use for LHC far from a straightforwardprocedure. Lots of issues to consider for real precision. Relatively few cases whereStandard Model discrepancies will not require some significant input from PDF physicsto determine real significance.


Different PDF sets

● MSTW08 – fit all previous types of data. Most up-to-date Tevatron jet data. Notmost recent HERA combination of data. PDFs at LO, NLO and NNLO.

● CT10 – very similar. PDFs at NLO. CT10 include HERA combination and moreTevatron data though also run I jet data. Not large changes from CTEQ6.6.CT10W gives higher weight to Tevatron asymmetry data.

● NNPDF2.1 – include all except HERA jet data (not strong constraint). NNPDF2.1improves on NNPDF2.0 by better heavy flavour treatment. PDFs at NLO and veryrecently NNLO and LO .

● HERAPDF1.0 – based on HERA inclusive structure functions, neutral and chargedcurrent. Use combined data. PDFs at NLO and (without uncertainties) NNLO.

● ABKM09 – fit to DIS and fixed target Drell-Yan data. PDFs at NLO and NNLO.Less conservative cuts at low W 2 than other groups – fit for higher twist correctionsrather than attempt to avoid them.

● GJR08 – fit to DIS, fixed target Drell-Yan and Tevatron jet data (not at NNLO.PDFs at NLO and NNLO.


|l

η|0 0.5 1 1.5 2 2.5 3

Lept

on c

harg

e as

ymm

etry

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

= 147 (12 pts.)e2χ = 530 (8 pts.), µ

2χMSTW08: = 58

e2χ = 97, µ

2χ: µ A∅Fit new D = 88

e2χ = 6, µ

2χWeight by 100: = 55

e2χ = 14,

µ2χCut BCDMS+NMCn/p:

= 42e2χ = 190, µ

2χ: µ A∅Deut. corr., fit old D = 75

e2χ = 6, µ

2χ: µ A∅Deut. corr., fit new D = 23

e2χ = 173, µ

2χ: e A∅Deut. corr., fit new D-1, L = 4.9 fbµ (prel.) A∅D

-1, L = 0.75 fbe

(publ.) A∅D-1, L = 0.17 fb

eCDF (publ.) A

> 25 GeVνTE > 35 GeV,

lT

p

MSTW (and NNPDF and CTEQ) have difficulty fitting new D0 lepton asymmetry(particularly muon in different ET bins) along with other data.

MSTW better when low number of data points sets given (slightly) more weight. Alsoimproved using deuterium corrections.


The inappropriateness of using ∆χ2 = 1 when including a large number of sometimesconflicting data sets is shown by examining the best value of σW and its uncertaintyusing ∆χ2 = 1 for individual data sets as obtained by CTEQ using Lagrange Multipliertechnique.


Predictions by various groups - parton luminosities – NLO. Plots by G. Watt.

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15


tt120 180 240

(GeV)HM

MSTW08 NLOCTEQ6.6

CT10

NNPDF2.1

G. W

att

(M

arch

201

1)

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Cross-section for tt̄ almost identical in PDF terms to 450GeV Higgs.

Also H + tt̄ at√

ŝ/s ∼ 0.1.


/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15


tt120 180 240

(GeV)HM

MSTW08 NLO

HERAPDF1.0

HERAPDF1.5

ABKM09

GJR08

G. W

att

(S

epte

mbe

r 20

11)

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Clearly some distinct variation between groups. Much can be understood in terms ofprevious differences in approaches.

Uncertainties not completely comparable.


/ ss

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Rat

io to

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TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15


W Z

MSTW08 NLOCTEQ6.6

CT10

NNPDF2.1

G. W

att

(M

arch

201

1)

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Many of the same general features for quark-antiquark luminosity. Some differencesmainly at higher x.


/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15


W Z

MSTW08 NLO

HERAPDF1.0

HERAPDF1.5

ABKM09

GJR08

G. W

att

(S

epte

mbe

r 20

11)

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Canonical example W, Z production, but higher ŝ/s relevant for WH or vector bosonfusion.

All plots and more at http://projects.hepforge.org/mstwpdf/pdf4lhc


Variations in Cross-Section Predictions – NLO

)2Z

(MSα0.114 0.116 0.118 0.12 0.122 0.124

(pb

)Hσ

10.5

11

11.5

12

12.5

13

68% C.L. PDFMSTW08

CTEQ6.6

NNPDF2.0HERAPDF1.0

ABKM09GJR08

= 120 GeVH



)2Z

(MSα0.114 0.116 0.118 0.12 0.122 0.124

(pb

)Hσ

10.5

11

11.5

12

12.5

13

Dotted lines show how central PDF predictions vary with αS(M2Z).

Again plots by G Watt using PDF4LHC benchmark criteria.


)2Z

(MSα0.114 0.116 0.118 0.12 0.122 0.124

(pb

)Hσ

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3

68% C.L. PDFMSTW08

CTEQ6.6

NNPDF2.0HERAPDF1.0

ABKM09GJR08

= 240 GeVH



)2Z

(MSα0.114 0.116 0.118 0.12 0.122 0.124

(pb

)Hσ

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3

Excluding GJR08 amount of difference due to αS(M2Z) variations 3 − 4%.


)2Z

(MSα0.114 0.116 0.118 0.12 0.122 0.124

) (

nb)

- l+ l→ 0

B(Z

⋅ 0Zσ

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

68% C.L. PDFMSTW08

CTEQ6.6

NNPDF2.0HERAPDF1.0

ABKM09GJR08

= 7 TeV)s at the LHC (-l+ l→ 0NLO Z


)2Z

(MSα0.114 0.116 0.118 0.12 0.122 0.124

) (

nb)

- l+ l→ 0

B(Z

⋅ 0Zσ

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

αS(M2Z) dependence now more due to PDF variation with αS(M

2Z).

Again variations somewhat bigger than individual uncertainties.


)2Z

(MSα0.114 0.116 0.118 0.12 0.122 0.124

-Wσ

/ +Wσ ≡ ±

R

1.4

1.42

1.44

1.46

1.48

1.5

68% C.L. PDFMSTW08

CTEQ6.6

NNPDF2.0HERAPDF1.0

ABKM09GJR08

= 7 TeV)s ratio at the LHC (-/W+NLO W


)2Z

(MSα0.114 0.116 0.118 0.12 0.122 0.124

-Wσ

/ +Wσ ≡ ±

R

1.4

1.42

1.44

1.46

1.48

1.5

Quite a variation in ratio. Shows variations in flavour and quark-antiquarkdecompositions.

All plots and more at http://projects.hepforge.org/mstwpdf/pdf4lhc


Deviations In predictions clearly much more than uncertainty claimed by each.

In some cases clear reason why central values differ, e.g. lack of some constrainingdata, though uncertainties then do not reflect true uncertainty.

Sometimes no good understanding, or due to difference in procedure which is simplya matter of disagreement, e.g. gluon parameterisation at small x affects predictedHiggs cross-section.

What is true uncertainty for comparing to unknown production cross section. Taskasked of PDF4LHC group.

Interim recommendation take envelope of global sets, MSTW, CTEQ NNPDF (checkother sets) and take central point as uncertainty.

Not very satisfactory, but not clear what would be an improvement, especially as ageneral rule.

Usually not a big disagreement, and factor of about 2 expansion of MSTW uncertainty.


/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15


tt120 180 240

(GeV)HM

MSTW08

CTEQ6.6NNPDF2.0

HERAPDF1.0

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15


tt120 180 240

(GeV)HM

MSTW08 NLOCTEQ6.6

CT10

NNPDF2.1

G. W

att

(M

arch

201

1)

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

MSTW, NNPDF and CTEQ are converging somewhat.


/ ss

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Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15


W Z

MSTW08

CTEQ6.6NNPDF2.0

HERAPDF1.0

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

/ ss

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Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15


W Z

MSTW08 NLOCTEQ6.6

CT10

NNPDF2.1

G. W

att

(M

arch

201

1)

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Same for quark-antiquark luminosities.


/ ss

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Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15


W Z

MSTW08 NLO

HERAPDF1.0

HERAPDF1.5

ABKM09

GJR08

G. W

att

(S

epte

mbe

r 20

11)

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

LO (

68%

C.L

.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

NLO

(68

% C

.L.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15


W Z

MSTW08 NNLO

HERAPDF1.0

HERAPDF1.5ABKM09

JR09

NNPDF2.1

G. W

att

(S

epte

mbe

r 20

11)

/ ss

-310 -210 -110

Rat

io to

MS

TW

200

8 N

NLO

(68

% C

.L.)

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

Not all luminosity differences the same at NLO as at NNLO, e.g. HERAPDF qq̄.


The PDFs are related to the issue of the use and uncertainty of αS(M2Z).

There is a significant systematic change in value from fit as one goes from NLO toNNLO. Seen in (most) other extractions. Also highlighted in stability of predictions.

Consider percentage change from NLO to NNLO in MSTW08 predictions for best fitαS compared to fixed αS(M

2Z) = 0.119.

σW (Z) 7TeV σW (Z) 14TeV σH 7TeV σH 7TeVMSTW08 best fit αS 3.0 2.6 25 24MSTW08 αS = 0.119 5.3 5.0 32 30

αS(M2Z) is not a physical quantity. In (nearly) all PDF related quantities (and many

others) shows tendency to decrease from order to order. Noticeable if one has fit atNNLO. Any settling on, or near common αS(M

2Z) has to take this into account.


(GeV)JETT

p210

T =

pµ

with

σ

Rat

io w

.r.t

NLO

0.6

0.7

0.8

0.9

1

1.1

1.2

1.31.4

| < 0.4JET0.0 < |y

Tp× = 0.5Fµ = Rµ

Tp× = 1.0Fµ = Rµ

Tp× = 2.0Fµ = Rµ

(GeV)JETT

p210

T =

pµ

with

σ

Rat

io w

.r.t

NLO

0.6

0.7

0.8

0.9

1

1.1

1.2

1.31.4

+ 2-loop thresholdσDashed lines: NLO σSolid lines: NLO

| < 0.8JET0.4 < |y

(GeV)JETT

p210

T =

pµ

with

σ

Rat

io w

.r.t

NLO

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

| < 1.2JET0.8 < |y

(GeV)JETT

p210

T =

pµ

with

σ

Rat

io w

.r.t

NLO

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

| < 1.6JET1.2 < |y

(GeV)JETT

p210

T =

pµ

with

σ

Rat

io w

.r.t

NLO

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

| < 2.0JET1.6 < |y

(GeV)JETT

p210

T =

pµ

with

σ

Rat

io w

.r.t

NLO

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

| < 2.4JET2.0 < |y

Run II inclusive jet data (cone, R = 0.7)∅D using MSTW08 NNLO PDFs)


(TeV)JJM0.2 0.3 0.4 0.5 1

T =

pµ

with

σ

Rat

io w

.r.t

NLO

0.6

0.7

0.8

0.9

1

1.1

1.2

1.31.4

< 0.4max

0.0 < |y|

Tp× = 0.5Fµ = Rµ

Tp× = 1.0Fµ = Rµ

Tp× = 2.0Fµ = Rµ

(TeV)JJM0.2 0.3 0.4 0.5 1

T =

pµ

with

σ

Rat

io w

.r.t

NLO

0.6

0.7

0.8

0.9

1

1.1

1.2

1.31.4

)/2T2

+pT1

(p≡ T

pσSolid lines: NLO

< 0.8max

0.4 < |y|

(TeV)JJM0.2 0.3 0.4 0.5 1

T =

pµ

with

σ

Rat

io w

.r.t

NLO

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

< 1.2max

0.8 < |y|

(TeV)JJM0.2 0.3 0.4 0.5 1

T =

pµ

with

σ

Rat

io w

.r.t

NLO

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

< 1.6max

1.2 < |y|

(TeV)JJM0.2 0.3 0.4 0.5 1

T =

pµ

with

σ

Rat

io w

.r.t

NLO

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

< 2.0max

1.6 < |y|

(TeV)JJM0.2 0.3 0.4 0.5 1

T =

pµ

with

σ

Rat

io w

.r.t

NLO

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

< 2.4max

2.0 < |y|

Run II dijet data (cone, R = 0.7)∅D using MSTW08 NNLO PDFs)


Shape of corrections as function of pT at NLO and also at approx. NNLO in inclusivecase. Problem at highest pT and rapidity even for inclusive jets.


NLO PDF (with NLO σ̂) µ = pT/2 µ = pT µ = 2pTMSTW08 1.45 (0.89) 1.08 (0.20) 1.05 (1.22)CTEQ6.6 1.62 (1.15) 1.56 (0.59) 1.61 (1.35)CT10 1.39 (0.88) 1.26 (0.37) 1.32 (1.29)NNPDF2.1 1.41 (0.87) 1.29 (0.20) 1.22 (0.96)HERAPDF1.0 1.73 (0.27) 1.84 (0.74) 1.83 (2.79)HERAPDF1.5 1.78 (0.29) 1.87 (0.75) 1.84 (2.81)ABKM09 1.39 (0.35) 1.43 (1.07) 1.63 (3.66)GJR08 1.90 (1.46) 1.34 (0.45) 1.03 (0.51)

NNLO PDF (with NLO+2-loop σ̂) µ = pT/2 µ = pT µ = 2pTMRST06 3.19 (5.00) 1.77 (3.22) 1.25 (1.50)MSTW08 1.95 (0.90) 1.23 (0.44) 1.08 (0.35)HERAPDF1.0, αS(M

2Z) = 0.1145 2.11 (0.37) 1.68 (0.35) 1.41 (0.63)

HERAPDF1.0, αS(M2Z) = 0.1176 2.28 (0.95) 1.50 (0.40) 1.17 (0.21)

ABKM09 1.68 (0.79) 1.55 (1.21) 1.63 (2.04)JR09 1.84 (0.47) 1.61 (0.36) 1.58 (0.50)

Table 3: Values of χ2/Npts. for the DØ Run II inclusive jet data using a cone jetalgorithm with Npts. = 110 and Ncorr. = 23, for different PDF sets and different scalechoices. At most a 1-σ shift in normalisation is allowed.


NLO PDF (with NLO σ̂) µ = pT/2 µ = pT µ = 2pTMSTW08 1.40 (+1.05) 1.08 (−0.55) 0.85 (−2.25)CTEQ6.6 1.52 (−1.61) 1.25 (−2.88) 1.01 (−4.02)CT10 1.39 (−0.66) 1.11 (−2.02) 0.90 (−3.35)NNPDF2.1 1.41 (+0.37) 1.23 (−1.22) 0.95 (−2.67)HERAPDF1.0 1.55 (−2.16) 1.38 (−3.51) 1.07 (−4.52)HERAPDF1.5 1.63 (−1.98) 1.45 (−3.35) 1.12 (−4.40)ABKM09 1.25 (−1.90) 1.04 (−3.20) 0.89 (−4.44)GJR08 1.72 (+2.14) 1.34 (+0.53) 0.98 (−1.05)

NNLO PDF (with NLO+2+loop σ̂) µ = pT/2 µ = pT µ = 2pTMRST06 2.92 (+2.66) 1.70 (+1.31) 1.25 (+0.44)MSTW08 1.87 (+1.34) 1.23 (+0.09) 1.08 (−0.87)HERAPDF1.0, αS(M

2Z) = 0.1145 2.11 (−0.82) 1.52 (−2.03) 1.14 (−2.61)

HERAPDF1.0, αS(M2Z) = 0.1176 2.28 (+0.94) 1.50 (−0.49) 1.11 (−1.23)

ABKM09 1.48 (−2.33) 1.13 (−3.35) 1.02 (−4.03)JR09 1.84 (+0.63) 1.61 (−0.60) 1.50 (−1.35)

Table 4: Values of χ2/Npts. for the DØ Run II inclusive jet data using a cone jetalgorithm with Npts. = 110 and Ncorr. = 23, for different PDF sets and different scalechoices. No restriction is imposed on the shift in normalisation and the optimal valueof “−rlumi.” is shown in brackets.Birmingham – February 2012 82

Comparison of the raw comparison to CDF inclusive jet data using the kT and conealgorithms.

(GeV)JETT

p210

Dat

a / T

heor

y

0.5

1

1.5

2

2.5

3

| < 0.1JET0.0 < |y

(GeV)JETT

p210

Dat

a / T

heor

y

0.5

1

1.5

2

2.5

3

| < 0.7JET0.1 < |y

(GeV)JETT

p210

Dat

a / T

heor

y

0.5

1

1.5

2

2.5

3

| < 1.1JET0.7 < |y

(GeV)JETT

p210

Dat

a / T

heor

y

0.5

1

1.5

2

2.5

3

| < 1.6JET1.1 < |y

(GeV)JETT

p210

Dat

a / T

heor

y

0.5

1

1.5

2

2.5

3

| < 2.1JET1.6 < |y

NNLO PDFs, 76 data points

= 342χMSTW08,

= 682χABKM09,

JETT

p× = 1.0Fµ = Rµ

Outer error bars: total (add in quadrature)Inner error bars: only uncorrelated

, D = 0.7)T

CDF Run II inclusive jet data (k(data points before systematic shifts, show total errors)

(GeV)JETT

p210

Dat

a / T

heor

y

0.5

1

1.5

2

2.5

3

3.5

4

| < 0.1JET0.0 < |y

(GeV)JETT

p210

Dat

a / T

heor

y

0.5

1

1.5

2

2.5

3

3.5

4

| < 0.7JET0.1 < |y

(GeV)JETT

p210

Dat

a / T

heor

y

0.5

1

1.5

2

2.5

3

3.5

4

| < 1.1JET0.7 < |y

(GeV)JETT

p210

Dat

a / T

heor

y

0.5

1

1.5

2

2.5

3

3.5

4

| < 1.6JET1.1 < |y

(GeV)JETT

p210

Dat

a / T

heor

y0.5

1

1.5

2

2.5

3

3.5

4

| < 2.1JET1.6 < |y


= 312χMSTW08,

= 512χABKM09,

JETT

p× = 1.0Fµ = Rµ


CDF Run II inclusive jet data (Midpoint)(data points before systematic shifts, show total errors)

Data/theory the same shape for both. Good compatibility. Verified by fits.


Comparison of the raw comparison to D0 inclusive jet data using the cone algorithmsand D0 dijet data.

(GeV)JETT

p210

Dat

a / T

heor

y

00.20.40.60.8

11.21.41.61.8

2

| < 0.4JET0.0 < |y


= 482χMSTW08, = 1332χABKM09,

(GeV)JETT

p210

Dat

a / T

heor

y

00.20.40.60.8

11.21.41.61.8

2

JETT

p× = 1.0Fµ = Rµ

| < 0.8JET0.4 < |y

(GeV)JETT

p210

Dat

a / T

heor

y

00.20.40.60.8

11.21.41.61.8

2

| < 1.2JET0.8 < |y

(GeV)JETT

p210

Dat

a / T

heor

y

00.20.40.60.8

11.21.41.61.8

2

| < 1.6JET1.2 < |y

(GeV)JETT

p210

Dat

a / T

heor

y

00.20.40.60.8

11.21.41.61.8

2


| < 2.0JET1.6 < |y

(GeV)JETT

p210

Dat

a / T

heor

y

00.20.40.60.8

11.21.41.61.8

2

| < 2.4JET2.0 < |y

Run II inclusive jet data (cone, R = 0.7)∅D(data points before systematic shifts, show total errors)

(TeV)JJM0.2 0.3 0.4 0.5 1

Dat

a / T

heor

y

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

< 0.4max

0.0 < |y|


= 232χMSTW08, = 1372χABKM09,

(TeV)JJM0.2 0.3 0.4 0.5 1

Dat

a / T

heor

y

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

)/2T2

+pT1

(p≡ T

pT

= pFµ = Rµ

< 0.8max

0.4 < |y|

(TeV)JJM0.2 0.3 0.4 0.5 1

Dat

a / T

heor

y

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

< 1.2max

0.8 < |y|

(TeV)JJM0.2 0.3 0.4 0.5 1

Dat

a / T

heor

y

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

< 1.6max

1.2 < |y|

(TeV)JJM0.2 0.3 0.4 0.5 1

Dat

a / T

heor

y0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8


< 2.0max

1.6 < |y|

(TeV)JJM0.2 0.3 0.4 0.5 1

Dat

a / T

heor

y

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

< 2.4max

2.0 < |y|

Run II dijet data (cone, R = 0.7)∅D(data points before systematic shifts, show total errors)

Not such good compatibility as for the two CDF sets.


Three-jet cross-sections

Recent results from D0 (arXiv 1104.1986) on three jets cross sections.

All the same work already done.


Broadly similar results.


Sometimes the reason forcross section differences isunexpected.

Warsinsky at recent Higgs-LHC working group meeting.

mb values bring CTEQand MSTW together butexaggerate NNPDF difference.

Couplings have assumed commonmass value.


Small-x Theory

Reason for this instability – at each order in αS each splitting function and coefficientfunction obtains an extra power of ln(1/x) (some accidental zeros in Pgg), i.e.Pij(x, αs(Q

2)), CPi (x, αs(Q2)) ∼ αms (Q

2) lnm−1(1/x).

BFKL equation for high-energy limit

f(k2, x) = fI(Q20)+

∫ 1

xdx′

x′ ᾱS∫ ∞0

dq2

q2K(q2, k2)f(q2, x),

where f(k2, x) is the unintegrated gluon distribution

g(x, Q2) =∫ Q2

0(dk2/k2)f(x, k2), and K(q2, k2) is a

calculated kernel known to NLO.

Physical structure functions obtained from

σ(Q2, x) =∫

(dk2/k2)h(k2/Q2)f(k2, x)

where h(k2/Q2) is a calculable impact factor.

The global fits usually assume that this is unimportantin practice, and proceed regardless.

Fits work well at small x, but could improve.


-3

-2

-1

0

1

2

10-5

10-4

10-3

10-2

10-1

1x

Q2=1GeV2xg

(x)

0

20

40

60

80

10-5

10-4

10-3

10-2

10-1

1x

Q2=100GeV2

NLL+NLL(2)+NLO+

Good recent progress in incorporatingln(1/x) resummation Altarelli-Ball-Forte, Ciafaloni-Colferai-Salam-Stastoand White-RT.

Include running coupling effects andvariety (depending on group) of othercorrections

By 2008 very similar results comingfrom the competing procedures,despite some differences in technique.

Full set of coefficient functions stillto come in some cases, but splittingfunctions comparable.

Note, in all cases NLO correctionslead to dip in functions below fixedorder values until slower growth(running coupling effect) at verysmall x.


A fit to data with NLO plus NLO resummation, with heavy quarks included (White,RT)performed.

0

0.5

1

1.5

2

2.5

3

3.5

4

1 10 102

103

x=5×10-4

x=6.32×10-4

x=8×10-4

x=1.3×10-3

x=1.61×10-3

x=2×10-3

x=3.2×10-3

x=5×10-3

x=8×10-3

H1ZEUSNMC

NLL+NLL(2)+NLO+

Q2(GeV2)

F 2p (

x,Q

2 ) +

0.2

5(9-

i)

-3

-2

-1

0

1

2

10-5

10-4

10-3

10-2

10-1

1x

Q2=1GeV2xg

(x)

0

20

40

60

80

10-5

10-4

10-3

10-2

10-1

1x

Q2=100GeV2

NLL+NLL(2)+NLO+

→ moderate improvement in fit to HERA data within global fit, and change inextracted gluon (more like quarks at low Q2).

Together with indications from Drell Yan resummation calculations (Marzani, Ball)few percent effect quite possible.


PDF Correlations

The PDF uncertainty analysis may be extended to define a correlation between theuncertainties of two variables, say X(~a) and Y (~a).

The correlations were calculated using the MCFM NLO program (versions 5.8 and 6.0)with a common set of input files for all groups. Each group did their own calculations.

For the groups using a Hessian approach the correlations were calculated using

cos ϕ=~∆X ·~∆Y∆X∆Y

=1

4∆X∆Y

N∑

i=1

(

X(+)i −X

(−)i

) (

Y(+)i − Y

(−)i

)

∆X =∣

∣

∣

~∆X∣

∣

∣=

1

2

√

√

√

√

N∑

i=1

(

X(+)i −X

(−)i

)2

or some similar variation. This included the most up-to-date published sets for eachgroup, i.e. , ABKM09, CT10, GJR 08, MSTW08. The basic results for CT10 andMSTW08 are PDF only, whereas ABKM09 and GJR08 include αS as a parameter inthe error matrix.


Due to the specific error calculation prescription for HERAPDF1.5 which includesparameterization and model errors, the correlations can not be calculated in exactlythe same way. An alternative way is to use a formula for uncertainty propagationin which correlations can be expressed via relative errors of compounds and theircombination:

σ2(

X

σ(X)+

Y

σ(Y )

)

= 2 + 2 cos ϕ,

where σ(O) is the PDF error of observable O calculated using the HERAPDFprescription.

The correlations for the NNPDF prescription are calculated using

ρ (X, Y ) =〈XY 〉rep − 〈X〉rep 〈Y 〉rep

σXσY

where the averages are performed over the Nrep = 100 replicas of the NNPDF2.1 set.

The averaging was done and diagrams made by J. Rojo.


Full study involves range of backgrounds shown by Huston at PDF4LHC- July 2011.Will be found at

https://twiki.cern.ch/twiki/bin/view/LHCPhysics/PDFCorrelations


And similar for signals. However, too detailed for concise presentation whenaveraging/comparing, and precision much higher than spread between groups.

Full list also not vital since W production is very similar to Z production, bothdepending on partons (quarks in this case) at very similar hard scales and x values.Similarly for WW and ZZ, and the subprocesses gg → WW(ZZ) and gg → H forMH = 200 GeV.


The up-to-date PDF4LHC average (CT10, MSTW08, NNPDF2.1) for the correlationsbetween all signal processes with other signal and background processes for Higgsproduction considered here. The processes have been classified in correlation classesof width 0.2.

120 GeVggH VBF WH ttH

ggH 1 -0.6 -0.2 -0.2VBF -0.6 1 0.6 -0.4WH -0.2 0.6 1 -0.2ttH -0.2 -0.4 -0.2 1W -0.2 0.6 0.8 -0.6

WW -0.4 0.8 1 -0.2WZ -0.2 0.4 0.8 -0.4Wγ 0 0.6 0.8 -0.6Wbb -0.2 0.6 1 -0.2

tt 0.2 -0.4 -0.4 1tb -0.4 0.6 1 -0.2

t(→ b)q 0.4 0 0 0


ggH 1 -0.6 -0.4 0.2VBF -0.6 1 0.6 -0.2WH -0.4 0.6 1 0ttH 0.2 -0.2 0 1W -0.4 0.4 0.6 -0.4

WW -0.4 0.6 0.8 -0.2WZ -0.4 0.4 0.8 -0.2Wγ -0.4 0.6 0.6 -0.6Wbb -0.2 0.6 0.8 -0.2

tt 0.4 -0.4 -0.2 0.8tb -0.4 0.6 1 0

t(→ b)q 0.6 0 0 0



ggH 1 -0.6 -0.4 0.4VBF -0.6 1 0.6 -0.2WH -0.4 0.6 1 0ttH 0.4 -0.2 0 1W -0.6 0.4 0.6 -0.4

WW -0.4 0.6 0.8 -0.2WZ -0.4 0.4 0.8 -0.2Wγ -0.4 0.4 0.6 -0.6Wbb -0.2 0.6 0.8 -0.2

tt 0.6 -0.4 -0.2 0.8tb -0.4 0.6 0.8 0

t(→ b)q 0.6 -0.2 0 0


ggH 1 -0.4 -0.2 0.6VBF -0.4 1 0.4 -0.2WH -0.2 0.4 1 0.2ttH 0.6 -0.2 0.2 1W -0.6 0.4 0.4 -0.6

WW -0.4 0.6 0.8 -0.2WZ -0.6 0.4 0.6 -0.4Wγ -0.6 0.4 0.4 -0.6Wbb -0.2 0.4 0.8 -0.2

tt 1 -0.4 0 0.8tb -0.4 0.4 0.8 -0.2

t(→ b)q 0.4 -0.2 0 -0.2


500 GeV ggH VBF WH ttH

ggH 1 -0.4 0 0.8VBF -0.4 1 0.4 -0.2WH 0 0.4 1 0ttH 0.8 -0.2 0 1W -0.6 0.4 0.2 -0.6

WW -0.4 0.6 0.6 -0.4WZ -0.6 0.4 0.6 -0.4Wγ -0.6 0.4 0.2 -0.6Wbb -0.4 0.4 0.6 -0.4

tt 1 -0.4 0 0.8tb -0.4 0.4 0.8 -0.2

t(→ b)q 0.2 -0.2 0 -0.2

Generally the results expected, i.e. gluon dominated processes correlated with eachother as are quark dominated processes. Little correlation between the two.

However, see that breakdown of correlation between gluon probed at different x values,e.g gg → H for MH = 120 GeV and tt since from momentum conservation gluonchanges in one place (high x) are compensated by those in another (low x), and thecrossing point is between 0.01 and 0.1 but varies slightly between groups.


The same for the correlations between background processes.

W WW WZ Wγ Wbb tt tb t(→ b)qW 1 0.8 0.8 1 0.6 -0.6 0.6 -0.2

WW 0.8 1 0.8 0.8 0.8 -0.4 0.8 0

WZ 0.8 0.8 1 0.8 0.8 -0.4 0.8 0

Wγ 1 0.8 0.8 1 0.6 -0.6 0.8 0

Wbb 0.6 0.8 0.8 0.6 1 -0.2 0.6 0

tt -0.6 -0.4 -0.4 -0.6 -0.2 1 -0.4 0.2

tb 0.6 0.8 0.8 0.8 0.6 -0.4 1 0.2

t(→ b)q -0.2 0 0 0 0 0.2 0.2 1

Similar conclusions as for signals.

What about variations between groups?


-1

-0.5

0

0.5

1

120 160 200 300

Parton Distributions and the Relation to LHC and Higgs Physics · 2012. 2. 17. · Parton...

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