Deep-inelastic scatteringDeep-inelastic scattering − from HERA to LHC − Sven-Olaf Moch [email protected] DESY, Zeuthen Proton colliders HERA: deep structure of proton at highest

Deep-inelastic scattering− from HERA to LHC −

Sven-Olaf [email protected]

DESY, Zeuthen

————————————————————————————————————–

– Festkolloquium fur Fridger Schrempp, Hamburg, February 19, 2007 –

Sven-Olaf Moch Deep-inelastic scattering – p.1

http://www-zeuthen.desy.de/~moch


Proton colliders

HERA: deep structure of proton at highest Q2 and smallest x

LHC: Higgs boson search at highest energies√

S = 14TeV

HERA LHC

Quantum Chromodynamics (QCD) ubiquitous at proton colliders

reliable understanding essential for precision and discoveryphysics



Perturbative QCD at colliders

Hard scattering at hadron collidersconstituent partons from incoming hadrons interact at shortdistance (large momentum transfer Q2 )

QCD factorizationseparate sensitivity to dynamics from different scales

DIS: photon momentum Q2 = −q2, Bjorken’s x = Q2/(2p · q)

pp : energy Q2 = 2p1 · p2, ratio to W/Z-boson mass x = M2W/Z/Q2



Hard scattering (I)Hard scattering cross sectionQCD factorization

σhad =

8

><

>:

P

ifi ⊗ σγi→X

“

αs(µ2), Q2, µ2

”

DISP

ijfi ⊗ fj ⊗ σij→X

“

αs(µ2), Q2, µ2

”

pp

Parton cross sections σγi→X and σij→X calculable pertubatively inpowers of αs

short distance interaction of constituent partons

Parton distributions fi → parton luminosityproton: very complicated multi-particle bound statecolliders: wide-band beams of quarks and gluons

Standard approach to uncertainties in theoretical predictions

variation of factorization scale µ:d

d ln µ2σhad = O(αl+1

s )



Asymptotic freedom of QCD

Effective coupling constant αs

depends on resolution, momentum scale Q

– screening (like in QED)

– anti-screening (color charge of g)Q2 (GeV2)

αS( Q2)

αS(M 2 ) = 0.115

1-loop

2-loop

3-loop

4-loop

Z

↓↓

↓

↓

t tZ

bb

cc−

−

−

0

0.1

0.2

0.3

0.4

0.5

0.6

1 10 102

103

104

At large scales: application of perturbation theory (but αs ≫ αQED)



Hard scattering (II)Approaches to the calculation of σhad

LO (leading order)Automated tree level calculations in Standard Model, MSSM, . . .(Madgraph,Alpgen, CompHEP, . . . )LO + parton showerString inspired techniques

NLO (next-to-leading order)Analytical (or numerical) calculations of diagrams yield partonlevel Monte Carlos (NLOJET++, MCFM, . . . )NLO + parton shower (MC@NLO, VINCIA)

NNLO (next-to-next-to-leading order)selected results known (mostly inclusive kinematics)

N3LO (next-to-next-to-next-to-leading order)very few . . .








easy

difficultSven-Olaf Moch Deep-inelastic scattering – p.6







easy

difficult

← level of talk here



Parton luminosity

Feynman diagrams in leading order

Proton in resolution 1/Q −→sensitive to lower momentumpartons



Parton luminosity

Feynman diagrams in leading order

Proton in resolution 1/Q −→sensitive to lower momentumpartons

Evolution equations for parton distributions fi

predictions from fits to reference processes (universality)d

d ln µ2fi(x, µ2) =

X

k

h

Pik(αs(µ2))⊗ fk(µ2)

i

(x)

Splitting functions P

P = αs P (0) + α2s P (1)

| {z }+ α3

s P (2) + . . .

NLO: standard approximation (large uncertainties)Sven-Olaf Moch Deep-inelastic scattering – p.7


Parton evolutionParton distributions in proton

Valence q − q (additive quantum numbers) sea (part with q + q)

x f(x,Q2) at Q2 = 15 GeV

x

valence

sea

gluon

0

1

2

3

4

5

6

10-2

10-1

1

Parameterization (bulk of data from deep-inelastic scattering)structure function F2 −→ quark distributionscale evolution (perturbative QCD) −→ gluon distribution



Parton evolutionParton distributions in proton

Valence q − q (additive quantum numbers) sea (part with q + q)

x f(x,Q2) at Q2 = 104 GeV

x

valence

sea

gluon

0

1

2

3

4

5

6

10-2

10-1

1

Parameterization (bulk of data from deep-inelastic scattering)structure function F2 −→ quark distributionscale evolution (perturbative QCD) −→ gluon distribution



PDFs from HERA to LHCPDFs from HERA to LHCHERA F2

0

1

2

3

4

5

1 10 102

103

104

105

F2 em

-log

10(x

)

Q2(GeV2)

ZEUS NLO QCD fit

H1 PDF 2000 fit

H1 94-00

H1 (prel.) 99/00

ZEUS 96/97

BCDMS

E665

NMC

x=6.32E-5 x=0.000102x=0.000161

x=0.000253

x=0.0004x=0.0005

x=0.000632x=0.0008

x=0.0013

x=0.0021

x=0.0032

x=0.005

x=0.008

x=0.013

x=0.021

x=0.032

x=0.05

x=0.08

x=0.13

x=0.18

x=0.25

x=0.4

x=0.65

HERA → LHC: scale evolution in Q2 over three orders of magnitude



Higgs boson production at LHC (I)

Dominant channel gg → H + X via top-quark loop

0

20

40

60

80

100 150 200 250 300

MH(GeV)

σ(pp → H+X) [pb]

µR = MH

NLO

√s = 14 TeV

LO

µR / MH

0.2 0.5 2 3

σ(pp → H+X) [pb]

MH = 120 GeV

LO

NLO

0

20

40

60

80

1

Estimate of uncertainty: apparent convergence, variation of scale µ

NLO approximation insufficient for reliable predictionsSven-Olaf Moch Deep-inelastic scattering – p.10


Our calculation in deep-inelastic scattering

"Loop technology" : optical theoremtotal cross section←→ imaginary part of Compton amplitude

2

f(p)

V ∗(q)

V ∗

f f

V ∗



Our calculation in deep-inelastic scattering

"Loop technology" : optical theoremtotal cross section←→ imaginary part of Compton amplitude

2

f(p)

V ∗(q)

V ∗

f f

V ∗

tree 1-loop 2-loop 3-loop

qγ 1 3 25 359

gγ 2 17 345

hγ 2 56

qW 1 3 32 589

qφ 1 23 696

gφ 1 8 218 6378

hφ 1 33 1184

sum 3 18 350 9607

more than 10 FTE years and a few CPU yearscomputer algebra updates: FORM → FORM 3.1→ FORM 3.2→ . . .

> 105 tabulated symbolic integrals ( > 3GB)Sven-Olaf Moch Deep-inelastic scattering – p.11


Splitting functions for a quarter of a century

P (0)ns (x) = CF(2pqq(x)+3δ(1− x))

P (0)ps (x) = 0

P (0)qg (x) = 2nf pqg(x)

P (0)gq (x) = 2CF pgq(x)

P (0)gg (x) = CA

(

4pgg(x)+113

δ(1− x))

−23

nf δ(1− x)

P(1)+ns (x) = 4CACF

(

pqq(x)[67

18− ζ2 +

116

H0 +H0,0

]

+ pqq(−x)[

ζ2 +2H−1,0 −H0,0

]

+143

(1− x)+δ(1− x)[17

24+

113

ζ2 −3ζ3

])

−4CFnf

(

pqq(x)[5

9+

13

H0

]

+23(1− x)

+δ(1− x)[ 1

12+

23

ζ2

])

+4CF2(

2pqq(x)[

H1,0 −34

H0 +H2

]

−2pqq(−x)[

ζ2 +2H−1,0

−H0,0

]

− (1− x)[

1−32

H0

]

−H0 − (1+ x)H0,0 +δ(1− x)[3

8−3ζ2 +6ζ3

])

P(1)−ns (x) = P(1)+

ns (x)+16CF

(

CF −CA

2

)(

pqq(−x)[

ζ2 +2H−1,0 −H0,0

]

−2(1− x)

− (1+ x)H0

)

P(1)ps (x) = 4CFnf

(209

1x−2+6x−4H0 + x2

[83

H0 −569

]

+(1+ x)[

5H0 −2H0,0

])

P(1)qg (x) = 4CAnf

(209

1x−2+25x−2pqg(−x)H−1,0 −2pqg(x)H1,1 + x2

[443

H0 −218

9

]

+4(1− x)[

H0,0 −2H0 + xH1

]

−4ζ2x−6H0,0 +9H0

)

+4CFnf

(

2pqg(x)[

H1,0 +H1,1 +H2

−ζ2

]

+4x2[

H0 +H0,0 +52

]

+2(1− x)[

H0 +H0,0 −2xH1 +294

]

−152−H0,0 −

12

H0

)

P(1)gq (x) = 4CACF

(1x

+2pgq(x)[

H1,0 +H1,1 +H2 −116

H1

]

− x2[8

3H0 −

449

]

+4ζ2 −2

−7H0 +2H0,0 −2H1x+(1+ x)[

2H0,0 −5H0 +379

]

−2pgq(−x)H−1,0

)

−4CFnf

(23

x

−pgq(x)[2

3H1 −

109

])

+4CF2(

pgq(x)[

3H1 −2H1,1

]

+(1+ x)[

H0,0 −72

+72

H0

]

−3H0,0

+1−32

H0 +2H1x)

P(1)gg (x) = 4CAnf

(

1− x−109

pgg(x)−139

(1x− x2

)

−23(1+ x)H0 −

23

δ(1− x))

+4CA2(

27

+(1+ x)[11

3H0 +8H0,0 −

272

]

+2pgg(−x)[

H0,0 −2H−1,0 − ζ2

]

−679

(1x− x2

)

−12H0

−443

x2H0 +2pgg(x)[67

18− ζ2 +H0,0 +2H1,0 +2H2

]

+δ(1− x)[8

3+3ζ3

])

+4CFnf

(

2H0

+23

1x

+103

x2 −12+(1+ x)[

4−5H0 −2H0,0

]

−12

δ(1− x))

.

1973

1980Sven-Olaf Moch Deep-inelastic scattering – p.12


Splitting functions at NNLONNLO splitting functions S.M. Vermaseren, Vogt

P(2)ps (x) = 16CACFnf

(43(1x

+ x2)[13

3H−1,0 −

149

H0 +12

H−1ζ2 −H−1,−1,0 −2H−1,0,0

−H−1,2

]

+23(1x− x2)

[163

ζ2 +H2,1 +9ζ3 +94

H1,0 −6761216

+57172

H1 +103

H2 +H1ζ2 −16

H1,1

−3H1,0,0 +2H1,1,0 +2H1,1,1

]

+(1− x)[182

9H1 +

1583

+39736

H0,0 −132

H−2,0 +3H0,0,0,0

+136

H1,0 +3xH1,0 +H−3,0 +H−2ζ2 +2H−2,−1,0 +3H−2,0,0 +12

H0,0ζ2 +12

H1ζ2 −94

H1,0,0

−34

H1,1 +H1,1,0 +H1,1,1

]

+(1+ x)[ 7

12H0ζ2 +

316

ζ3 +9118

H2 +7112

H3 +11318

ζ2 −82627

H0

+52

H2,0 +163

H−1,0 +6xH−1,0 +316

H0,0,0 −176

H2,1 +11720

ζ22 +9H0ζ3 +

52

H−1ζ2 +2H2,1,0

+12

H−1,0,0 −2H−1,2 +H2ζ2 −72

H2,0,0 +H−1,−1,0 +2H2,1,1 +H3,1 −12

H4

]

+5H−2,0 +H2,1

+H0,0,0,0 −12

ζ22 +4H−3,0 +4H0ζ3 −

329

H0,0 −2912

H0 −23512

ζ2 −51112

−9712

H1 +334

H2 −H3

−112

H0ζ2 −112

ζ3 −32

H2,0 −10H0,0,0 +23

x2[83

4H0,0 −

2434

H0 +10ζ2 +511

8+

978

H1 −43

H2

−4ζ3 −H0ζ2 +H3 +H2,0 −6H−2,0

])

+16CFnf2( 2

27H0 −2−H2 + ζ2 +

23

x2[

H2 − ζ2 +3

−196

H0

]

+29(1x− x2)

[

H1,1 +53

H1 +23

]

+(1− x)[1

6H1,1 −

76

H1 + xH1 +3527

H0 +18554

]

+13(1+ x)

[43

H2 −43

ζ2 + ζ3 +H2,1 −2H3 +2H0ζ2 +296

H0,0 +H0,0,0

])

+16CF2nf

(8512

H1

−254

H0,0 −H0,0,0 +58312

H0 −10154

+734

ζ2 −734

H2 +H3 −5H2,0 −H2,1 −H0ζ2 + x2[55

12

−8512

H1 −223

H0,0 −109

6−

1354

H0 +289

ζ2 −289

H2 −163

H0ζ2 +163

H3 +4H2,0 +43

H2,1 −263

ζ3

+223

H0,0,0

]

+43(1x− x2)

[2312

H1,0 −523144

H1 −3ζ3 +5516

+12

H1,0,0 +H1,1 −H1,1,0 −H1,1,1

]

+(1− x)[1

2H1,0,0 +

712

H1,1 −2743

72H0 −

5312

H0,0 −25112

H1 −54

ζ2 +54

H2 −83

H1,0 +3xH1,0

+3H0ζ2 −3H3 −H1,1,0 −H1,1,1

]

+(1+ x)[1669

216+

52

H0,0,0 +4H2,1 +7H2,0 +10xζ3 −3710

ζ22

−7H0ζ3 +6H0,0ζ2 −4H0,0,0,0 +H2,0,0 −2H2,1,0 −2H2,1,1 −4H3,0 −H3,1 −6H4

])

.

P (2)qg (x) = 16CACF nf

(

pqg(x)[39

2H1ζ3 −4H1,1,1 +3H2,0,0 −

154

H1,2 +94

H1,1,0 +3H2,1,0

+H0ζ3 −2H2,1,1 +4H2ζ2 −17312

H0ζ2 −55172

H0,0 +643

ζ3 − ζ22 −

494

H2 −32

H1,0,0,0 −13

H1,0,0

−38572

H1,0 −312

H1,1 −11312

H1 +494

H2,0 +52

H1ζ2 +796

H0,0,0 +17312

H3 −1259

32+

2833216

H0

+6H2,1 +3H1,−2,0 +9H1,0ζ2 +6H1,1ζ2 +H1,1,0,0 +3H1,1,1,0 −4H1,1,1,1 −3H1,1,2 −6H1,2,1

−6H1,3 +494

ζ2

]

+ pqg(−x)[17

2H−1ζ3 −

52

H−1,−1,0 −52

H−1,2 −92

H−1,0 +52

H−2,0 +32

H−1,0,0

−2H3,1 −2H4 −6H−2,2 +6H−2,−1,0 −6H−2,0,0 +2H0,0ζ2 +9H−2ζ2 +3H−1,−2,0 −2H−1,2,1

−6H−1,−1,−1,0 +6H−1,−1,0,0 +6H−1,−1,2 +9H−1,0ζ2 −9H−1,−1ζ2 −2H−1,2,0 −112

H−1,0,0,0

−6H−1,3

]

+(1x− x2)

[5512

−4ζ3 +239

H1,0 −43

H1,1,0

]

+(1x

+ x2)[2

3H1,0,0 −

371108

H1 +239

H1,1

−23

H1,1,1

]

+(1− x)[

6H2,1,0 +3H2,1,1 −56

H1,1,1 −7H2,0,0 −2H1,2 +39H0ζ3 −4H2ζ2 −163

ζ3

+H1,1,0 +154

3H0ζ2 +

89924

H0,0 +12110

ζ22 +

60736

H2 −52

H1ζ2 +656

H1,0,0 −2912

H1,0 −1318

H1,1

−1189108

H1 −673

H2,1 −29H2,0 −94936

ζ2 −672

H0,0,0 −142

3H3 +

21532

−398948

H0 +2H−3,0

]

+(1+ x)[

H−1,0,0 −10H−2ζ2 +6H−2,0,0 +2H0,0ζ2 −9H−1,−1,0 −7H−1,2 −9H−2,0 −2H3,1

−4H−2,−1,0 −4H4 −4H3,0 −4H0,0,0,0 +372

H−1,0 +52(1+ x)H−1ζ2

]

−4H−2,0,0 +2H0,0ζ2

+H2ζ2 −3H1,1,0 +2H0,0,0,0 +H−3,0 −9H2,1,0 −92

H2,1,1 +113

H1,1,1 +192

H2,0,0 +92

H1,2

−912

H0ζ3 +8H−2ζ2 +52

H−1,−1,0 +52

H−1,2 +92

H−1,0 +392

H−2,0 −47312

H0ζ2 −1853

48H0,0

−21712

ζ3 −594

ζ22 −

16918

H2 −134

H1ζ2 −23

H1,0,0 +16724

H1,0 +19118

H1,1 +1283108

H1 +18512

H2,1

+754

H2,0 +170

9ζ2 +

854

H0,0,0 +42512

H3 +7693192

+3659

48H0 −2x

[

xH2,2 +4H3,0 −4H−2,2

])

+16CAnf2(1

6pqg(x)

[

H1,2 −H1ζ2 −H1,0,0 −H1,1,0 −H1,1,1 −22918

H0 +43

H0,0 +112

]

+ x[1

6H2

−5318

H0 +176

H0,0 − ζ3 +1118

ζ2 −139108

]

+13

pqg(−x)H−1,0,0 −53162

(1x− x2)−

29(1− x)

[

6H0,0,0

−76

xH1 −H0,0 +72

xH1,1

]

+79

x(1+ x)H−1,0 +74

H0 −1954

H1 +H0,0,0 +59

H1,1 +59

H−1,0

−85

216

)

+16CA2nf

(

pqg(x)[

3H1,3 +316

H1,0,0 −172

H2,1 +75

ζ22 −

5512

H1,1,0 +3112

H3 −312

H1ζ3

−5

12H2,0 −

638

H1,0 −2312

H1,2 −155

6ζ3 +

2524

H2 −2537

27H0 +

8678

−232

H−1,0,0 +3H4 −H1,1,1

+38372

H1,1 −252

H−2,0 −38

ζ2 −74

H1ζ2 −3H0,0ζ2 −3112

H0ζ2 +103216

H1 +52

H1,0,0,0 +2561

72H0,0

+H1,1,1 −2H2,0,0 −3H1,−2,0 −5H1,0ζ2 +3H0,0,0 −H1,1ζ2 −H1,1,0,0 −4H1,1,1,0 +2H1,1,1,1

−2H1,1,2 −2H1,2,0

]

+ pqg(−x)[

H−1,−1ζ2 −2H−1,2 −6H−1,−1,0 +H1,1,1 +2H−2ζ2 −H−2,0,0

+72736

H−1,0 −H−1ζ2 −2H−2,2 −52

H−1ζ3 −H−1,−2,0 +2H−1,−1,0,0 +2H−1,−1,2 −32

H−1,0,0,0

+6H−1,−1,−1,0 −2H−1,3 +2H−1,2,1

]

+(1x− x2)

[23

H2,1 +329

ζ2 −2H1,0,0 +43

H1,1,0 −109

H1,1

−83

H−1,0,0 +32

H1,0 +6ζ3 +16136

H1 −2351108

]

+23(1x

+ x2)[26

3H−1,0 −

289

H0 −2H−1,−1,0

−2H−1,2 +H1ζ2 +H−1ζ2 +103

H2 +H1,1,1

]

+(1− x)[

15H0,0,0,0 −5H2ζ2 −656

ζ3 +116

H1,1,1

−32

H4 +52

H0,0ζ2 +H1,1,0 −316

H2,0 +1712

H1,0 −55120

ζ22 −

294

H1,0,0 −113

4H2 +

1869172

H0

+2243108

+265

6H−1,0,0 +

332

H2,0,0 +19H2,1 +3112

H1,1 +232

H−2,0 −49736

ζ2 +296

H1ζ2 −14312

H3

−116

H1,1,1 −1912

H0ζ2 +1223

72H1 −

436

H0,0,0 −3011

36H0,0

]

+(1+ x)[

8H2,1,0 −4H−1,2

+7H−1,−1,0 −356

H1,1,1 −5H−2ζ2 −11H−2,0,0 +13

H−1,0 +152

H−1ζ2 +8H3,1 −10H−2,−1,0

+5H2ζ2 +4H2,1,1 −H−3,0 +36H0ζ3 −5H2ζ2

]

+2H−1,2 +6H−1,−1,0 −6H2,1,0 −3H2,1,1

−11H0,0,0,0 −5H3,1 +254

H1,1,1 +132

H−2ζ2 +272

H−2,0,0 +112

H−3,0 +132

H2ζ2 −174

H1,0,0

+13H−2,−1,0 −1712

H1,1,1 −34

H4 −14

H0,0ζ2 +H1,2 +112

H1,1,0 +7912

H2,0 +678

H1,0 +263

8ζ2

2

+119

3ζ3 +

96724

H2 −30512

H−1,0 −24H0ζ3 +H−1ζ2 −13375

72H0 −

188918

−38H−1,0,0 −212

H2,1

−794

H2,0,0 −21724

H1,1 −72

H−2,0 +7972

ζ2 +43

H1ζ2 +1712

H1,1,1 +1712

H0ζ2 +3118

H1 +3H0,0,0

+14512

H3 +1553

24H0,0

)

+16CFnf2(7

6H0,0,0 +

1136

H1 −73996

+16324

H0 +7

24H0,0 +2H0,0,0,0

−59

H1,1 −59

H2 −5

18H1,0 +

59

ζ2 +16

pqg(x)[

H2,1 +912−

353

H0 −223

H0,0 +H1,1,1 +6H0,0,0

−ζ3 −2H1,0,0 +79

H1

]

+7781

(1x− x2)+(1− x)

[ 112

H1 −6463432

−4H0,0,0,0 −163

H0,0,0 +79

xH1,1

+79

xH2 +89

xH1,0 −79

xζ2

]

− (1+ x)[3475

216H0 +

10312

H0,0

])

+16CF2nf

(

pqg(x)[

7H1,3 +7H4

−2H−3,0 −7H1ζ3 +5H2,2 +6H3,0 +6H3,1 +H2,1,0 +4H2,0,0 +3H2,1 +2H2,1,1 +52

H2,0

+618

H2 −618

ζ2 +878

H1 +112

H1,2 +618

H1,1 +172

H1,0 −7H0,0ζ2 +52

H1,0,0 +52

H1,1,0 −192

ζ3

+8132

+112

H3 −112

H0ζ2 −72

H1ζ2 +152

H0,0,0 +878

H0 +115

ζ22 +3H1,1,1 −5H2ζ2 −7H0ζ3

+11H0,0 −2H1,−2,0 −7H1,0ζ2 +3H1,0,0,0 −5H1,1ζ2 +4H1,1,0,0 +H1,1,1,0 +2H1,1,1,1 +5H1,1,2

+6H1,2,0 +6H1,2,1

]

+4pqg(−x)[

H0,0,0,0 −H−2,0 +H−1,−1,0 −H−2,0,0 +12

H−1,−2,0 −58

H−1,0

−54

H−1,0,0 −12

H−3,0 +12

H−1ζ2 +H−1,−1,0,0 −14

H−1,0,0,0

]

+2(1− x)[

H2,1,0 −H2,0,0 −H2,2

−H3,1 −2H3,0 −2H−1ζ2 +H1,2 −H1,0,0 −H1,1,0 +H2ζ2 − ζ22 +

438

H2 +498

ζ2 +138

H1,1

−3316

H1 +52

H1,0 +72

H0,0ζ2 +214

ζ3 +47964

−12

H1,1,1 −12

H3 +14

H2,1 +12

H2,1,1 +32

H0ζ2

+12

H0ζ3 −72

H4 +H1ζ2 −192

H0,0,0 −23916

H0,0 −40532

H0

]

+8(1+ x)[

H−1,−1,0 −H−1,0,0

−H0,0,0,0 +34

H−2,0 −94

H−1,0

]

−4H−1,−1,0 +5H0,0,0,0 +5H−1,0,0 −13H−2,0 +12

H−1,0

+4xH−2,0,0 −113

8H2 −

718

ζ2 −354

H1 −112

H1,2 −338

H1,1 −72

H1,0 −72

H0,0ζ2 −52

H1,0,0

−52

H1,1,0 −52

ζ3 −15764

−94

H1,1,1 −94

H3 −54

H2,1 −12

H2,1,1 +14

H0ζ2 +H2ζ2 +52

H0ζ3

+95

ζ22 +

72

H4 +72

H1ζ2 +494

H0,0,0 +39116

H0,0 +40116

H0 −H2,0,0 −H2,1,0 +H2,2 +H3,1

+2H3,0 +6H−1ζ2 +12

H2,0 +2H−2ζ2 +4H−2,−1,0

)

P(2)gq (x) = 16CACFnf

(29

x2[25

6H1 −

1314

+3ζ2 −H−1,0 −3H2 +H1,1 +125

6H0 −H0,0

]

+56

pgq(x)[

H1,2 +H2,1 +967120

+25190

H1 −3910

H1,1 −3ζ3 −25

H0ζ2 −15

H1ζ2 −43

H1,0 +H1,1,0

−25

H1,0,0 +H1,1,1 +25

H2,0

]

+23

pgq(−x)[

2H−1ζ2 +74

ζ2 +4112

H−1,0 −15172

H0 +12

H−2,0

+53

H2 +2H−1,−1,0 −H−1,0,0 −H−1,2

]

+23(1− x)

[

H−2,0 +2ζ3 −H3

]

+(1+ x)[179

108H1

+59

ζ2 +259

H−1,0 −5

36H1,1 −

16736

H0,0 −13

H2,1 −43

H0ζ2

]

−19372

+14

H1 +19

H−1,0 +4H2

−14

H1,1 +22718

H0 −3512

H0,0 −H2,1 −23

H0ζ2 +103

H−2,0 +3ζ3 +2H3 +23

H0,0,0 + x[11

4ζ2

−523144

−1936

H2 +271108

H0 −56

H1,0

])

+16CACF2(

x2[7

2+

17354

H1 −2ζ3 −23

H1,1,1 −269

H1,1

−6H2 +2H2,1 +6ζ2 +33554

H0 −289

H0,0 −83

H0,0,0

]

+ pgq(x)[3

2H1ζ3 +

16332

−5ζ2 +274

ζ3

+6503432

H1 +29

H1,1 +353

H1,1,1 +4H2 +92

H2,1 +4H1,0,0 +2H2,0,0 −H2ζ2 +4112

H1,2 +H2,2

+19124

H1,0 +3H2,0 −2H2,1,1 −32

H−1ζ2 −5912

H1ζ2 +5H1,−2,0 +H1,0ζ2 +52

H1,0,0,0 −2H1,1ζ2

+1

12H1,1,0 +5H1,1,0,0 −3H1,1,1,0 −4H1,1,1,1 −H1,1,2 −2H1,2,1 +H2,1,0

]

+ pgq(−x)[

H−1,0

+H−1,0ζ2 +32

H−1,0,0 +2710

ζ22 −3H−1,−1,0 −

112

H−1ζ3 −3H−1,−2,0 −32

H−1,0,0,0 −3H−1,2

+5H−1,−1ζ2 −4H−1,−1,0,0 −2H−1,−1,2 +6H−1,−1,−1,0 +2H−1,2,1

]

+(1− x)[

H2ζ2 −H2,2

+2312

H1,0 −7061432

H0 −4631144

H0,0 −383

H0,0,0 −H−3,0 −2H3,0 −4433432

H1 −2H2,0,0 −212

H1,0,0

−25

ζ22 −

72

H1,2 +232

H1ζ2 −4H0ζ3

]

+(1+ x)[49

6H3 −H−2,0 −

556

H0ζ2 −12

H3,1 −1159

36ζ2

+655576

−1516

ζ3 −18518

H1,1 +16

H1,1,1 −959

H2 +296

H2,1 −171

4H−1,0 −12H−1,0,0 +7H−1ζ2

+16H−1,−1,0 +53

H2,0 +32

H2,1,1 +4H0,0,0,0

]

−35H−2,0 −17927

H0 +2041144

H0,0 −196

H0,0,0

−2H3,0 −132

H0ζ2 −13H−3,0 −132

H3,1 +152

H3 −2005

64+

1574

ζ2 +8ζ3 +1291432

H1 +5512

H1,1

+32

H2 +12

H2,1 +274

H−1,0 −112

H1,0,0 −8H2,0,0 −4ζ22 +

32

H1,2 −H2,2 +52

H1ζ2 +8H−1,−1,0

+4H2,0 +32

H2,1,1 −H−1ζ2 +7H2ζ2 +6H−2ζ2 +12H−2,−1,0 −6H−2,0,0 + x[

3H1,1,1 −H0,0ζ2

+92

H−1,0,0 −358

H1,0 +2H4 +3H1,1,0 +H−1,2

])

+16CA2CF

(

x2[2

3H1ζ2 −

210581

−7718

H0,0

−6H3 +163

ζ3 −10H−1,0 −143

H2,0 −23

H−1ζ2 −143

H0,0,0 +104

9H2 −

43

H1,0,0 +379

H1,1

+43

H−1,−1,0 −1049

ζ2 −83

H2,1 +14518

H1,0 +43

H−1,2 +23

H1,1,1 −10927

H1 +83

H−1,0,0 +6H0ζ2

+4H−2,0 +58427

H0

]

+ pgq(x)[7

2H1ζ3 +

1383052592

−13

H2,0 +134

H−1ζ2 +2H2,1,1 +112

H1,0,0

+4H3,1 −436

H1,1,1 −10912

ζ2 −173

H2,1 −7124

H1,0 −116

H−2,0 −212

ζ3 +32

H1,0,0,0 −H1,−2,0

+39554

H0 −2H1,0ζ2 −H1,1ζ2 −5512

H1,1,0 +2H1,1,0,0 +4H1,1,1,0 +2H1,1,1,1 +4H1,1,2 −5512

H1,2

+6H1,2,0 +4H1,2,1 +4H1,3 +3H2,1,0 +3H2,2

]

+ pgq(−x)[23

2H−1ζ3 +5H−2ζ2 +2H−2,−1,0

+10912

H−1,0 +H0ζ3 +175

ζ22 +

16

H1ζ2 +2H2ζ2 −6524

H1,1 −192

H−1,−1,0 −4H3,0 −3H2,0,0

−7H−2,0,0 −32

H−1,2 +3379216

H1 −4H−2,2 −496

H−1,0,0 −112

H−1,0,0,0 −13H−1,−1ζ2 −8H−1,3

−6H−1,−1,−1,0 +12H−1,−1,0,0 +10H−1,−1,2 +10H−1,0ζ2 +5H−1,−2,0 −2H−1,2,0 −2H−1,2,1

+116

H0ζ2

]

+(1− x)[41699

2592−3H−2,−1,0 −

32

H−2ζ2 −128

9ζ2 −4H3,0 +

263

ζ3 −52

H−2,0,0

−7H1ζ2 +9712

H1,0,0 +103

H−1,0,0 +24512

H3 −8H0,0,0,0

]

+(1+ x)[

4H3,1 −H2,1,1 +296

H−1,2

+176

H−2,0 −12H2,0 −3112

H2,1 +12

H2,0,0 −H2ζ2 +6136

H1,0 −4H0ζ3 −133

H−1ζ2 −463

H−1,−1,0

+254

H4 +934

H0ζ2 −559

H1,1 −7118

H2 +4918

H0,0 −132

H0,0ζ2 −4740

ζ22]

+61312592

−312

H−2ζ2

−15H−2,−1,0 +92

H−1,0,0 −3H2,1,1 −94

H2,1 +533

H−2,0 −12

H−2,0,0 −5H2,0 −76

H1,1,1 −8H0ζ3

−6740

ζ22 +

296

H−1,2 −H−1,0 +8H−2,2 +25H0ζ2 +412

9H1 +

9289

H0 +14

H4 −65H3 −38H0,0

−9H−3,0 −173

H0,0,0 + x[27

2H−1,0 −

12

H0,0,0,0 +34

H0,0ζ2 +12

H−3,0 −14H0,0,0 +1

12H1,1,1

−4336

ζ2 −12

H2ζ2 +772

H0 +74954

H1 +135

4ζ3 +

9724

H1,0 +4312

H1ζ2 −8512

H−1ζ2 −133

H1,0,0

+5312

H2 +394

H1,1 −2H3,1 +136

H−1,−1,0 +74

H2,0,0 −4H1,1,0 −4H1,2

])

+16CFnf2(1

9−

19

1x

+29

x−16

xH1 +16

pgq(x)[

H1,1 −53

H1

])

+16CF2nf

(49

x2[

H0,0 −116

H0 −72

+H−1,0

]

+13

pgq(x)[

H1,2 −H1,0 −H1ζ2 +9ζ3 +8312

H1,1 +2H−2,0 −736

H1 +2H0ζ2 −162548

+32

H1,0,0

+2H1,1,0 −52

H1,1,1

]

+3118

pgq(−x)[95

93H0 − ζ2 −H−1,0

]

+13(2− x)

[

6H0,0,0,0 −H3 −13051

288

−132

ζ3 −4H−2,0 −H2,0 −12

H1,0 −12

H2,1 +2H0,0,0 −65324

H0,0

]

+(1+ x)[

H0ζ2 −1187216

H0

+89

H2 −8518

H−1,0 −10118

ζ2

]

−8027

H0 +2318

ζ2 −13

H1,1 +54

xH1,1 −19

H1 −3712

xH1 +2318

H−1,0

+1501

54+H0ζ2 −H0,0,0 +

1013

H0,0 −13

H1,0

)

+16CF3(

pgq(x)[

3H1,1ζ2 +3H1ζ2 +72

ζ2

−238

H1,1 −8H1ζ3 −6H1,−2,0 −2H1,0ζ2 +3H1,1,0 −3H1,1,0,0 −H1,1,1,0 +2H1,1,1,1 −3H1,1,2

−2H1,2,0 −2H1,2,1 −92

H1,1,1 −32

H1,0,0 −4716

−4716

H1 −152

ζ3

]

+ pgq(−x)[

2H−1,−2,0

+6H−1,−1,0 +3H−1ζ2 +74

H1,0 −165

ζ22 −6H−1,0,0 −

72

H−1,0 +4H−1,−1,0,0 −2H−1,0ζ2

−H−1,0,0,0

]

+(1− x)[

9H1,0,0 +H1,1,1 −10H1ζ2 +3H0ζ3 +H2,2 −H2ζ2 +H0,0,0 +5H2,0,0

−4H3 +H2,1,1 +3H0,0ζ2 +3H3,1 −3H4 +21116

H1 +4920

ζ22]

+(1+ x)[

11ζ3 +14

H1,1 +14

H1,0

+9116

H0 +36H−1,0 +8H−1,0,0 −14H−1,−1,0 −7H−1ζ2 +2H1,2 +4H0ζ2 −H2,1 +2H−2,0,0

+5H−2,0 +112

H2 −2H0,0,0,0

]

−2H−1,−1,0 −H−1ζ2 −134

ζ2 +94

H1,0 +9

20ζ2

2 +28732

+1116

H1

+4H−1,0,0 +16H−3,0 −4H−2ζ2 −8H−2,−1,0 −5H2ζ2 +194

H2 +H2,2 −358

H0,0 +9H0ζ3

+25H−2,0 +6H−2,0,0 +32

x[58

3ζ2 −

73

H1ζ2 +4H1,1 −32

H1,1,1 +52

H1,0,0 −17596

+H3,1 +193

ζ3

+2H2,0 −14H0 +H0,0ζ2 −H−1,0 −H4 −32

H2,1 +13

H2,1,1 +3H2,0,0 −56

H3 −H1,2 −76

H0ζ2

+23

H1,1,0 −296

H0,0,0 −185

8H0,0

])

.

P (2)gg (x) = 16CACFnf

(

x2[4

9H2 +3H1,0 −

9712

H1 +83

H−2,0 −23

H0ζ2 +10327

H0 −163

ζ2 +2H3

−6H−1,0 +2H2,0 +12718

H0,0 −51112

]

+ pgg(x)[

2ζ3 −5524

]

+43(1x− x2)

[1724

H1,0 −4318

H0

−521144

H1 −6923432

−12

H2,1 +2H1ζ2 +H0ζ2 −2H1,0,0 +1

12H1,1 −H1,1,0 −H1,1,1

]

−17512

H2

+6H−1,0 +8H0ζ3 −6H−2,0 −536

H0ζ2 −492

H0 +1854

ζ2 +51112

−12

H2,0 −3H1,0 −4H0,0,0,0

−6712

H0,0 +432

ζ3 −H2,1 +9712

H1 −4ζ22 −

92

H3 −8H−3,0 +332

H0,0,0 +43(1x

+ x2)[1

2H2 −H2,0

+113

H−1,0 +H−2,0 +196

ζ2 +2ζ3 −H−1ζ2 −4H−1,−1,0 −12

H−1,0,0 −H−1,2

]

+(1− x)[

9H1ζ2

+12H0,0,0,0 −293108

+616

H0ζ2 −73

H1,0 −85736

H1 −9H0ζ3 +16H−2,−1,0 −4H−2,0,0 +8H−2ζ2

−132

H1,0,0 +34

H1,1 −H1,1,0 −H1,1,1

]

+(1+ x)[1

6H2,0 −

953

H−1,0 −14936

H2 +3451108

H0

−7H−2,0 +302

9H0,0 +

196

H3 −99136

ζ2 −163

6ζ3 −

353

H0,0,0 +176

H2,1 −4310

ζ22 +13H−1ζ2

+18H−1,−1,0 −H3,1 −6H4 −4H−1,2 +6H0,0ζ2 +8H2ζ2 −7H2,0,0 −2H2,1,0 −2H2,1,1 −4H3,0

−9H−1,0,0

]

−241288

δ(1− x))

+16CAnf2(19

54H0 −

124

xH0 −1

27pgg(x)+

1354

(1x− x2)

[53−H1

]

+(1− x)[11

72H1 −

71216

]

+29(1+ x)

[

ζ2 +1312

xH0 −12

H0,0 −H2

]

+29

288δ(1− x)

)

+16CA2nf

(

x2[

ζ3 +119

ζ2 +119

H0,0 −23

H3 +23

H0ζ2 +1639108

H0 −2H−2,0

]

+13

pgg(x)[10

3ζ2

−20936

−8ζ3 −2H−2,0 −12

H0 −103

H0,0 −203

H1,0 −H1,0,0 −203

H2 −H3

]

+109

pgg(−x)[

ζ2

+2H−1,0 +3

10H0ζ2 −H0,0

]

+13(1x− x2)

[

H3 −H0ζ2 −133

H2 +5443108

−3H1ζ2 +20536

H1

−133

H1,0 +H1,0,0

]

+(1x

+ x2)[151

54H0 −

83

ζ2 +13

H−1ζ2 − ζ3 +2H−1,−1,0 −23

H−1,0,0

−379

H−1,0 +23

H−1,2

]

+(1− x)[5

6H−2,0 +H−3,0 +2H0,0,0 −

26936

ζ2 −4097216

−3H−2ζ2

−6H−2,−1,0 +3H−2,0,0 −72

H1ζ2 +67772

H1 +H1,0 +74

H1,0,0

]

+(1+ x)[193

36H2 −

112

H−1ζ2

+3920

ζ22 −

712

H3 −539

H0,0 +7

12H0ζ2 −

52

H0,0ζ2 +5ζ3 −7H−1,−1,0 +776

H−1,0 +92

H−1,0,0

+2H−1,2 −3H2ζ2 −23

H2,0 +32

H2,0,0 +32

H4

]

+19

ζ2 +7H−2,0 +2H2 +45827

H0 +H0,0ζ2

+32

ζ22 +4H−3,0 − x

[13112

H0,0 −83

H0ζ2 +72

H3 −H0,0,0,0 +76

H0,0,0 +1943216

H0 +6H0ζ3

]

−δ(1− x)[233

288+

16

ζ2 +1

12ζ2

2 +53

ζ3

])

+16CA3(

x2[

33H−2,0 +33H0ζ2 −1249

18H0,0

−44H0,0,0 −110

3H3 −

443

H2,0 +856

ζ2 +6409108

H0

]

+ pgg(x)[245

24−

679

ζ2 −3

10ζ2

2 +113

ζ3

−4H−3,0 +6H−2ζ2 +4H−2,−1,0 +113

H−2,0 −4H−2,0,0 −4H−2,2 +16

H0 −7H0ζ3 +679

H0,0

−8H0,0ζ2 +4H0,0,0,0 −6H1ζ3 −4H1,−2,0 +10H2,0,0 −6H1,0ζ2 +8H1,0,0,0 +8H1,1,0,0 +8H4

+134

9H1,0 +

116

H1,0,0 +8H1,2,0 +8H1,3 +134

9H2 −4H2ζ2 +8H3,1 +8H2,2 +

116

H3 +10H3,0

+8H2,1,0

]

+ pgg(−x)[11

2ζ2

2 −116

H0ζ2 −4H−3,0 +16H−2ζ2 −12H−2,2 −134

9H−1,0 +2H2ζ2

+8H−2,−1,0 +12H−1ζ3 −18H−2,0,0 +8H−1,−2,0 −16H−1,−1ζ2 +24H−1,−1,0,0 +16H−1,−1,2

+18H−1,0ζ2 −16H−1,0,0,0 −4H−1,2,0 −16H−1,3 −5H0ζ3 −8H0,0ζ2 +4H0,0,0,0 +2H3,0

−679

ζ2 +679

H0,0 +8H4

]

+(1

x− x2

)[16619162

+223

H2,0 −552

ζ3 −112

H0ζ2 −679

H2 −679

H1,0

−413108

H1 −112

H1ζ2 +332

H1,0,0

]

+11(1x

+ x2)[71

54H0 −

16

H3 −389198

ζ2 −23

H−2,0 −12

H−1ζ2

+H−1,−1,0 −523198

H−1,0 +83

H−1,0,0 +H−1,2

]

+(1− x)[31

36H1 +

272

H1,0 −252

H1,0,0 −4H−3,0

−26312

H0,0 −293

H0,0,0 −193

H−2,0 −11317

108−4H−2ζ2 −8H−2,−1,0 −12H−2,0,0 −

32

H1ζ2

]

+(1+ x)[27

2H0ζ2 −

436

H3 +293

H2,0 +4651216

H0 −32918

ζ2 +112

(1+ x)ζ3 −435

ζ22 −

2156

H−1,0

−22H0,0ζ2 −8H0ζ3 −3H−1,−1,0 +38H−1,0,0 +25H−1,2 +10H2,0,0 −4H2ζ2 +16H3,0 +26H4

−158

9H2 −

532

H−1ζ2

]

−29H0,0 −403

H0,0,0 +27H−2,0 +413

H0ζ2 −20H3 −24H2,0 +536

ζ2

+60112

H0 +24ζ3 +2ζ22 +27H2 −4H0,0ζ2 −16H0ζ3 −16H−3,0 +28xH0,0,0,0 +δ(1− x)

[7932

−ζ2ζ3 +16

ζ2 +1124

ζ22 +

676

ζ3 −5ζ5

])

+16CFnf2(2

9x2

[116

H0 +H2 − ζ2 +2H0,0 −9]

+13

H2

−13

ζ2 −103

H0 −13

H0,0 +2+29(1x− x2)

[83

H1 −2H1,0 −H1,1 −7718

]

− (1− x)[1

3H1,0 +

16

H1,1

+49

+136

H1 + xH1

]

+13(1+ x)

[689

H0 −43

H2 +43

ζ2 +296

H0,0 − ζ3 +2H0ζ2 −H0,0,0 −2H3

−H2,1 −2H2,0

]

+11

144δ(1− x)

)

+16CF2nf

(43

x2[163

16+

278

H0 +72

H0,0 −H2,0 − ζ2 +94

H1,0

−H2,1 +12

H0,0,0 +8516

H1 +H2 −2H−2,0 −32

ζ3

]

+43(1x− x2)

[3116

H1 −1116

−54

H1,0 +12

H1,0,0

−H1ζ2 −H1,1 +H1,1,0 +H1,1,1 + ζ3

]

+43(1x

+ x2)[

H−1ζ2 +2H−1,−1,0 −H−1,0,0

]

+21512

H0,0

+203

H0 −131

6+3H2,0 +

20512

xζ2 −3H1,0 +H2,1 −8512

H1 +114

H2 +8H−2,0 +2ζ22 −H0ζ2

+H3 +6H0ζ3 +8H−3,0 −4xH0,0,0 +(1− x)[107

12H1 −

56

H1,0 −4ζ2 +H0ζ3 −8H−2,−1,0

−4H−2ζ2 +4H−2,0,0 −4H1ζ2 +72

H1,0,0 −7

12H1,1 +H1,1,0 +H1,1,1

]

+(1+ x)[5

4H2 +

338

−994

H0,0 −8H2,0 −54124

H0 −4H2,1 −32

H0,0,0 −2xζ3 +92

ζ22 +5H0ζ2 −5H3 −4H−1ζ2

−8H−1,−1,0 +673

H−1,0 +4H−1,0,0 +2H0,0ζ2 −2H0,0,0,0 −4H2ζ2 +3H2,0,0 +2H2,1,0

+2H2,1,1 +H3,1 −2H4

]

+1

16δ(1− x)

)

.

2004



Evolution at small xPerturbative stability of evolution

Scale derivatives of quark and gluon distributions at Q2 ≈ 30 GeV2

-0.4

-0.2

0

0.2

0.4

10-5

10-4

10-3

10-2

10-1

1x

d ln q / d ln Q2

LO

NLO

x

d ln g / d ln Q2

αS = 0.2, Nf = 4-0.4

-0.2

0

0.2

0.4

10-5

10-4

10-3

10-2

10-1

1



Evolution at small xPerturbative stability of evolution

Scale derivatives of quark and gluon distributions at Q2 ≈ 30 GeV2

-0.4

-0.2

0

0.2

0.4

10-5

10-4

10-3

10-2

10-1

1x

d ln q / d ln Q2

LO

NLONNLO

x

d ln g / d ln Q2

αS = 0.2, Nf = 4-0.4

-0.2

0

0.2

0.4

10-5

10-4

10-3

10-2

10-1

1

Expansion very stable except for very small momenta x <∼ 10−4



Impact on precision of LHC predictions

W±, Z-boson rapidity distribution (scale variationmW,Z

2≤ µ ≤ 2mW,Z )

Anastasiou, Petriello, Melnikov ‘05

NNLO QCD theoretical uncertainties (renormalization / factorization scale)at level of 1% Dissertori et al. ‘05

one of the few cross sections known to NNLO in pQCD

"Standard candle" process for parton luminosity



CTEQ (I)Updates of PDFs (exp)New experimental data

results from neutrino-nucleon DIS for strange quark PDFs (s 6= s)

Uncertainty on u, d doubles from 1.5% to 3% at Q2 ≃M2W MSTW ‘07

s, s feed into F2 NC DIS constraint 4/9(u + u) + 1/9(d + d + s + s)



CTEQ (I)Updates of PDFs (exp)New experimental data

results from neutrino-nucleon DIS for strange quark PDFs (s 6= s)

Uncertainty on u, d doubles from 1.5% to 3% at Q2 ≃M2W MSTW ‘07

s, s feed into F2 NC DIS constraint 4/9(u + u) + 1/9(d + d + s + s)

Updates of PDFs (th)Improved heavy quark (charm) threshold

matching consistent with QCD factorization CTEQ ‘08

Significant changes due to larger light flavor PDFs



CTEQ (II)Cross sections at LHC

0.9 1 1.1 1.2 1.3

W+

W-

Z0

W+h0H120LW-h0H120L

t t-

H171Lgg®h0H120L

h+H200L

Σ±∆ΣPDF in units of ΣHCTEQ66MLLHC,NLO

CTEQ6.6CTEQ6.1IC-Sea

KNNLO

Predictions for W±/Z cross sections at LHC shift by 8% betweenPDF sets CTEQ6.6 and CTEQ6.1 (improved theory!)

sensitivity to PDFs in the x ∼ 10−3 range

W±/Z-ratio golden calibration measurement



LEDLarge extra dimensions

Sensitivity of LHC dijet cross section to large extra dimensions Ferrag ‘04

large extra dimensions accelerate running of αs ascompactification scale Mc is approached

PDF uncertaintiespotential sensitivity to Mc reduced from 6 TeV to 2 TeV

Mc = 2 TeV no PDF error Mc = 2 TeV with PDF error

2 XDs

4XDs

6XDs

Standard Model zone



Drell-Yan process and Higgs production

Mapping of DIS to Drell-Yan lepton-pair production(or to Higgs production in gluon fusion)

re-engineering the soft and collinear limit

threshold enhanced terms at N3LO (numerically most important)S.M., Vogt ‘05; Laenen, Magnea ‘05; Idilbi et al. ‘05

DIS DY

from P(2)gg Higgs



Drell-Yan process and Higgs production

Mapping of DIS to Drell-Yan lepton-pair production(or to Higgs production in gluon fusion)

re-engineering the soft and collinear limit

threshold enhanced terms at N3LO (numerically most important)S.M., Vogt ‘05; Laenen, Magnea ‘05; Idilbi et al. ‘05

DIS DY

from P(2)gg Higgs

Recycling of

theory



Anatomy 1Anatomy of DIS result (1 loop)

∫

dLIPS(1)

S(1)F (1)

T b1 = 2 ReF1 δ(1− x) + S1

Forward Compton amplitude Tn in D = 4− 2ǫ-dimensions combinesvirtual corrections Fn (dependent on δ(1− x))pure real-emission contributions Sn

(dependent on D-dimensional +-distributions)

Infrared finiteness implies cancellation of poles between Fn and Sn

Kinoshita ‘62; Lee, Nauenberg ‘64

Constructive approach to form factor Fn and Sn



Anatomy 2Anatomy of DIS result (2 loops)

∫

dLIPS(1)

∫

dLIPS(2)

F (2)

(F (1))2

S(2)

F (1)S(1)

T b2 = (2 ReF2 + |F1|2)δ(1− x) + 2 ReF1S1 + S2



Anatomy 3Anatomy of DIS result (3 loops)

∫

dLIPS(1)

∫

dLIPS(2)

F (1)S(2)

(F (1))2S(1)

∫

dLIPS(3)

S(3)

∫

dLIPS(1)

F (2)S(1)

F (3)

F (2)F (1)

T b3 = (2 ReF3 + 2 |F1F2|) δ(1− x) + (2 ReF2 + |F1|2)S1 + 2 ReF1S2 + S3



DY 1Drell-Yan (1 loop)

∫

dLIPS(1)

S(1)F (1)

Construction of cross sections for hadron-hadron scattering

form factor with time-like kinematics Q2 > 0

soft emission with D-dimensional +-distributions

Drell-Yan lepton-pair production in qq-annihilation

Higgs production from gluon fusion



DY 2Drell-Yan (2 loops)

∫

dLIPS(1)

∫

dLIPS(2)

F (2)

(F (1))2

S(2)

F (1)S(1)

Checks at two loopsDrell-YanHamberg, van Neerven, Matsuura ‘91; Harlander, Kilgore ’02

Higgs productionHarlander, Kilgore ‘02; Anastasiou, Melnikov ‘02; Ravindran, Smith, van Neerven ‘03



DY 3Drell-Yan (3 loops)

∫

dLIPS(1)

∫

dLIPS(2)

F (1)S(2)

(F (1))2S(1)

∫

dLIPS(3)

S(3)

∫

dLIPS(1)

F (2)S(1)

F (3)

F (2)F (1)



Higgs boson production at LHC (II)

0

20

40

60

80

100 150 200 250 300

MH(GeV)

σ(pp → H+X) [pb]

µR = MH

NLO

N2LO

N3LOapprox.

√s = 14 TeV

LO

µR / MH

0.2 0.5 2 3

σ(pp → H+X) [pb]

MH = 120 GeV

LO

NLO

N2LO

N3LOapprox

0

20

40

60

80

1

N3LOapprox. increase at µr = MH 5% (NNLO PDF’s) S.M., Vogt ’05

µr variation 4%

Overall accuracy of 5% reached with approx. N3LO prediction



Instanton induced processes at LHC

Multi-gluon production in instanton backgroundtransfer of DIS phenomenology to Drell-Yan lepton-pair productionBrandenburg, Ringwald, Utermann ‘06; Petermann, Schrempp ‘08

amplitudes related by crossing

}∆Q5 = 2nf

I }ng≃

γ∗

}ng

}uL, uR, dL, dR, . . .DIS: I-inducedphoton-gluon scattering

≃

}ng

}∆Q5 = 2nf

I γ/Z/W γ/Z/W

}ng

}uL, uR, dL, . . .

pp : I-induced qq-annihilation

Characteristic final state signatureisotropic multi-particle production, very high multiplicity



Summary

HERADeep-inelastic scattering (electron-proton collision)

wealth of experimental information on proton structure

QCD precision predictionsradiative corrections for parton evolution

HERA PDFs have strong impact on measurements at LHC



Summary





LHCTheory results transferred to proton-proton collision

Higgs boson production

Instanton induced multi-particle production



Summary





LHCTheory results transferred to proton-proton collision

Higgs boson production

Instanton induced multi-particle production

OutlookIf past performance is an indicator, we are well prepared for futurechallenges . . .



Documents

Deep-inelastic scatteringDeep-inelastic scattering − from HERA to LHC − Sven-Olaf Moch [email protected] DESY, Zeuthen Proton colliders HERA: deep structure of proton at highest