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Deep-inelastic scattering− from HERA to LHC −
Sven-Olaf MochSven-Olaf.Moch@desy.de
DESY, Zeuthen
————————————————————————————————————–
– Festkolloquium fur Fridger Schrempp, Hamburg, February 19, 2007 –
Sven-Olaf Moch Deep-inelastic scattering – p.1
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
Sven-Olaf Moch Deep-inelastic scattering – p.2
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
Sven-Olaf Moch Deep-inelastic scattering – p.3
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 )
Sven-Olaf Moch Deep-inelastic scattering – p.4
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)
Sven-Olaf Moch Deep-inelastic scattering – p.5
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 . . .
Sven-Olaf Moch Deep-inelastic scattering – p.6
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
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
difficult
← level of talk here
Sven-Olaf Moch Deep-inelastic scattering – p.6
Parton luminosity
Feynman diagrams in leading order
Proton in resolution 1/Q −→sensitive to lower momentumpartons
Sven-Olaf Moch Deep-inelastic scattering – p.7
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
Sven-Olaf Moch Deep-inelastic scattering – p.8
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
Sven-Olaf Moch Deep-inelastic scattering – p.8
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
Sven-Olaf Moch Deep-inelastic scattering – p.9
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 ∗
Sven-Olaf Moch Deep-inelastic scattering – p.11
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
Sven-Olaf Moch Deep-inelastic scattering – p.13
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
Sven-Olaf Moch Deep-inelastic scattering – p.14
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
Sven-Olaf Moch Deep-inelastic scattering – p.14
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
Sven-Olaf Moch Deep-inelastic scattering – p.15
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)
Sven-Olaf Moch Deep-inelastic scattering – p.16
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
Sven-Olaf Moch Deep-inelastic scattering – p.16
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
Sven-Olaf Moch Deep-inelastic scattering – p.17
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
Sven-Olaf Moch Deep-inelastic scattering – p.18
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
Sven-Olaf Moch Deep-inelastic scattering – p.19
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
Sven-Olaf Moch Deep-inelastic scattering – p.19
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
Sven-Olaf Moch Deep-inelastic scattering – p.20
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
Sven-Olaf Moch Deep-inelastic scattering – p.21
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
Sven-Olaf Moch Deep-inelastic scattering – p.22
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
Sven-Olaf Moch Deep-inelastic scattering – p.23
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
Sven-Olaf Moch Deep-inelastic scattering – p.24
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)
Sven-Olaf Moch Deep-inelastic scattering – p.25
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
Sven-Olaf Moch Deep-inelastic scattering – p.26
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
Sven-Olaf Moch Deep-inelastic scattering – p.27
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
Sven-Olaf Moch Deep-inelastic scattering – p.28
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
LHCTheory results transferred to proton-proton collision
Higgs boson production
Instanton induced multi-particle production
Sven-Olaf Moch Deep-inelastic scattering – p.28
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
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 . . .
Sven-Olaf Moch Deep-inelastic scattering – p.28
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