Hard QCD at hadron colliders

Transcription

1 Hard QCD at hadron colliders Sven-Olaf Moch DESY, Zeuthen 1st Johns Hopkins Workshop Physics at the LHC A Challenge for Theory and Experiment, August, 007, Heidelberg Sven-Olaf Moch Hard QCD at hadron colliders p.1

2 LHC LHC (the big picture) Sven-Olaf Moch Hard QCD at hadron colliders p.

3 The Crossbig section picture for proton-proton scattering Large rates expected for many Standard Model processes b-quarks W ± and Z-bosons jets (even with high p t -cuts) t-quarks New physics search requires precision predictions Higgs production superpartners in MSSM (squarks, gluinos,...) Kaluza-Klein modes in UED models LHC will be a QCD machine perturbative QCD is essential and established part of toolkit (we no longer test QCD) σ (nb) proton - (anti)proton cross sections σ tot σ b σ jet (E T jet > s/0) σ W σ Z σ jet (E T jet > 100 GeV) σ t σ jet (E T jet > s/4) σ Higgs (M H = 150 GeV) σ Higgs (M H = 500 GeV) Tevatron s (TeV) Sven-Olaf Moch Hard QCD at hadron colliders p. LHC events/sec for L = 10 cm - s -1

4 Perturbative QCD at colliders Hard hadron-hadron scattering constituent partons from each incoming hadron interact at short distance (large momentum transfer Q ) p f i i Q µ µ QCD factorization separate sensitivity to dynamics from different scales j f j p σ pp X = X ijk f i (µ ) f j (µ ) ˆσ ij k α s (µ ),Q, µ D k X (µ ) factorization scale µ, subprocess cross section ˆσ ij k for parton types i, j and hadronic final state X Sven-Olaf Moch Hard QCD at hadron colliders p.4

5 Hard scattering cross (I) section Standard approach to uncertainties in theoretical predictions d variation of factorization scale µ: dln µ σ pp X = O(α l+1 s ) σ pp X = X ijk f i (µ ) f j (µ ) ˆσ ij k α s (µ ), Q, µ D k X (µ ) Parton cross section ˆσ ij k calculable pertubatively in powers of α s constituent partons from incoming protons interact at short distances of order O(1/Q) Parton luminosity f i f j proton: very complicated multi-particle bound state colliders: wide-band beams of quarks and gluons Final state X: hadrons, mesons, jets,... fragmentation function D k X (µ ) or jet algorithm interface with showering algorithms (Monte Carlo) Sven-Olaf Moch Hard QCD at hadron colliders p.5

6 Hard Approaches scattering to the(ii) calculation of σ pp X LO (leading order) Automated tree level calculations in Standard Model, MSSM,... (Madgraph,Alpgen, CompHEP,... ) LO + parton shower String inspired techniques NLO (next-to-leading order) Analytical (or numerical) calculations of diagrams yield parton level Monte Carlos (NLOJET++, MCFM,... ) NLO + parton shower (MC@NLO, VINCIA) NNLO (next-to-next-to-leading order) selected results known (mostly inclusive kinematics) N LO (next-to-next-to-next-to-leading order) very few... Sven-Olaf Moch Hard QCD at hadron colliders p.6

7 Hard Approaches scattering to the(ii) calculation of σ pp X easy difficult LO (leading order) Automated tree level calculations in Standard Model, MSSM,... (Madgraph,Alpgen, CompHEP,... ) LO + parton shower String inspired techniques NLO (next-to-leading order) Analytical (or numerical) calculations of diagrams yield parton level Monte Carlos (NLOJET++, MCFM,... ) NLO + parton shower (MC@NLO, VINCIA) NNLO (next-to-next-to-leading order) selected results known (mostly inclusive kinematics) N LO (next-to-next-to-next-to-leading order) very few... Sven-Olaf Moch Hard QCD at hadron colliders p.6

8 Parton luminosity Feynman diagrams in leading order Proton in resolution 1/Q sensitive to lower momentum partons Sven-Olaf Moch Hard QCD at hadron colliders p.7

9 Parton luminosity Feynman diagrams in leading order Proton in resolution 1/Q sensitive to lower momentum partons Evolution equations for parton distributions f i predictions from fits to reference processes (universality) d d ln µ f i(x, µ ) = X h i P ik (α s (µ )) f k (µ ) (x) k Splitting functions P P = α s P (0) + α s P (1) {z } + α s P () +... NLO: standard approximation (large uncertainties) Sven-Olaf Moch Hard QCD at hadron colliders p.7

10 Parton distributions evolution in proton Valence q q (additive quantum numbers) sea (part with q + q) 6 5 x f(x,q ) at Q = 15 GeV 4 gluon sea 1 valence x Parameterization (bulk of data from deep-inelastic scattering) structure function F quark distribution scale evolution (perturbative QCD) gluon distribution Sven-Olaf Moch Hard QCD at hadron colliders p.8

11 Parton distributions evolution in proton Valence q q (additive quantum numbers) sea (part with q + q) 6 5 x f(x,q ) at Q = 10 4 GeV 4 gluon sea 1 valence x Parameterization (bulk of data from deep-inelastic scattering) structure function F quark distribution scale evolution (perturbative QCD) gluon distribution Sven-Olaf Moch Hard QCD at hadron colliders p.8

12 PDFs from HERA to LHC to LHC HERA F em F -log10 (x) 5 x=6.e-5 x= x= x= x= x= x= x= x=0.001 ZEUS NLO QCD fit H1 PDF 000 fit H H1 (prel.) 99/00 ZEUS 96/97 4 x=0.001 x=0.00 BCDMS E665 NMC x=0.005 x=0.008 x=0.01 x=0.01 x=0.0 x=0.05 x=0.08 x=0.1 1 x=0.18 x=0.5 x=0.4 x= Q (GeV ) Precision HERA data on F Scale evolution of PDFs in Q over two to three orders Sven-Olaf Moch Hard QCD at hadron colliders p.9

13 Evolution Perturbativeat stability small xof evolution Scale derivatives of quark and gluon distributions at Q 0 GeV 0.4 d ln q / d ln Q 0.4 d ln g / d ln Q LO NLO 0-0. α S = 0., N f = x x Sven-Olaf Moch Hard QCD at hadron colliders p.10

14 Evolution Perturbativeat stability small xof evolution Scale derivatives of quark and gluon distributions at Q 0 GeV 0.4 d ln q / d ln Q 0.4 d ln g / d ln Q LO NLO NNLO -0. α S = 0., N f = x Expansion very stable except for very small momenta x < 10 4 x Sven-Olaf Moch Hard QCD at hadron colliders p.10

15 WImpact andon Z precision of LHC predictions W ±, Z-boson rapidity distribution (scale variation m W,Z Anastasiou, Petriello, Melnikov 05 µ m W,Z ) 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 we do believe to know it very well "Standard candle" process for parton luminosity Sven-Olaf Moch Hard QCD at hadron colliders p.11

16 CTEQ Updates(I) of PDFs Continuous improvements (not only MRST MSTW) new results for neutrino-nucleon DIS to fit strange quark PDFs use no longer as input s = s = κ [ū + d] (κ 0.5) Uncertainty on ū, d doubles from 1.5% to % at Q M W MSTW) independent ansatz for s and s feeds into F NC DIS constraint 4/9(u + ū) + 1/9(d + d + s + s) Heavy quark (charm) threshold matching consistent with QCD factorization CTEQ Sven-Olaf Moch Hard QCD at hadron colliders p.1

17 CTEQ Updates(I) of PDFs Continuous improvements (not only MRST MSTW) new results for neutrino-nucleon DIS to fit strange quark PDFs use no longer as input s = s = κ [ū + d] (κ 0.5) Uncertainty on ū, d doubles from 1.5% to % at Q M W MSTW) independent ansatz for s and s feeds into F NC DIS constraint 4/9(u + ū) + 1/9(d + d + s + s) Heavy quark (charm) threshold matching consistent with QCD factorization CTEQ Significant changes Sven-Olaf Moch Hard QCD at hadron colliders p.1

18 CTEQ Cross sections (II) at LHC Predictions for W ± /Z cross sections at LHC shift by 8% between PDF sets CTEQ6.5 and CTEQ6.1 sensitivity to PDFs in the x 10 range W ± /Z-ratio still golden calibration measurement Sven-Olaf Moch Hard QCD at hadron colliders p.1

19 LED Large extra dimensions Sensitivity of LHC dijet cross section to large extra dimensions Ferrag 04 large extra dimensions accelerate running of α s as compactification scale M c is approached PDF uncertainties potential sensitivity to M c reduced from 6 TeV to TeV M c = TeV no PDF error M c = TeV with PDF error Standard Model zone XDs 4XDs 6XDs Sven-Olaf Moch Hard QCD at hadron colliders p.14

20 Parton cross sections How reliable are background estimates? Gianotti, Mangano 05 Sven-Olaf Moch Hard QCD at hadron colliders p.15

21 Pythia SUSY searches vs BSM (II) SM background in channel pp Z( ν ν) + 4jets from Alpgen Gianotti, Mangano 05 Njet 4 E T(1,) > 100GeV E T(,4) > 50GeV MET = M eff + max(100,m eff /4) M eff = MET + P i E Ti Sven-Olaf Moch Hard QCD at hadron colliders p.16

22 Pythia SUSY searches vs BSM (II) SM background in channel pp Z( ν ν) + 4jets from Alpgen Gianotti, Mangano 05 Njet 4 E T(1,) > 100GeV E T(,4) > 50GeV MET = M eff + max(100,m eff /4) M eff = MET + P i E Ti Early ATLAS TDR studies with Pythia are overly optimistic Background largely underestimated in high-end tail of missing E T (normalization of Z νν + jets from experiment Z e + e + jets) Gianotti, Mangano 05 Shape of BSM signal indistinguishable from background shape at LO Significance of potential disagreement between data and Alpgen? Sven-Olaf Moch Hard QCD at hadron colliders p.16

23 Exp LHC priority wishlist wishlist process (V {γ,w ±, Z}) pp V V + 1 jet pp H + jets pp t tb b pp t t + jets pp V V b b pp V V + jets pp V + jets pp V V V Les Houches 005 [hep-ph/060410] background to t th, new physics H production by vector boson fusion (VBF) t th t th VBF V V, t th, new physics VBF V V various new physics signatures SUSY trilepton Sven-Olaf Moch Hard QCD at hadron colliders p.17

24 Exp wishlist (full) Original experimenter s wishlist Tevatron Run II Monte Carlo workshop April 001 Sven-Olaf Moch Hard QCD at hadron colliders p.18

25 QCD NLO NLO QCD corrections essential NLO important for rates (background); large K-factors, new parton channels may dominate beyond tree level e.g. W + 4 jets is O(α 4 s) and (α LO s ) 10% gives (σ LO ) 40% Sven-Olaf Moch Hard QCD at hadron colliders p.19

26 QCD NLO NLO QCD corrections essential NLO important for rates (background); large K-factors, new parton channels may dominate beyond tree level e.g. W + 4 jets is O(α 4 s) and (α LO s ) 10% gives (σ LO ) 40% Why are one-loop corrections difficult? Outline of a generic NLO calculation Real corrections - subtractions (IR-divergent) Cancellation of singularities Finite partonic cross sections Phase space integration Convolution with PDFs Monte Carlo All conceptual issues solved ( just technical work) However, no general libraries available Speed and stability are the important criteria in practice Virtual corrections + subtractions (IR-divergent) Sven-Olaf Moch Hard QCD at hadron colliders p.19

27 Theory status LO Efficient techniques for computing tree amplitudes exist recursion relations Berends, Giele 87 NLO Straightforward in principle hard in practice with known bottlenecks one-loop virtual corrections (tensor integrals) Z I µ 1,µ,... (k1,...) = d D p µ 1 1 p pµ... 1 (p 1 m 1 )((p 1 k 1 ) m )... Alternative methods for tensor reduction improved Passarino-Veltman; multi-loop inspired techniques; sector decomposition + contour deformation; numerical approach to loop integration;... New recursive on-shell approach makes use of well-known methods colour ordering; helicity amplitudes; supersymmetry; unitarity; factorization of amplitudes Sven-Olaf Moch Hard QCD at hadron colliders p.0

28 Unitarity Fundamental concept in quantum field theory cutting rules for Feynman diagrams (optical theorem) Cutkosky;... 1 n Fusing rules for amplitudes Bern, Dixon, Dunbar, Kosower 94;... Sew tree level amplitudes together and get real from imaginary part example (triangle): calculate iπ ln( s) deduce ln ( s) k 1 k k + 1 = c 4,i + c,j + i j k c,k Sven-Olaf Moch Hard QCD at hadron colliders p.1

29 Unitarity Fundamental concept in quantum field theory cutting rules for Feynman diagrams (optical theorem) Cutkosky;... 1 n Fusing rules for amplitudes Bern, Dixon, Dunbar, Kosower 94;... Sew tree level amplitudes together and get real from imaginary part example (triangle): calculate iπ ln( s) deduce ln ( s) k 1 k k + 1 = c 4,i + c,j + i j k All terms with logarithmic dependence are cut-constructible supersymmetric decomposition of amplitude with gluon in loop A g n (and all external gluons) A g n = A g n + 4A f n + A s n 4 A f n + A s n + A s n {z } {z } {z} N = 4 SUSY N = 1 chiral SUSY N = 0 scalar Real difficulty: rational (non-logarithmic) terms of A N=0 n c,k Sven-Olaf Moch Hard QCD at hadron colliders p.1

30 Six-gluon amplitude Analytic computation of one-loop corrections Bedford, Berger, Bern, Bidder, Bjerrum-Bohr, Brandhuber, Britto, Buchbinder, Cachazo, Dixon, Dunbar, Feng, Forde, Kosower, Mastrolia, Perkins, Spence, Travaglini, Xiao, Yang, Zhu Amplitude N =4 N =1 N =0 N =0 cut rat BDDK 94 BDDK 94 BDDK 94 BDK BDDK 94 BDDK 94 BBST 04 BBDFK 06 XYZ BDDK 94 BDDK 94 BBST 04 BBDFK 06 XYZ BDDK 94 BBDD 04 BBDI 05 BFM 06 BBDFK BDDK 94 BBDP 05 BBCF 05 BFM 06 XYZ BDDK 94 BBDP 05 BBCF 05 BFM 06 XYZ 06 Numerical evaluation at one loop Ellis, Giele, Zanderighi 06 timing 107 sec/ events Sven-Olaf Moch Hard QCD at hadron colliders p.

31 NLO Complete complete NLO results Complete NLO calculations for many processes (e.g. for hadron collider) pp jets, γγ + jet, V + jets, t th, b bh, t bh, b bv, HHH Bern et al.; Kunszt et al.; Kilgore, Giele; Campbell et al.; Nagy; Del Duca et al.; Campbell, Ellis; Beenakker et al.; Dawson et al.; Dittmaier et al.; Peng et al.; Plehn, Rauch; Febres Cordero et al new: pp t t + jet at NLO Dittmaier, Uwer, Weinzierl 07 new: pp ZZZ at NLO Lazopoulos, Melnikov, Petriello 07 4 processes electroweak corrections to e + e 4 fermions Denner, Dittmaier, Roth, Wieders 05 extremely diffcult hexagon integrals with masses electroweak corrections to e + e ν νhh Boudjema, Fujimoto, Ishikawa, Kaneko, Kato, Kurihara, Shimizu, Yasui 05 e e W e + Z Z µ d µ ν µ u d Sven-Olaf Moch Hard QCD at hadron colliders p.

32 t t+ jet production 6 σ[pb] 5 4 p p t t+jet+x s = 1.96TeV p T,jet > 0GeV NLO (CTEQ6M) LO (CTEQ6L1) 1500 σ[pb] 1000 pp t t+jet+x s = 14TeV p T,jet > 0GeV barjet@ NLO (CTEQ6M) LO (CTEQ6L1) µ/m t Impressive state-of-the-art NLO QCD calculation Dittmaier, Uwer, Weinzierl 07 Much improved scale dependence µ/m t Differential distributions underway (will test parton shower predictions) 10 Sven-Olaf Moch Hard QCD at hadron colliders p.4

33 Jets Caseat for NNLO Hadronic di-jets: large statistics even with high-p T cuts gluon jets constrain gluon PDF at medium/large x searches for quark sub-structure (di-jet angular correlations) NNLO for di-jets important for scale uncertainty, PDF determination, y modelling of jets,... cut y cut y cut Calculation of NNLO cross sections cancellation of IR divergencies between virtual and real corrections highly non-trivial (two-loop) virtual amplitudes Anastasiou, Bern, v.d.bij, De Freitas, Dixon, Ghinculov, Glover, Oleari, Schmidt, Tejeda-Yeomans, Wong and Garland, Gehrmann, Glover, Koukoutsakis, Remiddi, 0; S.M., Uwer, Weinzierl 0 numerical phase space integration very difficult Anastasiou, Del Duca, Frixione, Gehrmann, Gehrmann-De Ridder, Glover, Grazzini, Heinrich, Kilgore, Melnikov, Petriello, Somogyi, Trócsányi, Weinzierl 0-07 Sven-Olaf Moch Hard QCD at hadron colliders p.5

34 epem-thruste + e jets Thrust distribution at Q = M Z partonic contributions LO γ q qg tree level NLO γ q qg one loop γ q q gg tree level γ q q q q tree level NNLO γ q qg two loop γ q q gg one loop γ q q q q one loop γ q q q q g tree level γ q q g g g tree level (1-T) 1/σ had dσ/d T NNLO NLO LO Q = M Z α s (M Z ) = T major milestone in perturbative QCD Gehrmann, Gehrmann-De Ridder, Glover, Heinrich 07 significantly improved determination of α s from jet observables Sven-Olaf Moch Hard QCD at hadron colliders p.6

35 Two Heavy-quark loop heavy-quark hadro-production results at two loops in QCD Amplitude in ultra-relativistic limit m s, t, u Result for q q-annihilation (interference with Born) S.M., Czakon, Mitov 07 number of colors N and light/heavy quarks n l /n h Re M (0) M () = (N 1) N A + B + 1 N C + Nn ld l + Nn h D h + n l N E l + n «h N E h + (n l + n h ) F Sven-Olaf Moch Hard QCD at hadron colliders p.7

36 Two Heavy-quark loop heavy-quark hadro-production results at two loops in QCD Amplitude in ultra-relativistic limit m s, t, u Result for q q-annihilation (interference with Born) S.M., Czakon, Mitov 07 number of colors N and light/heavy quarks n l /n h Re M (0) M () = (N 1) N A + B + 1 N C + Nn ld l + Nn h D h + n l N E l + n «h N E h + (n l + n h ) F A = 1 { x ε 4 x + 1 }+ 1ε { [ 4 Lm x x+ 1 ] [ + Ls x + x 1 ]+ 1x 4 1x 4 + ( Lx x +x 1)+ 19 }+ 1ε { LmLs[ x 8 + x 1 ] [ + L s x x+ 1 ] [ 9x + Lm 6 9x 6 ( +Lx x + x 1 ) + ] + Ls [ 19x x 6 + ( Lx 4x 4x+ ) 1 ] + ( x 1 5x + 5 ) L x + ( 6x x 6 )Lx + 17x x ( 7 + π x 6 + x 6 1 ) 1 05 } + 1 { L m [ x 144 ε + x 1 ] + LmL [ s x x+1 ] + L s [ x 6 + x 1 ] [ ( +L m x + x+lx x x+ 1 ) 1 ] + LmLs [ 7x + 7x + ( Lx 4x 4x+ ) 1 ] 6 +L s [ x + x + ( Lx 4x + 4x ) ] [( 1 + Lm 4 4 x ) ( x L x )Lx + x 47x x 1 5 ] [( + Ls 4x + 5x 5 ) ( 8x L x x + 1 )Lx + 487x 6 487x 6 ( x +π x + 1 ) ] ( x x 1 ( )L x + 5x ( + Ly x + x 1 ) + ) L x 4 4 ( +Li(x) x + x 1 ) ( 4x Lx + 151x ( 4x 1 + π 5x ) ) + 10 Lx x x ( 4 + π x 7 + 5x ) ( + Li(x) x x+ 1 ) + ( x x 6 17 ) ζ } [ x + L 4 m x ] [ x + L mls 8 x + 1 ] + LmL s [ 4x + 4x ] [ x + L 4 s x + 1 ] + L m [ 11x x ( 18 + Lx x + x 1 ) 5 ] 6 6 +L mls [ 5x + 5x + ( Lx x + x 1 ) 5 ] + LmL s [ 4x 6 + 4x + ( Lx 4x + 4x ) 5 ] [ 14x + L s 9 14x ( 8x 9 + Lx 8x + 4 ) + 10 ] [( x + L m ( x )L x 8 + x ) Lx x 6 47x ] [( + LmLs x 1 )L x + ( x x ) Lx + x 7 x + 8 ] 1 [( +L s 4x 5x+ 5 ( 14x )L x + 11x + 10 )Lx 7x 4 + 7x ( 4 + π x + x 1 ) 6 5 ] [ x L x + Lm ( 8 + x ( + Ly x + x 1 ) + 1 ) ( L x + Li(x) x + x 1 ) Lx 4 4 ( + 4x + 19x ( 4 + π x x + 1 ) )Lx 781x x ( 7 + π 7x 1 + x 1 ) 4 ( +Li(x) x x+ 1 ) ( 7x + 10x + 5 ) ζ 499 ] ) + Ls [( x 144 x+1 L x ( ( 4x + + Ly x x+ 1 ) + 1 ) L x + Li(x)( 4x x+1 ) Lx + ( 86x + 17x 6 ( +π 8x + 5x 5 ) 49 )Lx + 00x x 16 + Li(x)( 4x + x 1 ) ( +π 4x x 6 91 ) ( x x + 17 ) ζ 919 ] ( + x x ) L 4 x 48 + ( 7x x ( ) 10x 1 + Ly x+1 7 ) L x + (( x 1 5x ) ( 7x L y x ) Ly + 101x ( π 5x 6 + 5x 1 5 ) x 617 ) L x S1,(x)( x 5x+ 11 ) ( 60x Lx + 19x ( π 5x 9 + 5x 6 47 )+Lyπ ( x x 6 17 ) 1 ( 5x + 1x + 1 ) ζ )Lx x x ( 59 + π4 11x 80 x ) 480 ( +Li4(x) x + x ) ( + S,(x) x + 5x 11 ( 1009x )+π 4 59x ) 864 +Li(x) ( 7x 1x 6 + ( Lx 8x + x 1 ) ( + Ly x + 5x 11 ) 1 ) + Li(x) (( 7x 6 7x + 7 ) ( 7x L x x ( 6 + Ly x 5x+ 11 ) + 1 )Lx + π ( x x 6 17 )) 1 ( +Ly x 5x+ 11 ) ζ + ( 14x x ) ζ , B = 1 { ε 4 x + x 1 }+ 1ε { Lm[ x + x 1 ] [ + Ls x x+1 ] 1x 4 + 1x 4 + ( Ly 4x ( +4x )+Lx 6x 6x+ ) 7 } + 1 { LmLs[ 4x 8 ε 4x+ ] + L [ s x + x 1 ] +Lm [ 47x x 6 + ( Ly 4x + 4x ) ( + Lx 6x 6x+ ) 5 ] [ 49x + Ls x 6 +Lx( 1x + 1x 6 ) ( + Ly 8x 8x+4 ) + 7 ] ( + 6x + 15x 1 15 ) ( 67x L x x 6 + ( Ly 4x 4x+ ) + 9 )Lx 415x x ( 6 + Ly 5x + 49x 0 ) ( 17x +π 1 17x ) ( + L y x x+ 1 ) 17 } + 1 { [ x L m 4 9 ε x + 1 ] +LmL [ s 4x + 4x ] [ 4x + L s 4x + ] [ ( + L m x x+lx x + x ) +Ly( x x+1 ) + 1 ] [ 5x + LmLs 5x + ( Lx 1x + 1x 6 ) ( + Ly 8x 8x+4 ) + 1 ] + L s [ 9x 6 + 9x + ( Ly 8x + 8x 4 ) + Lx( 1x 1x+6 ) 5 ] [( x + Lm 4 ) ( L x + x 9x ( )Lx 16x 4 + L y x 1 ) + 16x + ( Ly x + x+1 ) ( 7x + π 6 7x ) + 5 ] [( + Ls 1x 15x+ 15 )L ( x x + 55x + ( Ly 8x + 8x 4 ) 14 )Lx + 85x 18 85x 18 + ( L y 4x + x 1 ) + π ( 17x x 6 17 ) ( 16x + Ly 1 10x 4 ) 1 ] ( + x x+ ) ( ( 15x L x Ly x x + 1 ) 9 ) L x 4 4 ( +Li(x) 6x x+ ) (( 1 Lx + )L x y Ly 50x + 17x ( 1 + π 1x + 41x 6 41 ) 1 15)Lx 419x x ( L y 4x 5 ) ( + Li(x) 6x + x ) + S1,(x) ( 4x + 6x ) ( x +L y 7x + 7 ( 6x )+π x 7 91 ) ( 86x + Ly x ( 8x 6 + π 11x + 11 ) + 47 ) ( 91x x ) ζ + 41 } + L 4 m [ x x 1 ]+ L [ m 4 Ls 4x + 4x ] [ 8x + LmL s 8x + 4 ] + L 4 s [ x + x 1 ] [ 11x + L m 18 11x ( 18 + Ly x + x 1 ) ( + Lx x x+ 1 ) 1 ]+ L [ m 6 Ls x + x + ( Ly 4x + 4x ) ( + Lx 6x 6x+ ) 1 ] + LmL s [ 14x x + ( Ly 8x + 8x 4 ) + Lx( 1x 1x+6 ) 1 ] [ 16x + L s 9 16x 9 + ( Lx 8x + 8x 4 ) ( 16x + Ly 16x + 8 ) + ] [( + L m 9 8 x ) ( 9x L x ( )Lx x 157x L y 4 x ) + 157x ( 6 + π x + x 1 ) ( + Ly x x 1 ) 9 ] [( + LmLs )L 7 x x +( 9x 6x ) Lx + 7x + L ( y (1 x) 7x+π 7x + 7x 7 ) ( + Ly 4x x ) ] [( + L s 1x + 15x 15 ) ( x L x x + ( Ly 8x 8x +4) 8 )Lx + 40x 9 40x ( 17x 9 + π 6 17x ) + L ( y 4x x+1 ) ( 8x + Ly 1 4x + 6 ) ] [ ( ( x + Lm x L x Ly x x + ) ) L x Li(x)( 6x x + ) ( Lx + 1x 57x ( 4 + π x + x ) ( + 6 )Lx 115x + L y x 1 ) + 115x ( +Li(x) 6x + x ) + S1,(x) ( 4x + 6x ) ( x + L y 4x + ( 9x )+π 4 x 5 ) ( + Ly 8x + 1x ( 4 + π x x+ ) 5 ) ( 7x + 8x + 14 ) ζ 67 ] 18 [ (x +Ls + 6x ) ( L x + x ( + Ly 6x + x 1 ) + 5 ) L x 6 + Li(x)( 1x + 6x ) Lx + ((x 1)L y + Ly + 100x 181x ( 6x 6 + π 41x + 41 ) + 68 ( )Lx 1957x 4 + L y 6 54 x ) x 54 + L y ( 4x + 14x 7 ( 67x )+π 6 9x ) + S1,(x) ( 8x 1x 7 +6)+Li(x) ( 1x 6x+ ) ( + Ly ( 17x + 57x+π 16x + x 11 ) 97 ) + ( 91x + 7x 7 ) ζ 55 ] ( + x + x )L ( 4x 16 + x 18 5x ( 1 + Ly x + 16x 8 ) + 7 ) (( 7x L x x 4 17 ) ( x L y x 1 1 ) Ly + 65x ( 95x π 6 10x ) x )L (( x x + 4x ) ( x L y + 1 )L (π ( y 4 + 4x + 15x 11 ) + )Ly 04x + 15x ( π 15x x ) + ( 54x + 45x 6 45 ) ζ 1181 )Lx x 8959x ( S,(x) 10x + 5x 1 ) + Li4(x) ( 6x x+ 1 ) ( + L 4 y x + 5x 1 5 ) + L y ( 7x x 9 1 ( 77x )+π x ) 40 +S1,(x) ( 4x + x 1 ) ( + L y 81x ( 6 + π 4x + 19x 19 ) ) x ( 14x +S1,(x) 47x + ( Ly 8x 8x+4 ) ( + Lx 10x 9x ) + 46 ) + Li(x) ( x + x ( 6 + Ly 10x x+ 15 ) ( + Lx 4x 10x+5 ) + 9 ) (( + Li(x) 1x + 1x 6 1 ( x )L x 4 + x ( 6 + Ly 10x + x 15 ) 9 ( )Lx + π 5x x )) 1 ( 4x x ) ( 50x ζ + Ly 89x ( π 50x 9 + 8x 5 ) ( 98x + 107x + 71 ) ζ )+π ( 797x x 108 +( x x+1 ) log() 5 ) , }{{}}{{} A Sven-Olaf Moch Hard QCD at hadron colliders p.7 B

37 Higgs production (I) at LHC Higgs production dominant in gg-fusion heavy top limit m t : effective gg Higgs vertex Largest rate for all values of Higgs mass m H (top-yukawa coupling) Signal significance 10 H γ γ + WH, tth (H γ γ ) WH, tth (H bb) H ZZ (*) 4 l H WW (*) lνlν H ZZ llνν H WW lνjj Total significance 10 5 σ 100 fb -1 (no K-factors) m (GeV) Sven-Olaf Moch Hard QCD at hadron colliders p.8

38 Higgs (II) Total Higgs cross section σ(pp H+X) [pb] M H = 10 GeV 0 σ(pp H+X) [pb] M H = 40 GeV NLO 10 NLO 0 N LO SV N LO LO 5 N LO SV N LO LO µ r / M H µ r / M H Variation of cross section at LHC with renormalizaion scale for different Higgs masses: M H = 10GeV (left) and M H = 40GeV (right) NNLO corrections Harlander, Kilgore 0; Anastasiou, Melnikov 0; Ravindran, Smith, van Neerven 0 complete soft N LO corrections S.M., Vogt 05 Sven-Olaf Moch Hard QCD at hadron colliders p.9

39 Summary Hard QCD Parton luminosity at hadron colliders Hard parton cross section W ± /Z-boson production jet cross sections hadro-production of top quarks Higgs total cross section Hadronic final state jet algorithms and fragmentation of (heavy) quarks parton shower Monte Carlo simulation Outlook QCD tool box ready for LHC challenges however, still much dedicated work to do Sven-Olaf Moch Hard QCD at hadron colliders p.0