Theory introduction to Standard Model processes at LHC. lecture one. Sven-Olaf Moch. DESY, Zeuthen

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1 Theory introduction to Standard Model processes at LHC lecture one Sven-Olaf Moch DESY, Zeuthen in collaboration with Martin zur Nedden DESY Academic Training, June 4, 2007, Zeuthen Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.1

2 Physics at LHC Theory S.M. Theory introduction to Standard Model processes at LHC Monday, June 4, 2007, 09:00-10:30h Higgs physics and theory for extensions of the Standard Model Tuesday, June 5, 2007, 10:00-11:30h Experiment Martin zur Nedden LHC: Experimental overview and Standard Model Physics Monday, June 11, 2007, 09:00-10:30h LHC: Higgs searches and Physics beyond the Standard Model Thursday, June 14, 2007, 10:00-11:30h Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.2

3 Plan Lecture 1 QCD factorization for hard scattering Parton luminosity at hadron colliders W ± and Z-boson production at LHC Jet-production Hadro-production of Top-Quarks Lecture 2 Higgs production at the LHC Motivation for extensions of the Standard Model Introduction to Supersymmetry and the MSSM Large Extra Dimensions Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.3

4 LHC LHC (the big picture) Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.4

5 The big picture The challenge LHC will measure many Standard Model processes to very high accuracy, e.g. W ±, Z gauge-bosons top quarks Experimental search requires precision predictions for hard scattering cross-sections Higgs production BSM particles (new physics), e.g. superpartners in MSSM (squarks, gluinos,...) (first) exited Kaluza-Klein modes in UED models Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.5

6 The big picture The challenge LHC will measure many Standard Model processes to very high accuracy, e.g. W ±, Z gauge-bosons top quarks Experimental search requires precision predictions for hard scattering cross-sections Higgs production BSM particles (new physics), e.g. superpartners in MSSM (squarks, gluinos,...) (first) exited Kaluza-Klein modes in UED models LHC will be a QCD machine provide accurate predictions (including QCD radiative corrections) perturbative QCD is essential and established part of toolkit (we no longer test QCD) Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.5

7 Proton-proton Cross section forscattering proton-proton scattering Experiment # of events N obs, N bkgrd efficiency ǫ, luminosity L proton - (anti)proton cross sections σ tot Tevatron LHC σ pp = N obs N bkgrd ǫl Large rates expected for many processes b-quarks W ± and Z-bosons jets (even with high p t -cuts) t-quarks σ (nb) σ b σ jet (E T jet > s/20) σ W σ Z σ jet (E T jet > 100 GeV) σ t σ jet (E jet T > s/4) σ Higgs (M H = 150 GeV) events/sec for L = cm -2 s σ Higgs (M H = 500 GeV) s (TeV) Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.6

8 Perturbative QCD at colliders Proton: very complicated multi-particle bound state Colliders: wide-band beams of quarks and gluons σ pp = X ij ˆσ ij f i f j p f f p Hard interactions of protons parton distributions (q, g) f p partonic cross sections ˆσ ff Hadron colliders: the energy frontier Presently: p p collider Tevatron with S = 2TeV Upcoming: pp collider LHC with S = 14TeV Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.7

9 Hard scattering at colliders QCD theory separate sensitivity to dynamics form different scales factorization of cross section σ pp (Q,m) = X ij ˆσ ij (Q/µ,α s (µ)) f i (µ, m) f j (µ, m) large momentum scale Q, factorization scale µ, soft scale m Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.8

10 Hard scattering at colliders QCD theory separate sensitivity to dynamics form different scales factorization of cross section σ pp (Q,m) = X ij ˆσ ij (Q/µ,α s (µ)) f i (µ, m) f j (µ, m) large momentum scale Q, factorization scale µ, soft scale m Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.8

11 Hard scattering at colliders QCD theory separate sensitivity to dynamics form different scales factorization of cross section σ pp (Q,m) = X ij ˆσ ij (Q/µ,α s (µ)) f i (µ, m) f j (µ, m) large momentum scale Q, factorization scale µ, soft scale m Constituent partons from incoming protons interact at short distances of order O(1/Q) Parton luminosity f i f j ("standard candle") Control theory uncertainties in ˆσ ij (variation of scale µ) Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.8

12 Feynman rules (I) Propagators fermions, gluons, ghosts covariant gauge i p j δ ij i /p m a, µ p b, ν δ ab i g µν p 2 + (1 λ) pµ p ν (p 2 ) 2 a p b δ ab i p 2 Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.9

13 Feynman rules (cont d) (II) Vertices a, µ i g (t a ) ji γ µ i j b, ν q a, µ p c, ρ r g f abc ((p q) ρ g µν + (q r) µ g νρ + (r p) ν g µρ ) a, µ b, ν c, ρ d, σ i g 2 f xac f xbd (g µν g ρσ g µσ g νρ ) i g 2 f xad f xbc (g µν g ρσ g µρ g νσ ) i g 2 f xab f xcd (g µρ g νσ g µσ g νρ ) a, µ b q c g f abc q µ Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.10

14 Soft and collinear singularities e + e -annihilation (massless quarks) Born cross section σ (0) = 4πα2 3s e e + q q Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.11

15 Soft and collinear singularities e + e -annihilation (massless quarks) Born cross section σ (0) = 4πα2 3s Study QCD corrections (real emissions) e e + q q e q e q g g e + q Cross section dimensional regularization D = 4 2ǫ (with f(ǫ) = 1 + O(ǫ 2 )) σ q qg = σ (0) 3 X q e 2 q f(ǫ) C F α s 2π scaled energies x 1 = 2 E q s and x 2 = 2 E q s Z e + dx 1 dx 2 x x 2 2 ǫ(2 x 1 x 2 ) (1 x 1 ) 1+ǫ (1 x 2 ) 1+ǫ q Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.11

16 NLO epem Soft and collinear divergencies (0 x 1, x 2 1 and x 1 + x 2 1) p k 1 x 1 = x 2 E g s (1 cos θ 2g ) and p k 1 x 2 = x 1 E g s (1 cos θ 1g ) Integrate over phase space for real emission contributions σ q qg = σ (0) 3 X q e 2 q f(ǫ) C F α s 2π 2 ǫ ǫ + 19 «2 + O(ǫ) Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.12

17 NLO epem Soft and collinear divergencies (0 x 1, x 2 1 and x 1 + x 2 1) p k 1 x 1 = x 2 E g s (1 cos θ 2g ) and p k 1 x 2 = x 1 E g s (1 cos θ 1g ) Integrate over phase space for real emission contributions σ q qg = σ (0) 3 X q e 2 q f(ǫ) C F α s 2π Divergencies cancel against virtual contributions 2 ǫ ǫ + 19 «2 + O(ǫ) e q e q 2 e + σ q q(g) = σ (0) 3 X q q e + e 2 q f(ǫ) C F α s 2π 2ǫ 2 3ǫ 8 + O(ǫ) «q Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.12

18 Infrared safety Total cross section (R(s)) is directly calculable in perturbation theory (finite) R(s) = 3 X q e 2 q n 1 + α o s π + O(α2 s) Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.13

19 Infrared safety Total cross section (R(s)) is directly calculable in perturbation theory (finite) R(s) = 3 X q e 2 q n 1 + α o s π + O(α2 s) e QCD factorization Collinear divergencies remain for hadronic observables factorization q q g µ e e e + q g q µ + q g q Left: single-hadron inclusive e + e -annihilation (time-like kinematics) Center: Drell-Yan process in pp-scattering (space-like kinematics) Right: Deep-inelastic e p-scattering (space-like kinematics) Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.13

20 Parton evolution Physical picture Proton is probed with increasing resolution 1/Q lower momentum partons are resolved Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.14

21 Parton evolution Physical picture Proton is probed with increasing resolution 1/Q lower momentum partons are resolved Feynman diagrams at leading order Evolution equations for f(x, µ 2 ) non-singlet (2n f 1 scalar) and singlet (2 2 matrix) equations Q 2 Q 2 " q g # = " P qq P gq P qg P gg # " q g # Splitting functions P ij Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.14

22 Parton evolution (cont d) Analytical results LO and NLO splitting functions P (0) ns (x) = C F (2p qq (x)+3δ(1 x)) P (0) ps (x) = 0 P (0) qg (x) = 2n f p qg (x) P (0) gq (x) = 2C F p gq (x) ( P gg (0) (x) = C A 4p gg (x)+ 11 ) 3 δ(1 x) 2 3 n f δ(1 x) NNLO splitting functions S.M., Vermaseren, Vogt 04 3 pages for nonsinglet 8 pages for singlet Coefficient functions for F 2 and F L at three loops O(100) pages S.M., Vermaseren, Vogt 05 Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.15

23 Parton evolution (cont d) Analytical results LO and NLO splitting functions P (0) ns (x) = C F (2p qq (x)+3δ(1 x)) P (0) ps (x) = 0 P (0) qg (x) = 2n f p qg (x) P (0) gq (x) = 2C F p gq (x) ( P gg (0) (x) = C A 4p gg (x)+ 11 ) 3 δ(1 x) 2 3 n f δ(1 x) NNLO splitting functions S.M., Vermaseren, Vogt 04 3 pages for nonsinglet 8 pages for singlet Coefficient functions for F 2 and F L at three loops O(100) pages S.M., Vermaseren, Vogt 05 ( P ns (2)+ 1 [ 10 (x) = 16C A C F n f 6 pqq(x) ζ2 9ζ3 H0 + 2H0ζ2 7H0,0 2H0,0, ] + 3H1,0,0 H3 + 1 [ 3 3 pqq( x) 2 ζ ζ2 H 2,0 2H 1ζ2 H 1,0 H 1,0, H 1, H0ζ2 + 5 [ 1 ]+(1 3 H0,0 + H0,0,0 257 H3 x) ζ H0 1 ] 6 H0,0 H1 [ 2 (1+x) 3 H 1,0 + 1 ] 2 H ζ2 + H0 + 1 [ 5 6 H0,0 + δ(1 x) ζ ζ ]) 18 ζ3 ( [ C A C F pqq(x) ζ ζ22 H 3,0 3H 2ζ2 14H 2, 1,0 + 3H 2,0 + 5H 2,0,0 4H 2, H0 + H0ζ2 H0ζ3 H0,0 4H0,0ζ H0,0,0 + 5H0,0,0, H3 24H1ζ3 16H1, 2, H1,0 2H1,0ζ2 + H1,0,0 + 11H1,0,0,0 + 8H1,1,0,0 8H1,3 + H ] [ 1 H2 2H2ζ H2,0 + 5H2,0,0 + H3,0 + pqq( x) 4 ζ ζ2 + ζ3 + 5H 3, H 2ζ2 4H 2, 1, H 2,0 + 21H 2,0,0 + 30H 2,2 6 3 H 1ζ2 42H 1ζ H0 4H 1, 2,0 + 56H 1, 1ζ2 36H 1, 1,0,0 56H 1, 1,2 134 H 1,0 42H 1,0ζ2 H3, H 1, H 1,0,0 + 17H 1,0,0,0 + H 1,2 + 2H 1,2,0 + H0ζ2 + H0ζ H0,0 + 13H0,0ζ ] [ 133 H0,0,0 5H0,0,0,0 7H2ζ H3 10H4 +(1 x) H0,0,0, ζ3 2H0ζ3 2H 3,0 + H 2ζ2 + 2H 2, 1,0 3H 2,0,0 + H0,0,0 H1 7H1ζ H1,0, ] [ 43 3 H1,0 +(1+x) 2 ζ2 3ζ H 2,0 31H 1ζ2 14H 1, 1,0 2 3 H 1,0 + 24H 1,2 + 23H 1,0, H0ζ2 + 5H0,0ζ2 + H0 H0,0 H2 + H2ζ2 15H ] + 2H2,0,0 3H4 5ζ2 1 2 ζ ζ3 2H 3,0 7H 2,0 H0ζ H0ζ2 2 9 H0 2H0,0ζ [ 151 H0,0 22H0,0,0 4H0,0,0, H2 + 6H3 + δ(1 x) ζ2ζ ζ ζ ]) [ 245 ζ ζ5 + 16C 2 A C F (pqq(x) ζ ζ ζ H0 + H 3,0 + 4H 2, 1, H 2,0 H 2,0,0 + 2H 2,2 H0ζ2 + 4H0ζ3 + H0,0 2H2,0, H0,0,0,0 + 9H1ζ3 + 6H1, 2,0 H1,0ζ H1,0,0 3H1,0,0,0 4H1,1,0,0 + 4H1, H0,0, ] [ H3 + H4 + pqq( x) 18 ζ2 ζ ζ3 H 3,0 + 8H 2ζ2 + H 2,0 4H 2,0, H 1,0,0, H 1ζ2 + 12H 1ζ3 16H 1, 1ζ2 + 8H 1, 1,0,0 + 16H 1, 1, H 1,0 ( P ns (2) (x) = P ns (2)+ (x)+16c A C F C F C )( [ A 134 pqq( x) 2 9 ζ2 4ζ22 11ζ3 4H 3,0 + 32H 2ζ H 2,0 16H 2,0,0 32H 2,2 + H 1ζ2 + 48H 1ζ3 64H 1, 1ζ H 1, 1,0,0 + 64H 1, 1, H 1,0 + 44H 1,0ζ2 + H 1,0,0 12H 1,0,0, H 1,2 32H 1,3 3H H0ζ2 16H0ζ3 H0,0 12H0,0ζ2 H0,0,0 + 4H0,0,0,0 + 8H2ζ ] [ H3 + 8H4 +(1 x) ζ22 + 2H 3,0 2H 2ζ2 4H 2, 1,0 10H 2,0 2H0,0 + 2H 2,0,0 + 2H0ζ3 + H0,0ζ2 H0,0,0,0 + 8H1ζ ] [ 3 H1 +(1+x) 32H 1ζ2 18ζ2 23ζ ] H 1,0 16H 1,0,0 32H 1,2 H0 29H0ζ2 + 5H0,0,0 + 24H H2 ( 2ζ2 2ζ3 + 32H0 + 14H0ζ2 + 2H0,0,0 16H3 )+16C F n f C F C )( [ A pqq( x) 2ζ ζ2 4 3 H 2, H 1ζ2 3 9 H 1,0 4 3 H 1,0, H 1, H0ζ H0, H0,0,0 4 [ 61 ]+(1 3 H3 x) 9 8 ] [ 3 H1 +(1+x) 2H0, H 1, H0 4 ]) 3 H2 ( C F C F C )( [ A pqq( x) 9ζ3 7ζ H 3,0 64H 2ζ2 16H 2, 1,0 6H 2, H 2,0,0 + 56H 2,2 12H 1ζ2 72H 1ζ3 16H 1, 2,0 + 96H 1, 1ζ2 80H 1, 1,0,0 96H 1, 1,2 80H 1,0ζ2 6H 1,0,0 + 44H 1,0,0,0 + 12H 1,2 + 8H 1,2,0 + 64H 1,3 + 3H0 ] + 3H0ζ2 + 26H0ζ3 + 28H0,0ζ2 + 9H0,0,0 12H0,0,0,0 12H2ζ2 6H3 4H3,0 24H4 [ (1 x) 15+8H 3,0 + 8H 2,0,0 + 61H0 + 6H0ζ3 + 2H0,0ζ2 6H0,0,0,0 + 12H1ζ2 + 60H1 ] [ + 8H1,0 +(1+x) 24ζ2 + 57ζ3 + 10H 2,0 48H 1ζ2 4H 1,0 + 40H 1,0,0 + 48H 1,2 ] + 59H0ζ2 22H0,0 35H0,0,0 22H2 4H2,0 44H3 + 8ζ2 42ζ3 4H 2,0 + 42H0 ) 38H0ζ2 + 14H0,0 16H2 + 26H0,0,0 + 24H3. P ns (2)s d abc dabc (x) = 16n f nc ( 1 2 (1 x) [ ζ2 5 4 ζ22 H 3,0 + H 2ζ2 H 2,0, H3 + 2H 2, 1, H0,0ζ2 1 2 H1ζ ] H1,0, H1 + 1 [H 1, 1,0 2 (1+x) 3 2 H 1ζ H H 1, H 1,0,0 + 2H 1,2 3 2 H 2, H0ζ2 + H0, H2 H2ζ2 1 2 H2,0,0 + 3 ] 2 H4 1 1 ] 3( x + x2)[ 3H 1ζ2 + 2H 1, 1,0 2H 1,0,0 2H 1,2 + H1ζ x2[ 5ζ3 2H3 ] + 2H 2,0 + 4H0ζ2 2H0,0,0 + 2H1ζ H0 + ζ3 9 2 ζ2 + ζ22 H0ζ3 H0ζ2 2H0,0ζ2 8H 2,2 + 11H 1,0ζ H 1,0,0 6 3 H 1,2 8H 1,3 3 4 H H0ζ2 4H0ζ H0,0 3H0,0ζ ] [ 1883 H0,0,0 + H0,0,0,0 + 2H2ζ H3 + 2H4 +(1 x) H0,0,0,0 + 11H1 2 H 2, 1, H 3,0 1 2 H 2ζ H 2,0,0 + H0 + H0ζ H0,0 5 H0,0,0 + 2H1ζ2 2 ] [ 2H1,0,0 +(1+x) 8H 1ζ2 + 4H 1, 1, H 1,0 5H 1,0,0 6H 1,2 3 3 ζ ζ ζ H 2,0 2 2 H0ζ2 1 2 H2ζ2 5 4 H0,0ζ2 + 7H2 1 4 H2,0,0 + 3H3 + 3 ] 4 H H0,0ζ ζ ζ2 + ζ3 + H 2, H H0ζ2 H0ζ H0, H0,0, H0,0,0,0 [ 1657 δ(1 x) ζ ζ ζ3 5 ]) ( 1 [ 2 ζ5 + 16C F nf 2 18 pqq(x) H0, ] 3 H0 [ 13 +(1 x) ] [ 17 9 H0 δ(1 x) ζ2 + 1 ]) ( 1 9 ζ3 + 16C 2 F n f [5ζ3 3 pqq(x) 4H1,0, H0 + H0ζ ] H0,0 H0,0,0 H1, H2 2H2,0 2H3 + 2 [ 5 3 pqq( x) 3 ζ ζ3 + H 2,0 + 2H 1ζ H 1,0 + H 1,0,0 2H 1,2 1 2 H0ζ2 5 ] 3 H0,0 H0,0,0 + H3 [ 10 (1 x) H0,0 4 3 H H1,0 + 4 ] [ H2 +(1+x) H 1, H0 + 1 ] 2 H0,0, H H0,0 + 4 [ 23 3 H2 δ(1 x) ζ ζ ]) ( [ 6 ζ C F pqq(x) 10 ζ22 2H 3,0 + 6H 2ζ2 + 12H 2, 1,0 6H 2,0, H H0ζ2 + H0ζ3 + H0,0 2H0,0,0,0 + 8H1, H1ζ3 + 8H1, 2,0 6H1,0,0 4H1,0,0,0 + 4H1,2,0 3H2,0 + 2H2,0,0 + 4H2,1,0 + 4H2,2 ] 7 + 4H3,0 + 4H3,1 + 2H4 + pqq( x)[ 2 ζ22 9 ζ3 6H 3,0 + 32H 2ζ2 + 8H 2, 1,0 + 3H 2,0 2 26H 2,0,0 28H 2,2 + 6H 1ζ2 + 36H 1ζ3 + 8H 1, 2,0 48H 1, 1ζ2 + 40H 1, 1,0,0 + 48H 1, 1,2 + 40H 1,0ζ2 + 3H 1,0,0 22H 1,0,0,0 6H 1,2 4H 1,2,0 32H 1,3 3 2 H0 3 2 H0ζ2 13H0ζ3 14H0,0ζ2 9 ] 2 H0,0,0 + 6H0,0,0,0 + 6H2ζ2 + 3H3 + 2H3,0 + 12H4 [ +(1 x) 2H 3, H 2,0,0 + H0,0ζ2 3H0,0,0,0 + 35H1 + 6H1ζ2 H1,0 + 5 ] 2 H2,0 [ 37 +(1+x) 10 ζ ζ2 ζ3 15H 2,0 + 30H 1ζ2 + 12H 1, 1,0 2H 1,0 26H 1,0, H 1, H0 28H0ζ2 + H0,0 + 20H0,0,0 + H2 3H2,0,0 2H3,0 + 13H ] H4 + 4ζ2 + 33ζ3 + 4H 3,0 + 10H 2, H0 + 6H0ζ3 + 19H0ζ2 25H0,0 17H0,0,0 2 [ 29 2H2 H2,0 4H3 + δ(1 x) 32 2ζ2ζ ζ ζ ]) 4 ζ3 15ζ H0,0 1 4 H0,0, H0,0,0,0 + H 2,0 H3 ). Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.15

24 PDFs from HERA to LHC to LHC HERA F 2 em F 2 -log10 (x) 5 x=6.32e-5 x= x= x= x= x= x= x= x= ZEUS NLO QCD fit H1 PDF 2000 fit H H1 (prel.) 99/00 ZEUS 96/97 4 x= x= BCDMS E665 NMC x= x=0.008 x=0.013 x= x=0.032 x=0.05 x=0.08 x= x=0.18 x=0.25 x=0.4 x= Q 2 (GeV 2 ) LHC parton kinematics Precision HERA data on F 2 Scale evolution of PDFs in Q over two to three orders Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.16

25 PDFs TEV4LHC from Tevatron σ Br (nb) 1 σ Br(W lν) 10-1 σ Br(Z l + l - ) theory curves: Martin, Roberts, Stirling, Thorne CDF (630) UA1 (µ) UA2 (e) CDF II (e+µ) CDF I (e) DO I (e) E cm (TeV) Data for Z/W ± production Drell-Yan process as monitor for parton luminosity Tevatron parton kinematics Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.17

26 Numerics for for PDF PDFs evolution Perturbative expansion of logarithmic scale derivative d dln µ 2 f f(x, µ 2 f ) = h i P(α s (µ f 2 )) f(µ f 2 ) (x) Default values n f = 4 and α s (µ 2 ) = 0.2 Singlet Parametrization of singlet quark distribution xq s (x, µ 0 2 ) = 0.6 x 0.3 (1 x) 3.5 ( x 0.8 ) xg(x, µ 0 2 ) = 1.6 x 0.3 (1 x) 4.5 (1 0.6 x 0.3 ) Code for evolution at NNLO in Mellin N-space QCD-Pegasus Vogt Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.18

27 Evolution Perturbativeat stability small xof evolution Scale derivatives of quark and gluon distributions at Q 2 30 GeV d ln q / d ln Q d ln g / d ln Q LO NLO α S = 0.2, N f = x x Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.19

28 Evolution Perturbativeat stability small xof evolution Scale derivatives of quark and gluon distributions at Q 2 30 GeV d ln q / d ln Q d ln g / d ln Q LO NLO NNLO -0.2 α S = 0.2, N f = x Expansion very stable except for very small momenta x < 10 4 x Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.19

29 Vector boson production Kinematical variables (inclusive) energy (cms) s = Q 2 (space-like) scaling variable x = M 2 W ± /Z /s Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.20

30 Vector boson production Kinematical variables (inclusive) energy (cms) s = Q 2 (space-like) scaling variable x = M 2 W ± /Z /s σ Br (nb) 1 σ Br(W lν) NNLO theory curves: Martin, Roberts, Stirling, Thorne σ Br(Z l + l - ) 20 years of measurements of W ± and Z cross sections at hadron colliders 10-1 CDF (630) D0 II (e) D0 II (µ) CDF II (e,1.2< η <2.8),223 pb -1 CDF II (e+µ),72pb -1 UA1 (µ) CDF I (e) CDF II Z(µ), 337pb -1 UA2 (e) DO I (e) CDF II Z(τ), 349pb E cm (TeV) Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.20

31 Kinematics (differential) Proton-proton scattering (two broad-band beams of incoming partons) cms of parton-parton scattering boosted wrt incoming protons Final state variables (simple transformations under longitud. boosts) p µ = (E, p x, p y, p z ) = (m t cosh y, p t sin φ,p t cos φ, m t sinh y) rapidity y = 1 «E + 2 ln pz E p z q transverse momentum p t and mass m t = p 2 t + m2 azimuthal angle φ Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.21

32 Kinematics (differential) Proton-proton scattering (two broad-band beams of incoming partons) cms of parton-parton scattering boosted wrt incoming protons Final state variables (simple transformations under longitud. boosts) p µ = (E, p x, p y, p z ) = (m t cosh y, p t sin φ,p t cos φ, m t sinh y) rapidity y = 1 «E + 2 ln pz E p z q transverse momentum p t and mass m t = p 2 t + m2 azimuthal angle φ Differences in rapidity y and azimuthal angle φ invariant under boosts In practice (for E m p ) pseudo-rapidity η = ln tan «θ 2 with angle from beam axis Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.21

33 Differential distributions Invariant mass distribution dσ dm 2 of lepton pair for Z-production in p p-collisions CDF data at s = 1.8 TeV and NLO QCD prediction Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.22

34 Differential distributions Invariant mass distribution dσ dm 2 of lepton pair for Z-production in p p-collisions CDF data at s = 1.8 TeV and NLO QCD prediction M 4 dσ dm 2 = σ (0) 1 N M 2 s Z 1 0 dx 1 dx 2 δ x 1 x 2 M2 s «X e 2 q {f q (x 1 ) f q (x 2 ) + f q (x 1 ) f q (x 2 )} q dσ Double-differential cross section dm 2 local in PDFs dy y = 1 «2 ln x1 lepton-pair rapidity x 2 Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.22

35 W ± asymmetry Rapidity distributions for W ± - and Z-production in p p-collisions CP invariance dσ for Z-production dy symmetric around y = 0 W ± rapidity asymmetry sensitive to flavor decomposition of proton A W (y) = dσ(w+ )/dy dσ(w )/dy dσ(w + )/dy + dσ(w )/dy u(x 1)d(x 2 ) d(x 1 )u(x 2 ) u(x 1 )d(x 2 ) + d(x 1 )u(x 2 ) Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.23

36 W -production at LHC at the LHC Impact of HERA measurement on precision predictions at LHC LHC W +, W,Z-rapidity distributions and their PDF uncertainties (NLO QCD analysis) Tricoli, Cooper-Sarkar, Gwenlan 05 cross section uncertainty (left) and proton PDFs (right) dσbe/dy W + HERA included xf Q = 10 GeV HERA included xg 2 2 Q = 100 GeV NLO cross section uncertainty 3.5% with HERA PDFs xg xs 2 2 Q = 1000 GeV uncorr. uncert. tot. uncert. xs 2 2 Q = GeV 20 xg xg y xs xs x Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.24

37 WDifferential and Z distributions at NNLO in QCD W ±, Z-boson rapidity distribution with scale variation m W,Z /2 µ 2m W,Z Anastasiou, Petriello, Melnikov 05 Reduction of theoretical uncertainties (renormalization / factorization scale) to level of 1% in NNLO QCD analysis Dissertori 05 Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.25

38 QCD jets Lessons from Tevatron Top search was the outstanding issue at the start of run I at Tevatron Initiated many developments in LO multi-parton generation for pp W ± + jets (e.g. numerical recursion, algebraic generation of tree level amplitudes) unexpected challenge: importance of matching issues between matrix elements and shower Monte Carlo s initiated development of numerical partonic NLO jet Monte Carlo s Expectations for LHC In the coming years all new challenges for NLO are encapsulated by Higgs searches at ATLAS/CMS large number of high multiplicity processes Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.26

39 Complete NLO results Complete NLO calculations for many 2 3 processes (e.g. for hadron collider) pp 3jets, γγ + jet, V + 2jets, 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 processes electroweak corrections to e + e 4 fermions Denner, Dittmaier, Roth, Wieders 05 extremely diffcult hexagon integrals with masses e e W electroweak corrections to e + e ν νhh Boudjema, Fujimoto, Ishikawa, Kaneko, Kato, Kurihara, Shimizu, Yasui 05 e + Z Z µ d µ ν µ u d Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.27

40 Exp LHC priority wishlist wishlist process (V {γ,w ±, Z}) pp V V + 1 jet pp H + 2 jets pp t tb b pp t t + 2 jets pp V V b b pp V V + 2 jets pp V + 3 jets pp V V V Les Houches 2005 [hep-ph/ ] 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 Theory introduction to Standard Model processes at LHC p.28

41 Exp wishlist (full) Original experimenter s wishlist Tevatron Run II Monte Carlo workshop April 2001 Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.29

42 Pythia How reliable vs BSM are background (I) estimates? Gianotti, Mangano 05 Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.30

43 Pythia SUSY searches vs BSM (II) SM background in channel pp Z( ν ν) + 4jets from Alpgen Gianotti, Mangano 05 Njet 4 E T(1,2) > 100GeV E T(3,4) > 50GeV MET = M eff + max(100,m eff /4) M eff = MET + P i E Ti Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.31

44 Pythia SUSY searches vs BSM (II) SM background in channel pp Z( ν ν) + 4jets from Alpgen Gianotti, Mangano 05 Njet 4 E T(1,2) > 100GeV E T(3,4) > 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 Theory introduction to Standard Model processes at LHC p.31

45 Jets definitions Historically: Sterman-Weinberg criterium for two-jet event energy fraction 1 ǫ in cone of half angle δ not practical for multi-particle events Modern modelling of jets cone- or k t -algorithms y cut y cut y cut JADE algorithm min (p i + p j ) 2 = min 2E i E j (1 cos θ ij ) > y cut s combines also soft gluons at large relative k t (disadvantage) e.g. potential three-jet event Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.32

46 Di-jet phase space in e + e annihilation phase space boundaries for region with two and three jets Sterman-Weinberg with (ǫ,δ) = (0.3,30) (solid lines) JADE algorithm with y cut = 0.1 (dashed lines) Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.33

47 Jet rates in e + e annihilation Ratio of rates f i = σ i jet σ for two and three jets JADE algorithm with y cut 0.3 Recall: three-jet cross section σ q qg σ q qg = σ (0) 3 X q e 2 q C F α s 2π Z dx 1 dx 2 x x 2 2 (1 x 1 )(1 x 2 ) Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.34

48 Cone k t -clustering algorithm k t -clustering algorithm Cone algorithm Jets in hadronic collisions 2min (E 2 i, E 2 j ) (1 cos θ ij ) > y cut s define cone of radius R in η,φ for R = q ( η) 2 + ( φ) 2 midpoint cone-algorithm is not infrared safe beyond NLO in QCD soft seed gives rise to extra hard jet (fixed for Tevatron run II) p t /GeV p t /GeV 400 (a) 400 (b) y y Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.35

49 Di-jets (Some) uses of hadronic di-jets Hadronic di-jets: large statistics even with high-p t cuts experimental calibration (HCAL uniformity, establish missing E t ) gluon jets constrain gluon PDF at medium/large x searches for quark sub-structure (di-jet angular correlations) Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.36

50 Gluon The gluon PDFdistribution CDF Run II Preliminary Cross Section Ratio (Data/Theory) Jet NLO pqcd EKS CTEQ 6.1M, (µ=p T /2) Midpoint R cone =0.7, f merge =0.75, R Sep =1.3 Data corrected to parton level 0.1< y <0.7 L = 385 pb Systematic uncertainty. Systematic uncertainty including hadronization and underlying event. NLO pqcd PDF uncertainty. Data/NLO pqcd(eks) MRST2004/CTEQ 6.1M 6% luminosity uncertainty not included -1 Gluon distribution at small x from DIS structure function data at intermediate x from jet cross section p T (GeV/c) Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.37

51 Top-production at LHC at LHC LHC will accumulate very high statistics for t t-pairs events/year in low luminosity run (10 times more in high luminosity run) mass measurement m t = O(1)GeV (constraints on Standard Model Higgs mass m h ) Use t t-pairs for calibration of jet energy scale (decay W 2 jets) t t + jets background to Higgs searches σ (nb) proton - (anti)proton cross sections σ tot σ b σ jet (E T jet > s/20) σ W σ Z σ jet (E T jet > 100 GeV) σ t σ jet (E jet T > s/4) σ Higgs (M H = 150 GeV) Tevatron LHC events/sec for L = cm -2 s σ Higgs (M H = 500 GeV) s (TeV) Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.38

52 Top-pair Top-quark production pair-production Top decay leptonic: t W + + b l + + ν + b hadronic: t W + + b q + q + b Leading order Feynman diagrams q + q Q + Q g + g Q + Q NLO in QCD Nason, Dawson, Ellis 88; Beenakker, Smith, van Neerven 89; Mangano, Nason, Ridolfi 92; Bernreuther, Brandenburg, Si, Uwer 04;... q q and gg dominant at NLO; neglect qg at NLO only O(1%) Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.39

53 Tevatron results Total cross section as function of energy s (theory uncertainty band from scale variation) σ(pp tt) (pb) CDF Run 1 Combined 110 pb -1 2 m t =170 GeV/c 2 m t =175 GeV/c 2 m t =180 GeV/c CDF Run 2 Preliminary -1 Combined 760 pb Cacciari et al. JHEP 0404:068 (2004) m t =175 GeV/c s (GeV) NNLO required for precision determinations of m t Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.40

54 QCD Perturbative NLO NLOand QCD beyond corrections essential NLO important for rates (background); large K-factors; new parton channels may dominate beyond tree level e.g. t t + 1 jet is O(α 3 s) and (α LO s ) 10% gives (σ LO ) 30% Dittmaier, Uwer, Weinzierl 07 Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.41

55 QCD Perturbative NLO NLOand QCD beyond corrections essential NLO important for rates (background); large K-factors; new parton channels may dominate beyond tree level e.g. t t + 1 jet is O(α 3 s) and (α LO s ) 10% gives (σ LO ) 30% Dittmaier, Uwer, Weinzierl 07 Case for NNLO NNLO QCD corrections needed for accuracy better than O(10%) t t pair-production total cross sections and differential distributions (large statistics even with high-p T cuts) NNLO important for scale uncertainty Top-mass precision measurements (decay t W b) perturbative heavy-quark fragmentation (b-fragmentation for J/ψ in b-decay) Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.41

56 Parton cross section (I) Recall our master formula σ pp (Q,m) = X ij ˆσ ij (Q/µ,α s (µ)) f i (µ, m) f j (µ, m) Parton cross section Expansion in terms of scaling functions f (k,l) ij PDFs!!!) ˆσ ij = α2 s m 2 " f (0,0) ij +! + 4πα s f (1,0) ij + ln µ2 m 2 f(1,1) ij + (not to be confused with + (4πα s ) 2 f (2,0) ij + ln µ2 m 2 f(2,1) ij + ln 2 µ 2 m 2 f(2,2) ij!# Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.42

57 The parton cross section (II) Numerical investigation of scaling functions f q q and f gg variable η = s 1 measures distance from t t-threshold 4m2 (1,0) in MS f qq (0,0) f qq η = s/(4m 2 ) (1,0) f gg Resummation of threshold logarithms ln(η) reorganize perturbative expansion stability η = s/(4m 2 ) - 1 (0,0) f gg O = α s `ln +ln +1 + α 2 4 s `ln + ln 3 + ln 2 + ln = `1 + α s 1 + α 2 s exp`α s ln 2 +α s ln +α 2 s ln +... Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.43

58 Parton luminosity Rewrite our master formula in terms of variable η = σ pp (Q,m) = X ij log 10 (S/4m 2 1) Z dlog 10 η s 4m 2 1 η 1 + η ln(10)φ ij(η,µ 2 ) ˆσ ij (Q/µ,α s (µ)) define parton luminosity Φ ij (η,µ 2 ) = f i (µ, m) f j (µ, m) ln(10)η/(1+η)φ qq (η,µ 2 ) 25 ln(10)η/(1+η)φ gg (η,µ 2 ) η = s/(4m 2 ) - 1 LHC kinematics with S = 14TeV and m = 175.0GeV scale variation m/2 µ 2m η = s/(4m 2 ) - 1 Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.44

59 LHC total cross cross section LHC kinematics give less weight to threshold region S = 14TeV, m = 172.5GeV Scale uncertainty at NLO is of order O(15%) additional dependence on parton luminosity σ pp [pb] at LHC m t = GeV cteq6me NLO MRST2001E NLO σ pp [pb] at LHC m t /2 < µ < 2m t cteq6me NLO µ/m m t [GeV] Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.45

60 Summary QCD factorization for hard scattering Parton luminosity at hadron colliders W ± and Z-boson production at LHC Jet-production Hadro-production of Top-Quarks Outlook Higgs production at the LHC Motivation for extensions of the Standard Model Introduction to Supersymmetry and the MSSM Large Extra Dimensions Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.46

61 Literature QCD and Collider Physics R.K. Ellis, W.J. Stirling and B.R. Webber Sven-Olaf Moch Theory introduction to Standard Model processes at LHC p.47