Physics at LHC. lecture seven. Sven-Olaf Moch. DESY, Zeuthen. in collaboration with Martin zur Nedden

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1 Physics at LHC lecture seven Sven-Olaf Moch DESY, Zeuthen in collaboration with Martin zur Nedden Humboldt-Universität, December 03, 2007, Berlin Sven-Olaf Moch Physics at LHC p.1

2 The Higgs boson We believe Higgs boson is key to our understanding of the origin of mass vacuum has non-trivial structure (Higgs quantum field) interaction of Higgs boson leads to effective mass of elementary particles Sven-Olaf Moch Physics at LHC p.2

3 Higgs mechanism The Waldegrave Higgs Challenge (1993) story: David Miller cartoons: Georges Boixader Sven-Olaf Moch Physics at LHC p.3

4 WpWm Vector boson scattering (I) Study structure of gauge theory at high energies s scattering (p + ) + (p ) (q + ) + (q ) Longitudinally polarization dominates at high energies ǫ L Amplitude A behaves as A(s, t) = A p4 M 4 W + B p2 M 2 W + C p M W Tree level diagrams Z/γ Z/γ A Z/γ (s,t) = g 2 W ( p 4 M 4 W 3 6cos θ cos 2 θ + p2 M 2 W W «) 2 cos θ 2cos2 θ Sven-Olaf Moch Physics at LHC p.4

5 WpWm scattering (II) A quartic (s, t) = g 2 W ( p 4 M 4 W 3 + 6cos θ + cos 2 θ + p2 M 2 W ) cosθ + 2cos 2 θ Higgs exchange H H A H (s, t) = g 2 W ( p 2 M 2 W cos θ «M2 H 4M 2 W s s M 2 H t + t MH 2!) Summing up for amplitude A(s, t) = A p4 MW 4 coefficients A = B = 0 + B p2 M 2 W + C gives Sven-Olaf Moch Physics at LHC p.5

6 WpWm Perturbative scattering unitarity(iii) General cut-off Λ from perturbative -boson scattering g 2 W Λ2 16π 2 M 2 W = 1 Λ 1.8TeV Vector boson scattering in presence of Higgs tree level amplitude A(s, t) not divergent in high energy limit perturbation theory requires M H 1TeV (otherwise strongly coupling W -sector) Z Z New electro-weak gauge bosons at the TeV-scale O(few TeV) Sven-Olaf Moch Physics at LHC p.6

7 Higgs (I) 10 9 proton - (anti)proton cross sections σ tot 10 8 Higgs production at LHC Tevatron LHC Expected production rates strongly depended on Higgs mass luminosity cm 2 s 1 (20 fb 1 /year) events/year for m h = 120 GeV events/year for m h = 800 GeV Branching ratios in Higgs decay also depended on Higgs mass 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 T jet > s/4) events/sec for L = cm -2 s σ Higgs (M H = 150 GeV) σ Higgs (M H = 500 GeV) s (TeV) 10-7 Sven-Olaf Moch Physics at LHC p.7

8 Higgs (I) 10 9 proton - (anti)proton cross sections σ tot 10 8 Higgs production at LHC Tevatron LHC Expected production rates strongly depended on Higgs mass luminosity cm 2 s 1 (20 fb 1 /year) events/year for m h = 120 GeV events/year for m h = 800 GeV Branching ratios in Higgs decay also depended on Higgs mass 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 T jet > s/4) events/sec for L = cm -2 s σ Higgs (M H = 150 GeV) σ Higgs (M H = 500 GeV) 10-6 Search here! s (TeV) 10-7 Sven-Olaf Moch Physics at LHC p.7

9 Ñ Ø ½ Î ÅÊËÌ»ÆÄÇ Higgs Dominant (II) production and decay modes ½¼¼ ½ Ï Ï ÔÔ À µ Ô À Ô ½ Ì Î Ø Ø ¼º½ ½¼ ÀÕÕ ¼º¼½ Ï À Ê Àµ À ½ Ø ØÀ ¼º¼¼½ ¼º¼¼¼½ ¼º½ ½¼¼¼ ½¼¼ ½ ¼ ½¼¼ ½¼¼¼ ¼¼ ¼¼ ¼¼ ¾¼¼ ½ ¼ Î Standard model Higgs Å À branching ratios for decay (left) and dominant production modes (right) Djouadi 05 Å À Î Sven-Olaf Moch Physics at LHC p.8

10 Higgs Gluon fusion (III) Largest rate for all values of Higgs mass M H (top-yukawa coupling) σ(pp H+X) [pb] M H = 120 GeV NLO N 3 LO SV LO N 2 LO heavy top limit m t : effective gg Higgs vertex Total cross section with QCD corrections Variation of renormalization scale for Higgs mass M H = 120GeV NNLO corrections Harlander, Kilgore 02; Anastasiou, Melnikov 02; Ravindran, Smith, van Neerven 03 complete soft N 3 LO corrections S.M., Vogt µ r / M H Sven-Olaf Moch Physics at LHC p.9

11 Higgs Differential (IV) distributions in gluon fusion Bin-integrated Higgs rapidity distribution including decay H γγ QCD corrections up to NNLO Anastasiou, Melnikov, Petriello 05; Catani, Grazzini 07 soft N 3 LO corrections Ravindran, Smith, van Neerven 06 Impact of kinematical cuts on higher order corrections left: Higgs mass M h = 125 GeV, no cuts on p t of jets right: Higgs mass M h = 165 GeV and veto on jets with p t > 40 GeV (k t algorithm for jet reconstruction with jet size D = 0.4) Sven-Olaf Moch Physics at LHC p.10

12 Higgs Weak vector-boson (V) fusion Channel qq qqh (with cuts on jets energies) Second largest rate (WWH coupling) mostly dominated by u, d-quarks Higgs-strahlung Channel q q W(Z)H Third largest rate (same couplings as vector boson fusion) Sven-Olaf Moch Physics at LHC p.11

13 Higgs in(vi) association with heavy quarks Channel pp t th driven by gluon luminosity and enhanced by large top-yukawa coupling, but process useful only in the low mass range m h < 135 GeV tagging of at least one top-quark required from t bw Sven-Olaf Moch Physics at LHC p.12