δm W = 15 MeV δm top = 1 GeV

Transcription

1 Precision SM physics at the LHC... what we hope to see (Bentvelsen, Grünewald) Repeat the electroweak fit changing the uncertainties δm W = 15 MeV δm top = 1 GeV same central values Michael Krämer Page 1 Herbstschule Maria Laach, September 2005

2 Herbstschule Maria Laach, September 2005 Physics at the Large Hadron Collider Michael Krämer (RWTH Aachen) Lecture 1: Review of the Standard Model Lecture 2: SM physics at hadron colliders Lecture 3: Higgs and SUSY searches at the LHC Michael Krämer Page 2 Herbstschule Maria Laach, September 2005

3 Introduction: The Higgs boson The Higgs mechanism is testable because all couplings are known: fermions: g ffh = 2m f /v gauge bosons: g V V H = 2M V /v with vacuum expectation value v 2 = 1/ 2G F (246 GeV) 2 The Higgs sector and the properties of the Higgs particle (lifetime, decay branching ratios, cross sections) are fixed in terms of the Higgs boson mass M H. Express Higgs potential in terms of (µ, λ) (v 2, M H ) Michael Krämer Page 3 Herbstschule Maria Laach, September 2005

4 Higgs boson mass Higgs search at LEP in associated ZH production e + e Z ZH provide a lower limit on the SM Higgs mass: M H > GeV (95% CL) Electroweak precision tests provide an upper limit on the SM Higgs mass: M H < 219 GeV (95% CL) Michael Krämer Page 4 Herbstschule Maria Laach, September 2005

5 Higgs boson mass Theoretical constraints Hambye, Riesselmann Running of the Higgs coupling: dλ dln µ 2 = 3 8π 2 [λ2 + λg 2 t G 4 t ] with λ = M 2 H/v 2 and G t = 2m t /v. 0 Landau Pole For M H > m t one has dλ/dln µ 2 λ 2 and thus λ(µ 2 ) = λ(v 2 ) 1 3λ(v2 ) 8π ln µ2 2 v 2 Vacuum Instability Requiring λ(λ) < yields M 2 H < 8π 2 v 2 3 ln (Λ 2 /v 2 ) Michael Krämer Page 5 Herbstschule Maria Laach, September 2005

6 Higgs boson decays Higgs decay modes and branching ratios 1 bb _ WW [HDECAY: Spira et al.] BR(H) ZZ τ + τ cc _ gg tt γγ Zγ M H [GeV] dominant decay into b b for M H < 130 GeV W W, ZZ for M H > 130 GeV Michael Krämer Page 6 Herbstschule Maria Laach, September 2005

7 Higgs boson decays Higgs decay width 10 2 Γ(H) [GeV] M H [GeV] direct measurement of Γ only for M Higgs > 300 GeV Michael Krämer Page 7 Herbstschule Maria Laach, September 2005

8 Higgs boson production at the LHC gg H (NNLO) σ(pp H + X) [pb] s = 14 TeV NLO / NNLO qq _ ' HW qq Hqq gg/qq _ tt _ H (NLO) qq _ HZ MRST M H [GeV] Michael Krämer Page 8 Herbstschule Maria Laach, September 2005

9 Higgs boson production at the LHC Precision calculations are needed for signal and background processes for Higgs discovery in W W decay channels (no reconstruction of mass peak possible) for a reliable determination of the discovery/exclusion significance for a precise measurement of the Higgs couplings test of the Higgs mechanism discrimination between SM and BSM (eg. SUSY) Recent progress for SM Higgs production includes NNLO QCD calculations for pp H [Harlander, Kilgore; Anastasiou, Melnikov; Ravindran, Smith, van Neerven; Anastasiou, Melnikov, Petriello;... (02-04)] NNLO QCD calculations for pp HZ, HW [Brein, Djouadi, Harlander (04)] (N)NLO QCD calculations for pp Q QH [Beenakker, Dittmaier, MK, Plümper, Spira, Zerwas; Dawson, Jackson, Orr, Reina, Wackeroth; Harlander, Kilgore; Campbell, Ellis, Maltoni, Willenbrock;... (01-05)] NLO QCD calculations for pp qqh [Figy, Oleari, Zeppenfeld; Berger, Campbell (03-04)] NLO EWK calculations for pp HZ, HW [Ciccolini, Dittmaier, MK (03)] (N)NLL resummation for pp H [Kulesza, Sterman, Vogelsang; Berger, Qiu; Catani, de Florian, Grazzini;... (03-04)] matching of NLO calculation with parton shower MC Herwig for pp H [Frixione, Webber (04)]; NNLO splitting functions and PDF fits, error estimates for PDF fits [Moch, Vermaseren, Vogt; MRST; CTEQ (02-05)]. Michael Krämer Page 9 Herbstschule Maria Laach, September 2005

10 Higgs boson production at the LHC Higgs production in gluon-gluon fusion 10 2 σ(pp H+X) [pb] [Harlander, Kilgore 02] s = 14 TeV NLO corrections: K NLO 1.7 NNLO corrections: K NNLO (m top M H ) 2 NNLO scale dependence < 15% 10 LO NLO NNLO M H [GeV] Michael Krämer Page 10 Herbstschule Maria Laach, September 2005

11 Higgs boson search at the LHC σ tot Tevatron LHC QCD background: σ b b 10 8 pb σ (nb) σ bbar σ jet (E T jet > s/20) σ W σ Z σ jet (E T jet > 100 GeV) σ ttbar σ jet (E T jet > s/4) events/sec for L = cm -2 s -1 Higgs signal: σ H+X 10 pb Higgs bosons/year ( L = 30 fb 1 ) 10-5 σ Higgs (M H = 150 GeV) σ Higgs (M H = 500 GeV) s (TeV) Higgs-search through associate production or/and through rare decays Michael Krämer Page 11 Herbstschule Maria Laach, September 2005

12 Higgs boson search at the LHC: signal significance The days of the Higgs boson are numbered! Signal significance 10 2 H γ γ tth (H bb) H ZZ (*) 4 l H WW (*) lνlν H ZZ llνν H WW lνjj Total significance 10 5 σ ATLAS L dt = 30 fb -1 (no K-factors) m H (GeV) Michael Krämer Page 12 Herbstschule Maria Laach, September 2005

13 Higgs boson search at the LHC: signal significance Signal significance 10 2 L dt = 30 fb -1 (no K-factors) ATLAS H γ γ tth (H bb) H ZZ (*) 4 l H WW (*) lνlν qqh qq WW (*) qqh qq ττ Total significance M H < 2M Z gg H (H γγ, ZZ, W W ( ) ) gg/q q t th (H b b, ττ) qq qqh q q W H (H γγ, W W, ττ) (H γγ) 10 M H > 2M Z { gg H (H ZZ, W W ) qq qqh (H ZZ, W W ) m H (GeV/c 2 ) [ + diffractive Higgs production] Michael Krämer Page 13 Herbstschule Maria Laach, September 2005

14 Higgs boson search at the Tevatron search at the Fermilab Tevatron current L = 0.8 fb 1 expectation in 2008: L = 4 6 fb 1 For M H < 140 GeV > 140 GeV use p p W H/ZH and H b b p p H and H W W Michael Krämer Page 14 Herbstschule Maria Laach, September 2005

15 Higgs boson physics at the LHC: the Higgs profile To test the Higgs mechanism we have to determine the profile of the Higgs boson: mass and lifetime external quantum numbers couplings to gauge bosons and fermions Higgs self-couplings Michael Krämer Page 15 Herbstschule Maria Laach, September 2005

16 Higgs boson physics at the LHC: the Higgs profile The Higgs mass The expected precision on M Higgs at the LHC is M/M 10 3 (for M Higgs < 500 GeV) Michael Krämer Page 16 Herbstschule Maria Laach, September 2005

17 Higgs boson physics at the LHC: the Higgs profile The measurement of Higgs couplings: The LHC measures σ(pp H) BR(H X) = σ(pp H) Γ(H X)/Γ tot Different production and decay channels provide measurements of combinations of partial decay widths X γ = Γ W Γ γ Γ tot from qq qqh, H γγ Y γ = Γ gγ γ Γ tot X τ = Γ W Γ τ Γ tot from qq qqh, H ττ Y Z = Γ gγ Z Γ tot X W = Γ2 W Γ tot from qq qqh, H W W ( ) Y W = Γ gγ W Γ tot from gg H γγ from gg H ZZ ( ) from gg H W W ( ) Problem: no direct measurement of Γ tot no observation of some decay modes (e.g. H gg) consider ratios of X or Y s Michael Krämer Page 17 Herbstschule Maria Laach, September 2005

18 Higgs boson physics at the LHC: the Higgs profile Ratios of Higgs couplings can be measured with an accuracy of 10-40%: Michael Krämer Page 18 Herbstschule Maria Laach, September 2005

19 Higgs boson physics at the LHC: the Higgs profile Reconstructing the Higgs potential at the LHC is difficult (impossible) Recall: In the SM we have V = M 2 H 2 H2 + λ 3 vh 3 + λ 4 4 H4 λ 3 = λ 4 = M 2 H 2v 2 To determine λ 3 and λ 4 need to measure multi-higgs production, e.g. g H g H H H H g H g H The measurement of λ 3 appears to be very difficult, the measurement of λ 4 impossible(?) Michael Krämer Page 19 Herbstschule Maria Laach, September 2005

20 Higgs boson physics at the LHC: summary The LHC will find the (or a?) Higgs boson (or something similar). The LHC will measure some of the Higgs boson properties. For a more precise and model independent determination of decay widths and a measurement of quantum numbers we will need the ILC. Higgs physics is exciting: reveals the mechanism of electroweak symmetry breaking points towards physics beyond the SM (hierarchy problem) Michael Krämer Page 20 Herbstschule Maria Laach, September 2005

21 The hierarchy problem: why is M Higgs M Planck? Quantum corrections to the Higgs mass have quadratic UV divergencies δm 2 H α π (Λ2 + m 2 F ) The cutoff Λ represents the scale up to which the Standard Model remains valid. need Λ of O(1 TeV) to avoid unnaturally large corrections In comparison: δm e α π m e ln(λ/m e ) 0.25m e electron mass is stabilized ( protected ) by the chiral symmetry An elegant way to solve the hierarchy problem is to introduce an additional symmetry that transforms fermions into bosons and vice versa: supersymmetry Quantum corrections due to superparticles cancel the quadratic UV divergences δm 2 H α π (Λ2 + m 2 F ) δm 2 H α π (m2 F m2 F ) no fine-tuning if m < O(1 TeV) Michael Krämer Page 21 Herbstschule Maria Laach, September 2005

22 The Minimal Supersymmetric Standard Model The MSSM particle spectrum Gauge Bosons S = 1 Gauginos S = 1/2 gluon, W ±, Z, γ gluino, W, Z, γ Fermions S = 1/2 Sfermions S = 0 ( )( ul ν e ) L )( (ũl ν e ) L d L e L d L ẽ L u R, d R, e R Higgs ( H 0 )( 2 H + 1 H2 H1 0 ) ( H 0 2 H 2 ũ R, d R, ẽ R Higgsinos )( H + 1 H 0 1 ) Michael Krämer Page 22 Herbstschule Maria Laach, September 2005

23 SUSY particle production at the LHC In the MSSM one imposes a symmetry to avoid proton decay SUSY particles produced pairwise R = ( 1) 3B+L+2S { = +1 SM = 1 SUSY lightest SUSY particle stable (dark matter candidate) The interactions of MSSM particles are determined by gauge symmetry and SUSY example: gluon µ, a p, i no new coupling! q, j squark squark = i g s (T a ) ij (p + q) µ SUSY particles would be produced copiously at the LHC through QCD processes, e.g. g g Michael Krämer Page 23 Herbstschule Maria Laach, September 2005

24 SUSY particle production at the LHC Cross section predictions χ o + 2 χ 1 σ tot [pb]: pp g g, q q, t 1t 1, χ 2 o χ + 1, ν ν, χ o 2 g, χ o 2 q ν ν t 1t 1 χ o 2 q χ o 2 g q q g g S = 14 TeV NLO LO m [GeV] e.g. σ(pp g g) 1 pb for M gluino = 1 TeV 10 4 events/year Michael Krämer Page 24 Herbstschule Maria Laach, September 2005

25 SUSY searches at the LHC Distinctive signature due to cascade decays: multiple jets (and/or leptons) with large amount of missing energy g q (high-p T ) jets high-p T jets Events/50 GeV/10 fb χ 0 2, χ ± 1 χ 0 1 l jets and/or leptons 10 2 missing E T M eff (GeV) discovery reach for squarks and gluinos: M q, g < 2.5 TeV Michael Krämer Page 25 Herbstschule Maria Laach, September 2005

26 SUSY searches at the LHC SUSY is broken: SUSY-masses SM-masses L = L(SUSY) + L(SUSY-breaking) soft-breaking -terms: 124 parameters in the MSSM (SUSY is not to blame. The large number of the MSSM parameters is a consequence of our ignorance of the dynamics of SUSY-breaking) What is the mechanism of SUSY-breaking? The bottom-up approach: Measure the parameters of the SUSY Lagrangian at the LHC and test models of SUSY breaking. Will the accuracy of SUSY measurements at the LHC be sufficient to discriminate among different models of SUSY-breaking? Michael Krämer Page 26 Herbstschule Maria Laach, September 2005

27 A crucial test of SUSY models: the light Higgs MSSM Higgs sector: two Higgs doublets to give mass to up- and down-quarks 5 physical states: h, H, A, H ± The MSSM Higgs sector determined by tan β = v 2 /v 1 and M A. The couplings in the Higgs potential and the gauge couplings are related by supersymmetry. At tree level one finds M h M Z. This relation is modified by radiative corrections so that M h < 130 GeV (in the MSSM) The existence of a light Higgs boson with mass M h < 200 GeV is a generic prediction of SUSY models. Michael Krämer Page 27 Herbstschule Maria Laach, September 2005

28 A crucial test of SUSY models: the light Higgs One of the SUSY Higgs bosons will be seen at the LHC Michael Krämer Page 28 Herbstschule Maria Laach, September 2005

29 A crucial test of SUSY models: the light Higgs but it may look like the SM Higgs... Consider σ MSSM (gg h γγ) σ SM (gg h γγ) [Dedes, Heinemeyer, Su, Weiglein] < >1.5 msugra gg >h >γγ differences < 10% Needs precision measurements & calculations for production cross sections and b ranching ratios tanβ (GeV) M A Michael Krämer Page 29 Herbstschule Maria Laach, September 2005

30 Summary The LHC will find a Higgs boson or something that does its job The LHC should find signatures of BSM physics (SUSY?) Fundamental questions: How is SUSY broken? Does SUSY provide a viable dark matter candidate? link between collider physics and cosmology Exploring BSM physics may be difficult and will require in put from collider physics low energy physics (g 2, B decays, EDMs,...) ν physics astroparticle physics (cosmic rays,...) cosmology Michael Krämer Page 30 Herbstschule Maria Laach, September 2005