Introduction: from W W -scattering to the Higgs boson

Transcription

1 Introduction: from W W -scattering to the Higgs boson Michael Krämer Page 2 Universität Bielefeld, Mai 2005

2 Introduction: from W W -scattering to the Higgs boson Fermi: weak interactions described by effective Lagrangian eg. for µ decay µ e ν e ν µ L = G F 2 [ ν µ γ λ (1 γ 5 )µ][ēγ λ (1 γ 5 )ν e ] with G F GeV 2 (Fermi coupling) Michael Krämer Page 2 Universität Bielefeld, Mai 2005

3 Introduction: from W W -scattering to the Higgs boson Fermi: weak interactions described by effective Lagrangian eg. for µ decay µ e ν e ν µ L = G F 2 [ ν µ γ λ (1 γ 5 )µ][ēγ λ (1 γ 5 )ν e ] with G F GeV 2 (Fermi coupling) Fermi theory at high energies: M[ ν µ e µ ν e ] G F 2 2π s violates unitarity Michael Krämer Page 2 Universität Bielefeld, Mai 2005

4 Introduction: from W W -scattering to the Higgs boson Fermi: weak interactions described by effective Lagrangian eg. for µ decay µ e ν e ν µ L = G F 2 [ ν µ γ λ (1 γ 5 )µ][ēγ λ (1 γ 5 )ν e ] with G F GeV 2 (Fermi coupling) Fermi theory at high energies: M[ ν µ e µ ν e ] G F 2 2π s violates unitarity Solution: interaction mediated by heavy vector boson W ± M[ ν µ e µ ν e ] G F s 2 2π M 2 W M 2 W s (with M W 100 GeV) Michael Krämer Page 2 Universität Bielefeld, Mai 2005

5 Introduction: from W W -scattering to the Higgs boson Consider W W W W M[W L W L W L W L ] s violates unitarity Michael Krämer Page 3 Universität Bielefeld, Mai 2005

6 Introduction: from W W -scattering to the Higgs boson Consider W W W W M[W L W L W L W L ] s violates unitarity Solution: strong W W interaction at high energies or new scalar particle H with g W W H M W M GF M 2H 4 2π Michael Krämer Page 3 Universität Bielefeld, Mai 2005

7 Introduction: from W W -scattering to the Higgs boson Consider W W W W M[W L W L W L W L ] s violates unitarity Solution: strong W W interaction at high energies or new scalar particle H with g W W H M W M GF M 2H 4 2π Unitarity properties of H: coupling g XXH particle mass M X M H < 1 TeV Michael Krämer Page 3 Universität Bielefeld, Mai 2005

8 Introduction: The ABEGHHK th Mechanism (Anderson, Brout, Englert, Guralnik, Hagen, Higgs, Kibble, t Hooft) Spontaneous symmetry breaking through scalar isodoublet φ L φ = D µ φ 2 + g d f ψ d Lφf d R + g u f ψ d L φf u R V (φ) scalar potential V = µ 2 φ 2 + λ φ 4 introduce Higgs field H: φ ( ) 0 (v+h)/ 2 (unitary gauge) Goldstone bosons longitudinal components of W, Z SM is renormalisable gauge field theory including W and Z boson masses and a physical Higgs particle Michael Krämer Page 4 Universität Bielefeld, Mai 2005

9 Introduction: The Higgs boson Michael Krämer Page 5 Universität Bielefeld, Mai 2005

10 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 Michael Krämer Page 5 Universität Bielefeld, Mai 2005

11 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 5 Universität Bielefeld, Mai 2005

12 ! " Higgs boson hunting: indirect searches Quantum corrections to precision observables m 2 t log M H Michael Krämer Page 6 Universität Bielefeld, Mai 2005

13 # % # # $ & Higgs boson hunting: indirect searches Quantum corrections to precision observables m 2 t log M H 200 High Q 2 except m t 68% CL m t [GeV] m t (TEVATRON) 140 Excluded Preliminary (a) m H [GeV] Michael Krämer Page 6 Universität Bielefeld, Mai 2005

14 ' ) ' ' ( * Higgs boson hunting: indirect searches Quantum corrections to precision observables m 2 t log M H 200 High Q 2 except m t 68% CL Experimental data consistent with SM m t [GeV] 180 m t (TEVATRON) M H < 260 GeV (95% CL) (LEPEWWG) Excluded Preliminary (a) m H [GeV] Michael Krämer Page 6 Universität Bielefeld, Mai 2005

15 ,. Higgs boson hunting: indirect searches Quantum corrections to precision observables m 2 t log M H 200 High Q 2 except m t 68% CL Experimental data consistent with SM m t [GeV] m t (TEVATRON) M H < 260 GeV (95% CL) (LEPEWWG) Note: Precision data also consistent with SUSY models 140 Excluded Preliminary (a) m H [GeV] No evidence for ESWB through new strong interactions (eg. technicolour) Michael Krämer Page 6 Universität Bielefeld, Mai 2005

16 Higgs boson hunting To establish the Higgs mechanism we need to discover the Higgs boson directly at a high-energy collider measure the couplings g XXφ M X reconstruct the Higgs potential Michael Krämer Page 7 Universität Bielefeld, Mai 2005

17 Higgs boson hunting: collider searches Higgs decay modes and branching ratios 1 bb _ WW [HDECAY: M. Spira et al.] BR(H) ZZ 10-1 τ + τ cc _ tt - gg 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 8 Universität Bielefeld, Mai 2005

18 Higgs boson hunting: past and present colliders search at the CERN LEP2 (e + e collider with s < 200 GeV) e + e / ZH M H > GeV (95% CL) (LEPHIGGSWG) Michael Krämer Page 9 Universität Bielefeld, Mai 2005

19 Higgs boson hunting: past and present colliders search at the CERN LEP2 (e + e collider with s < 200 GeV) e + e / ZH M H > GeV (95% CL) (LEPHIGGSWG) search at the Fermilab Tevatron (p p collider with s = 2 TeV) current L = 0.7 fb 1 expectation in 2008: L = 4 6 fb 1 Michael Krämer Page 9 Universität Bielefeld, Mai 2005

20 The Large Hadron Collider LHC pp collider located at CERN circumference 27 km s = 14 TeV L = fb 1 /year in operation from April 2007 Michael Krämer Page 10 Universität Bielefeld, Mai 2005

21 We will start in 2007 CMS HB+1 CMS HB-1 Installation of readout boxes started source calibration in Insertion in vacuum tank: Summer Michael Kra mer Page 11 Universita t Bielefeld, Mai 2005

22 Higgs boson search at the LHC 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 Universität Bielefeld, Mai 2005

23 Higgs boson searches 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 13 Universität Bielefeld, Mai 2005

24 0 / / / Higgs boson searches at the LHC: cross section predictions 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] 0 / Michael Krämer Page 14 Universität Bielefeld, Mai 2005

25 Higgs boson searches 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 15 Universität Bielefeld, Mai 2005

26 Higgs boson searches at the LHC: why precision calculations? Higgs discovery through resonance peak, eg. H γγ Events / 2 GeV Signal-background, events / 2 GeV m γγ (GeV) m γγ (GeV) Michael Krämer Page 16 Universität Bielefeld, Mai 2005

27 Higgs boson searches at the LHC: why precision calculations? Higgs discovery through resonance peak, eg. H γγ Events / 2 GeV Signal-background, events / 2 GeV m γγ (GeV) m γγ (GeV) However, need precision calculations 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) Michael Krämer Page 16 Universität Bielefeld, Mai 2005

28 Higgs boson searches at the LHC: why precision calculations? Example: MSSM Higgs sector two Higgs doublets to give mass to up- and down-quarks 5 physical states: h, H, A, H ± MSSM Higgs sector determined by tan β = v 2 /v 1 and M A Michael Krämer Page 17 Universität Bielefeld, Mai 2005

29 Higgs boson searches at the LHC: why precision calculations? Example: MSSM Higgs sector two Higgs doublets to give mass to up- and down-quarks 5 physical states: h, H, A, H ± MSSM Higgs sector determined by tan β = v 2 /v 1 and M A 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 branching ratios tanβ (GeV) M A Michael Krämer Page 17 Universität Bielefeld, Mai 2005

30 Particle production at hadron colliders Example: Drell-Yan process :;=< ;?> E C F=GHI B KJ F H MLJ N N E Michael Krämer Page 18 Universität Bielefeld, Mai 2005

31 Particle production at hadron colliders Example: Drell-Yan process OP=Q P?R W V X=YZ[ UDV S U ]\ X Z _^\ `` W T S Cross section: σ pp l + l = q dx 1 dx 2 f q (x 1 ) f q (x 2 ) ˆσ q q l + l Michael Krämer Page 18 Universität Bielefeld, Mai 2005

32 Particle production at hadron colliders Example: Drell-Yan process ab=c b?d i h j=klm gdh e g on j l qpn r r i f e Cross section: σ pp l + l = q dx 1 dx 2 f q (x 1 ) f q (x 2 ) ˆσ q q l + l f q, q (x) dx: probability to find (anti)quark with momentum fraction x process independent, measured in DIS Michael Krämer Page 18 Universität Bielefeld, Mai 2005

33 Particle production at hadron colliders Example: Drell-Yan process st=u t?v { z =}~ ydz w y ~ ƒ { x w Cross section: σ pp l + l = q dx 1 dx 2 f q (x 1 ) f q (x 2 ) ˆσ q q l + l f q, q (x) dx: probability to find (anti)quark with momentum fraction x process independent, measured in DIS ˆσ q q l + l : hard scattering cross section calculable in perturbation theory Michael Krämer Page 18 Universität Bielefeld, Mai 2005

34 Particle production at hadron colliders Factorization is non-trivial beyond leading order Michael Krämer Page 19 Universität Bielefeld, Mai 2005

35 Particle production at hadron colliders Factorization is non-trivial beyond leading order virtual corrections ˆŠ ˆ UV divergences IR divergences Michael Krämer Page 19 Universität Bielefeld, Mai 2005

36 Œ Œ Particle production at hadron colliders Factorization is non-trivial beyond leading order virtual corrections ŽŠ Ž real corrections Š UV divergences IR divergences IR divergences collinear divergences Michael Krämer Page 19 Universität Bielefeld, Mai 2005

37 Particle production at hadron colliders Factorization is non-trivial beyond leading order virtual corrections Š real corrections œš š ž œ š UV divergences IR divergences IR divergences collinear divergences UV divergences renormalization (α s (µ ren ) etc.) IR divergences cancel between virtual and real (KLN) collinear initial state divergences can be absorbed in pdfs Michael Krämer Page 19 Universität Bielefeld, Mai 2005

38 Ÿ Particle production at hadron colliders Initial state collinear singularities, eg. process independent divergence in dk 2 T as k2 T 0 Michael Krämer Page 20 Universität Bielefeld, Mai 2005

39 ª Particle production at hadron colliders Initial state collinear singularities, eg. process independent divergence in dk 2 T as k2 T 0 absorb singularity in parton densities: f q (x, µ fac ) = f q (x) + { divergent part of µ 2 fac 0 dk 2 T } Michael Krämer Page 20 Universität Bielefeld, Mai 2005

40 «Particle production at hadron colliders Initial state collinear singularities, eg. process independent divergence in dk 2 T as k2 T 0 absorb singularity in parton densities: f q (x, µ fac ) = f q (x) + { divergent part of µ 2 fac 0 dk 2 T } Hadron collider cross section σ = dx 1 f P i (x 1, µ F ) dx 2 f P j (x 2, µ F ) n α n s (µ R ) C n (µ R, µ F ) + O(Λ QCD /Q) (Collins, Soper, Sterman and many others) Michael Krämer Page 20 Universität Bielefeld, Mai 2005

41 Particle production at hadron colliders Scale dependence σ = dx 1 fi P (x 1, µ F ) dx 2 f P j (x 2, µ F ) n α n s (µ R ) C n (µ R, µ F ) finite order in perturbation theory artificial µ-dependence: dσ d ln µ 2 R N = αs n (µ R ) C n (µ R, µ F ) n=0 = O(α s (µ R ) N+1 ) scale dependence theoretical uncertainty due to HO corrections Michael Krämer Page 21 Universität Bielefeld, Mai 2005

42 Particle production at hadron colliders Scale dependence Example: rapidity distribution in pp W +X σ = dx 1 fi P (x 1, µ F ) dx 2 f P j (x 2, µ F ) [Anastasiou, Dixon, Melnikov, Petriello 03] n α n s (µ R ) C n (µ R, µ F ) finite order in perturbation theory artificial µ-dependence: dσ d ln µ 2 R N = αs n (µ R ) C n (µ R, µ F ) n=0 = O(α s (µ R ) N+1 ) scale dependence theoretical uncertainty due to HO corrections significant reduction of µ dependence at (N)NLO Michael Krämer Page 21 Universität Bielefeld, Mai 2005

43 Particle production at hadron colliders pdf uncertainties σ W. B lν (nb) MRST NLO and NNLO partons NNLO NLO [Martin, Roberts, Stirling, Thorne 03] Tevatron Q 2 cut = 7 GeV2 Q 2 = 10 GeV2 cut x cut = pdf < 5% (CTEQ, MRST, Alekhin,...) Michael Krämer Page 22 Universität Bielefeld, Mai 2005

44 Particle production at hadron colliders Precision physics at hadron colliders requires the calculation of QCD corrections at (N)NLO; the precision determination of input pdfs; the resummation of large logarithmic corrections; matching of fixed order calculations with parton showers & hadronization; the inclusion of electroweak corrections. Michael Krämer Page 23 Universität Bielefeld, Mai 2005

45 ² ± Higgs production cross sections: theoretical status Higgs production in gluon-gluon fusion ³ ³ Michael Krämer Page 24 Universität Bielefeld, Mai 2005

46 µ Higgs production cross sections: theoretical status Higgs production in gluon-gluon fusion NLO corrections: K NLO 1.7 [Spira, Djouadi, Graudenz, Zerwas; Dawson, Kauffman] Michael Krämer Page 24 Universität Bielefeld, Mai 2005

47 Higgs production cross sections: theoretical status Higgs production in gluon-gluon fusion ¹ ¹ NLO corrections: K NLO 1.7 [Spira, Djouadi, Graudenz, Zerwas; Dawson, Kauffman] NNLO corrections: K NNLO (m top M H ) 2 [Harlander, Kilgore; Anastasiou, Melnikov 02; Ravindran et al. 03] consistent with calculations based on soft/collinear gluon approximations [MK, Laenen, Spira; Catani et al.] Michael Krämer Page 24 Universität Bielefeld, Mai 2005

48 » º Higgs production cross sections: theoretical status Higgs production in gluon-gluon fusion ¼ ¼ NLO corrections: K NLO 1.7 [Spira, Djouadi, Graudenz, Zerwas; Dawson, Kauffman] 10 2 σ(pp H+X) [pb] [Harlander, Kilgore 02] s = 14 TeV NNLO corrections: K NNLO (m top M H ) 2 [Harlander, Kilgore; Anastasiou, Melnikov 02; Ravindran et al. 03] consistent with calculations based on soft/collinear gluon approximations [MK, Laenen, Spira; Catani et al.] 10 LO NLO NNLO M H [GeV] Michael Krämer Page 24 Universität Bielefeld, Mai 2005

49 ¾ ½ Higgs production cross sections: theoretical status Higgs production in gluon-gluon fusion NLO corrections: K NLO 1.7 [Spira, Djouadi, Graudenz, Zerwas; Dawson, Kauffman] 10 2 σ(pp H+X) [pb] [Harlander, Kilgore 02] s = 14 TeV NNLO corrections: K NNLO (m top M H ) 2 [Harlander, Kilgore; Anastasiou, Melnikov 02; Ravindran et al. 03] consistent with calculations based on soft/collinear gluon approximations [MK, Laenen, Spira; Catani et al.] 10 LO NLO NNLO NNLO scale dependence < 15% M H [GeV] Michael Krämer Page 24 Universität Bielefeld, Mai 2005

50 à à À Á?Â Ä À Á? à à Higgs production cross sections: theoretical status Vector boson fusion discovery channel & measurement of Higgs couplings [Kauer, Plehn, Rainwater, Zeppenfeld] NLO QCD corrections (cf DIS) +10% [Han, Valencia, Willenbrock] Michael Krämer Page 25 Universität Bielefeld, Mai 2005

51 È È Å Æ?Ç É Å Æ?Ç È È Higgs production cross sections: theoretical status Vector boson fusion Associated VH production ÑÓÒ Ô Î Ï Ê ËÍÌ Ð Î discovery channel & measurement of Higgs couplings [Kauer, Plehn, Rainwater, Zeppenfeld] NLO QCD corrections (cf DIS) +10% [Han, Valencia, Willenbrock] crucial for Tevatron search (M H < 130 GeV) NLO QCD corrections +(30 40)% [Han, Willenbrock] NNLO QCD corrections +10% [Brein, Djouadi, Harlander 03] NLO electroweak corrections 10% [Ciccolini, Dittmaier, MK 03] Michael Krämer Page 25 Universität Bielefeld, Mai 2005

52 Associated W H and ZH production: QCD + EW corrections K WH (LHC) QCD QCD+EW M H [GeV] K WH (Tevatron) QCD QCD+EW M H [GeV] K ZH (LHC) QCD QCD+EW K ZH (Tevatron) QCD QCD+EW M H [GeV] M H [GeV] Michael Krämer Page 26 Universität Bielefeld, Mai 2005

53 Õ Õ Ö Higgs production cross sections: theoretical status Higgs production in association with top quarks Ö Ø Michael Krämer Page 27 Universität Bielefeld, Mai 2005

54 Ù Û Ù Ú Higgs production cross sections: theoretical status Higgs production in association with top quarks Ú Ü σ(t th) < 1 pb (LHC, M H > 115 GeV) but: distinctive final state: pp t( W + b) t( W b) H( b b) important contribution to 5σ discovery for M H < 130 GeV Michael Krämer Page 27 Universität Bielefeld, Mai 2005

55 Ý ß Ý Þ Higgs production cross sections: theoretical status Higgs production in association with top quarks Þ à σ(t th) < 1 pb (LHC, M H > 115 GeV) but: distinctive final state: pp t( W + b) t( W b) H( b b) important contribution to 5σ discovery for M H < 130 GeV cross section g 2 tth direct measurement of top Yukawa coupling δg tth /g tth 15% (exp.) [Drollinger, Müller, Denegri] Michael Krämer Page 27 Universität Bielefeld, Mai 2005

56 á ã á â Higgs production cross sections: theoretical status Higgs production in association with top quarks â ä σ(t th) < 1 pb (LHC, M H > 115 GeV) but: distinctive final state: pp t( W + b) t( W b) H( b b) important contribution to 5σ discovery for M H < 130 GeV cross section g 2 tth direct measurement of top Yukawa coupling δg tth /g tth 15% (exp.) [Drollinger, Müller, Denegri] [Beenakker, Dittmaier, MK, Plümper, Spira, Zerwas] σ(pp tt _ H + X) [fb] s = 14 TeV M H = 120 GeV µ 0 = m t + M H /2 LO NLO µ/µ 0 Michael Krämer Page 27 Universität Bielefeld, Mai 2005

57 å ç å æ Higgs production cross sections: theoretical status Higgs production in association with top quarks æ è σ(t th) < 1 pb (LHC, M H > 115 GeV) but: distinctive final state: pp t( W + b) t( W b) H( b b) important contribution to 5σ discovery for M H < 130 GeV cross section g 2 tth direct measurement of top Yukawa coupling δg tth /g tth 15% (exp.) [Drollinger, Müller, Denegri] [Beenakker, Dittmaier, MK, Plümper, Spira, Zerwas] σ(pp tt _ H + X) [fb] s = 14 TeV M H = 120 GeV µ 0 = m t + M H /2 LO NLO NLO scale dependence < 15% [Beenakker, Dittmaier, MK, Plümper, Spira, Zerwas 01; Dawson, Jackson, Orr, Reina, Wackeroth 01-03] µ/µ 0 Michael Krämer Page 27 Universität Bielefeld, Mai 2005

58 Higgs production cross sections: theoretical status Recent progress for SM Higgs production includes NNLO QCD calculations for pp H [Harlander, Kilgore; Anastasiou, Melnikov; Ravindran, Smith, van Neerven; Anastasiou, Melnikov, Petriello; Blümlein, Ravindran;... (02-05)] 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 28 Universität Bielefeld, Mai 2005

59 Higgs production in the MSSM: associated b bh production Associated b bh/h production is crucial for MSSM Higgs searches at large tan β Bottom-Higgs Yukawa coupling: g MSSM bbh = sin α cos β gsm bbh } tan β 1 { tan β g SM bbh (M h M A M Z ) g MSSM bbh = cos α cos β gsm bbh tan β g SM bbh (M H M A M Z ) Michael Krämer Page 29 Universität Bielefeld, Mai 2005

60 Higgs production in the MSSM: associated b bh production Associated b bh/h production is crucial for MSSM Higgs searches at large tan β Bottom-Higgs Yukawa coupling: g MSSM bbh = sin α cos β gsm bbh } tan β 1 { tan β g SM bbh (M h M A M Z ) g MSSM bbh = cos α cos β gsm bbh tan β g SM bbh (M H M A M Z ) [Spira] At tan β 1 associated b bh/h production becomes the dominant MSSM Higgs production mechanism Cross-section (pb) h H Hbb tan β = 30 Maximal mixing gg H (SM) Hqq gg H 10-2 Htt HZ HW m h/h (GeV) Michael Krämer Page 29 Universität Bielefeld, Mai 2005

61 Associated b bh production mechanism At leading order Michael Krämer Page 30 Universität Bielefeld, Mai 2005

62 Associated b bh production mechanism At leading order }{{}}{{}}{{} M Q M H : α 2 s ln 2 (M H /M Q ) α 2 s ln(m H /M Q ) α 2 s Michael Krämer Page 30 Universität Bielefeld, Mai 2005

63 Associated b bh production mechanism At leading order }{{}}{{}}{{} M Q M H : α 2 s ln 2 (M H /M Q ) α 2 s ln(m H /M Q ) α 2 s Summation of ln(m H /M Q ) terms by using heavy quark PDFs [Collins, Olness, Tung; Barnett, Haber, Soper; Dicus, Willenbrock,... ] M Q M H Michael Krämer Page 30 Universität Bielefeld, Mai 2005

64 Associated b bh production: two calculational schemes 4-flavour scheme 5-flavour scheme Michael Krämer Page 31 Universität Bielefeld, Mai 2005

65 Associated b bh production: two calculational schemes 4-flavour scheme 5-flavour scheme + exact g b b splitting & mass effects no summation of ln(m H /M b ) terms Michael Krämer Page 31 Universität Bielefeld, Mai 2005

66 Associated b bh production: two calculational schemes 4-flavour scheme 5-flavour scheme + exact g b b splitting & mass effects no summation of ln(m H /M b ) terms + summation of ln(m H /M b ) terms LL approximation to g b b splitting Michael Krämer Page 31 Universität Bielefeld, Mai 2005

67 Associated b bh production: two calculational schemes 4-flavour scheme 5-flavour scheme + exact g b b splitting & mass effects no summation of ln(m H /M b ) terms + summation of ln(m H /M b ) terms LL approximation to g b b splitting The 4- and 5-flavour schemes are both theoretically consistent & well-defined represent different ways of ordering perturbation theory should agree at sufficiently high order do not match exactly at finite order Michael Krämer Page 31 Universität Bielefeld, Mai 2005

68 Associated b bh production: two calculational schemes Comparison at leading order strong scale dependence σ(b b H) σ(gg b bh) at µ = M H Michael Krämer Page 32 Universität Bielefeld, Mai 2005

69 Associated b bh production: two calculational schemes Comparison at leading order strong scale dependence σ(b b H) σ(gg b bh) at µ = M H Michael Krämer Page 32 Universität Bielefeld, Mai 2005

70 Associated b bh production: two calculational schemes Comparison at leading order strong scale dependence σ(b b H) σ(gg b bh) at µ = M H discrepancy reduced at µ F = M H /4 ( Harlander, Kilgore) [see also Spira; Maltoni, Sullivan, Willenbrock; Boos, Plehn] Michael Krämer Page 32 Universität Bielefeld, Mai 2005

71 Associated b bh production: (N)NLO corrections Comparison of 4- and 5-flavour schemes at (N)NLO (SM Higgs, LHC) [Harlander, Kilgore; Dittmaier, MK, Spira] 10 3 σ(pp bb _ h + X) [fb] s = 14 TeV µ = (2m b + M h )/ bb _ h (NNLO) 10 gg bb _ h (NLO) M h [GeV] Michael Krämer Page 33 Universität Bielefeld, Mai 2005

72 Higgs background calculations Example: pp H γγ/w W backgrounds γγ background NLO parton level MC program pp γγ (DIPHOX) [Binoth, Guillet, Heinrich, Pilon, Werlen] gg γγ at NLO (2-loop) [Bern, De Freitas, Dixon, Schmidt 02] W W background jet veto effects [Catani, De Florian, Grazzini] NLO parton level MC program pp W + W [Frixione, Nason, Ridolfi; Baur, Han, Ohnemus] NLO spin correlations in leptonic W decays [Dixon, Kunszt, Signer] t t backgrounds including finite width effects [Kauer, Zeppenfeld] NLO parton level MC program pp W/Z + b b [Campbell, Ellis, Veseli] gluon-gluon induced contributions to pp W W lνlν [Binoth, Ciccolini, Kauer, MK 05] Michael Krämer Page 34 Universität Bielefeld, Mai 2005

73 W W production: a background to Higgs searches pp H W W l ν l ν is an important Higgs search channel W W pair production is the dominant background: σ BR 5 times larger than signal a Higgs mass peak cannot be reconstructed from leptonic W decays theoretical control of the background is important ( 5%!) Michael Krämer Page 35 Universität Bielefeld, Mai 2005

74 W W production: a background to Higgs searches pp H W W l ν l ν is an important Higgs search channel W W pair production is the dominant background: σ BR 5 times larger than signal a Higgs mass peak cannot be reconstructed from leptonic W decays theoretical control of the background is important ( 5%!) experimental selection cuts to enhance the signal/background ratio may amplify the importance of higher-order corrections for background processes Michael Krämer Page 35 Universität Bielefeld, Mai 2005

75 W W production: a background to Higgs searches pp H W W l ν l ν is an important Higgs search channel W W pair production is the dominant background: σ BR 5 times larger than signal a Higgs mass peak cannot be reconstructed from leptonic W decays theoretical control of the background is important ( 5%!) experimental selection cuts to enhance the signal/background ratio may amplify the importance of higher-order corrections for background processes example: gg W W l ν l ν [Binoth, Ciccolini, Kauer, MK (05)] g d W e d ν µ g d W + u ν e µ + formally NNLO but enhanced by Higgs search cuts gg q q (NLO) corr. σ tot 54 fb 1373 fb 4% σ bkg 1.39 fb 4.8 fb 30% Michael Krämer Page 35 Universität Bielefeld, Mai 2005

76 Summary and Conclusions Michael Krämer Page 36 Universität Bielefeld, Mai 2005

77 Summary and Conclusions The LHC will find the (or a or various) Higgs boson(s) (or some new strong interactions in the gauge boson sector) Michael Krämer Page 36 Universität Bielefeld, Mai 2005

78 Summary and Conclusions The LHC will find the (or a or various) Higgs boson(s) (or some new strong interactions in the gauge boson sector) Higgs physics is exciting: reveals the mechanism of electroweak symmetry breaking points towards physics beyond the SM (hierarchy problem) Michael Krämer Page 36 Universität Bielefeld, Mai 2005

79 Summary and Conclusions The LHC will find the (or a or various) Higgs boson(s) (or some new strong interactions in the gauge boson sector) Higgs physics is exciting: reveals the mechanism of electroweak symmetry breaking points towards physics beyond the SM (hierarchy problem) Exploring Higgs physics at the LHC needs precision measurements and precision calculations signal cross sections are now known within 15% or better more work is needed to improve prediction of background processes Michael Krämer Page 36 Universität Bielefeld, Mai 2005

80 Summary and Conclusions The LHC will find the (or a or various) Higgs boson(s) (or some new strong interactions in the gauge boson sector) Higgs physics is exciting: reveals the mechanism of electroweak symmetry breaking points towards physics beyond the SM (hierarchy problem) Exploring Higgs physics at the LHC needs precision measurements and precision calculations signal cross sections are now known within 15% or better more work is needed to improve prediction of background processes Exciting times ahead! Michael Krämer Page 36 Universität Bielefeld, Mai 2005