Predictions for Higgs signal and background processes with many-particle final states at the LHC Stefan Dittmaier MPI Munich PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 1
Contents 1 Introduction 2 The decays Higgs → WW/ZZ → 4 fermions 3 Higgs production via weak vector-boson fusion 4 Background processes with multi-particle final states 5 Technical issues in “NLO multi-leg calculations” 6 Conclusions PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 2
1 Introduction Experiments at LEP/SLC/Tevatron • confirmation of Standard Model as quantum field theory (quantum corrections significant) • top mass m t indirectly constrained by quantum corrections ↔ in agreement with m t measurement of Tevatron • Higgs mass M H indirectly constrained by quantum corrections ֒ → impact on Higgs searches m Limit = 144 GeV 6 Theory uncertainty ∆α had = ∆α (5) Great success of precision physics 5 0.02758 ± 0.00035 0.02749 ± 0.00012 – M H > 114 . 4 GeV incl. low Q 2 data (LEPHIGGS ’02) 4 e + e − − / → ZH at LEP2 ∆χ 2 3 – M H < 144 GeV (LEPEWWG ’07) 2 fit to precision data 1 i.e. via quantum corrections Excluded Preliminary 0 30 100 300 m H [ GeV ] PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 3
Higgs search at present and future colliders Higgs bosons couple proportional to particle masses: W , Z ¯ f ∝ m f ∝ M W H H f W , Z ⇒ Higgs production mainly via coupling to W/Z bosons or top quarks PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 4
Higgs search at present and future colliders Higgs bosons couple proportional to particle masses: W , Z ¯ f ∝ m f ∝ M W H H f W , Z ⇒ Higgs production mainly via coupling to W/Z bosons or top quarks Processes at hadron colliders ( p¯ p / pp ): q t H t t W , Z t H H H W , Z t W , Z t ¯ W , Z t q PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 4
Higgs search at present and future colliders Higgs bosons couple proportional to particle masses: W , Z ¯ f ∝ m f ∝ M W H H f W , Z ⇒ Higgs production mainly via coupling to W/Z bosons or top quarks Processes at hadron colliders ( p¯ p / pp ): q t H t t W , Z t H H H W , Z t W , Z t ¯ W , Z t q Processes at e + e − colliders: t ν e ¯ e + e + e + H W H H Z γ, Z W Z ¯ t e − e − e − ν e PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 4
Cross sections and significance of the Higgs signal at the LHC Spira et al. ’98 ATLAS ’03 Signal significance H → γ γ σ (pp → H+X) [ pb ] ∫ L dt = 30 fb -1 ttH (H → bb) 10 2 √ s = 14 TeV H → ZZ (*) → 4 l (no K-factors) H → WW (*) → l ν l ν ATLAS M t = 175 GeV gg → H 10 2 qqH → qq WW (*) 10 CTEQ4M qqH → qq ττ Total significance 1 qq → Hqq _ ’ → HW -1 qq 10 -2 10 10 _ → Htt _ gg,qq -3 10 _ → Hbb _ favoured _ → HZ gg,qq qq -4 10 0 200 400 600 800 1000 1 M H [ GeV ] 100 120 140 160 180 200 m H (GeV/c 2 ) Typical size perturbative corrections at next-to-leading order (NLO): QCD: O ( α s ) ∼ 10 − 100% Electroweak: O ( α ) ∼ 10% ֒ → calculate / control higher orders to reduce theoretical uncertainty down to the level of PDF ( q ¯ q ∼ 5% , gg ∼ 10% ) and experimental uncertainties Complication: many channels involve multi-particle final states. PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 5
1000 1 � b b W W �( H ) [GeV℄ Z Z 100 � t t 2 The decays Higgs → WW/ZZ → 4 fermions 0.1 � � g g 10 Hdecay Hdecay � 1 0.01 BR( H ) 0.1 � � 0.001 s � s 0.01 �� Z � 0.0001 0.001 100 130 160 200 300 500 700 1000 100 130 160 200 300 500 700 1000 M [GeV℄ M [GeV℄ H H Importance of decays H → WW ( ∗ ) / ZZ ( ∗ ) at the LHC: – most important Higgs decay channels for M H > ∼ 125 GeV – most precise determination of M H via H → ZZ → 4 l for M H > ∼ 130 GeV PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 6
Theoretical description of H → WW ( ∗ ) / ZZ ( ∗ ) : • previous work on partial decay widths not sufficient: ⋄ O ( α ) corrections to H → WW / ZZ with stable W’s/Z’s Fleischer, Jegerlehner ’81; Kniehl ’91; Bardin, Vilenskii, Khristova ’91 ⋄ lowest-order predictions for H → WW ( ∗ ) / ZZ ( ∗ ) e.g. by Hdecay (Djouadi, Kalinowski, Spira ’98) • however: proper description of distributions required ⋄ for the kinematical reconstruction of Z’s, W’s, and H ֒ → invariant-mass distributions ⋄ for the verification of spin 0 and CP parity of the Higgs boson Nelson ’88; Soni, Xu ’93; Chang et al.’93; ֒ → angular and invariant-mass distributions Skjold, Osland ’93; Barger et al.’93; Arens, Sehgal ’94; Buszello et al.’02; Choi et al.’03 Recent progress: • PROPHECY4 F : Monte Carlo generator for H → WW / ZZ → 4 f with EW and QCD corrections Bredenstein, Denner, S.D., Weber ’06 • combination of production and decay: Anastasiou et al. ’07,’08; ( gg → H in NNLO QCD ) ⊗ (H → WW / ZZ → 4 l in LO ) Frederix, Grazzini ’08; Grazzini ’08 PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 7
Survey of Feynman diagrams for NLO EW and QCD corrections to H → 4 f f ❵ V f Lowest order: H f V f ❵ Typical one-loop diagrams: # diagrams = O (200 − 400) f f f pentagons boxes f V f f f V V f V f V V H H H f S f f V V f f V f f f f f f f V vertices self-energies V V f S f f V f V V V S f f V f V f H f f H f V H H V V V V f f f f + photon / gluon bremsstrahlung PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 8
Features of PROPHECY4 F : Bredenstein, Denner, S.D., Weber ’06 • O ( α ) and O ( α s ) corrections to all channels H → WW / ZZ → 4 f • final-state radiation off leptons beyond O ( α ) via structure functions • leading 2-loop heavy-Higgs effects ∝ G 2 µ M 4 H Ghinculov ’95; Frink, Kniehl, Kreimer, Riesselmann ’96 • multi-channel Monte Carlo integration (checked by VEGAS ) Berends, Kleiss, Pittau ’94; Kleiss, Pittau ’94 • improved Born approximation for simplified evaluation Main complications in the loop calculation: • numerical instabilities in Passarino–Veltman reduction of tensor integrals ֒ → new reduction methods developed Denner, S.D. ’02,’05 • gauge-invariant treatment of W and Z resonances ֒ → “complex-mass scheme” Denner, S.D., Roth, Wieders ’05 New concepts already used in O ( α ) correction to e + e − → 4 f Denner, S.D., Roth, Wieders ’05 PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 9
The complex-mass scheme for unstable particles Problem of unstable particles: description of resonances requires resummation of propagator corrections ֒ → mixing of perturbative orders potentially violates gauge invariance Dyson series and propagator poles (scalar example) = + + + . . . i i i i G φφ ( p ) p 2 − m 2 iΣ( p 2 ) = p 2 − m 2 + p 2 − m 2 + . . . = p 2 − m 2 + Σ( p 2 ) Σ( p 2 ) = renormalized self-energy, m = ren. mass Im { Σ( p 2 ) } = 0 at p 2 ∼ m 2 stable particle: → propagator pole for real value of p 2 , ֒ Σ( m 2 ) = 0 renormalization condition for physical mass m : Im { Σ( p 2 ) } � = 0 at p 2 ∼ m 2 unstable particle: → location µ 2 of propagator pole is complex, ֒ µ 2 = M 2 − i M Γ possible definition of mass M and width Γ : PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 10
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