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Finding the Higgs boson

Finding the Higgs boson. Sally Dawson, BNL XIII Mexican School of Particles and Fields Lecture 1, Oct, 2008. Properties of the Higgs boson Higgs production at the Tevatron and LHC Discovery vs spectroscopy. Collider Physics Timeline. First collisions in Spring, 2009. Tevatron. LHC.

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Finding the Higgs boson

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  1. Finding the Higgs boson Sally Dawson, BNL XIII Mexican School of Particles and Fields Lecture 1, Oct, 2008 • Properties of the Higgs boson • Higgs production at the Tevatron and LHC Discovery vs spectroscopy

  2. Collider Physics Timeline First collisions in Spring, 2009 Tevatron LHC LHC L Upgrade ILC 2007 2008 2015 e+e- @ 500 GeV, earliest possible date, 202x 15+ billion $’s Planned shut-down in 2010

  3. proton-proton collider at CERN (2008) 14 TeV energy 7 mph slower than the speed of light cf. 2 TeV @ Fermilab ( 307 mph slower than the speed of light) Typical energy of quarks and gluons 1-2 TeV Large Hadron Collider (LHC)

  4. Detectors of Unprecedented Scale • Two large multi-purpose detectors • CMS is 12,000 tons (2 x’s ATLAS) • ATLAS has 8 times the volume of CMS

  5. Standard Model Synopsis • Group: SU(3) x SU(2) x U(1) • Gauge bosons: • SU(3): Gi, i=1…8 • SU(2): Wi, i=1,2,3 • U(1): B • Gauge couplings: gs,g, g • SU(2) Higgs doublet:  QCD Electroweak Gauge symmetry forbids gauge boson masses

  6. The Problem of Mass • Why are the W and Z boson masses non-zero? • U(1) gauge theory with spin-1gauge field, A • U(1) local gauge invariance:

  7. The Problem of Masses • Mass term for A would look like: • Mass term violates local gauge invariance • We understand why MA = 0 Gauge invariance is guiding principle

  8. SM Higgs Mechanism • Standard Model includes complex Higgs SU(2) doublet • With SU(2) x U(1) invariant scalar potential • 2 > 0, boring….. (Minimum at =0, gauge bosons stay massless)

  9. SM Higgs Mechanism • If 2 < 0, then spontaneous symmetry breaking • Minimum of potential at: • Choice of minimum breaks gauge symmetry • Why is 2 < 0?

  10. More on SM Higgs Mechanism • Couple  to SU(2) x U(1) gauge bosons (Wi, i=1,2,3; B) • Gauge boson mass terms from: Higgs mechanism gives gauge bosons mass

  11. More on SM Higgs Mechanism MW=gv/2 MZ=(g2+g'2)v/2 • Massive gauge bosons: W = (W1 W2) /2 Z 0 = (g W3 - g'B )/ (g2+g'2) • Orthogonal combination to Z is massless photon A 0 = (g' W3+gB )/ (g2+g'2)

  12. More on SM Higgs Mechanism • Weak mixing angle defined • Z = - sin WB + cosWW3 • A = cos WB + sinWW3 MW=MZ cos W Natural relationship in SM—Provides stringent restriction on Beyond the SM models

  13. Recap • Generate mass for W,Z using Higgs mechanism • Higgs VEV breaks SU(2) x U(1)U(1)em • Single Higgs doublet is minimal case • Before spontaneous symmetry breaking: • Massless Wi, B, Complex  • After spontaneous symmetry breaking: • Massive W,Z; massless ; physical Higgs boson H Exercise: Count degrees of freedom

  14. Muon decay • EW Theory: • Consider  e e • Fermi Theory:     W e e e e GF=1.16637 x 10-5 GeV-2

  15. Higgs Parameters • GF measured precisely • Higgs potential has 2 free parameters, 2,  • Trade 2,  for v2, MH2 • Large MHstrong Higgs self-coupling • A priori, Higgs mass can be anything

  16. What about Fermion Masses? Forbidden by SU(2)xU(1) gauge invariance • Fermion mass term: • Left-handed fermions are SU(2) doublets • Scalar couplings to fermions: • Effective Higgs-fermion coupling • Mass term for down quark 

  17. Fermion Masses, 2 • Mu from c=i2* (not allowed in SUSY) • For 3 generations, , =1,2,3 (flavor indices)

  18. Fermion masses, 3 • Unitary matrices diagonalize mass matrices • Yukawa couplings are diagonal in mass basis • Neutral currents remain flavor diagonal • Not necessarily true in models with extended Higgs sectors Exercise: Prove this!

  19. Review of Higgs Couplings • Higgs couples to fermion mass • Largest coupling is to heaviest fermion • Top-Higgs coupling plays special role? • No Higgs coupling to neutrinos • Higgs couples to gauge boson masses • Only free parameter is Higgs mass! • Everything is calculable….testable theory

  20. Review of Higgs Boson Feynman Rules • Higgs couples to heavy particles • No tree level coupling to photons () or gluons (g) • MH2=2v2large MH is strong coupling regime

  21. Higgs Decays • Hff proportional to mf2 • Identifying b quarks important for Higgs searches For MH<2MW, decays to bb most important

  22. Higgs Decays to Gluons g • Top quark contribution most important • Doesn’t decouple for large mt • Decoupling theorem doesn’t apply to particles which couple to mass (ie Higgs!) • Decay sensitive to extra generations H g

  23. Higgs Decays to Photons • Dominant contribution is W loops • Contribution from top is small W top

  24. Higgs Decays to W/Z W+ • Tree level decay • Below threshold, H→WW* with branching ratio W* →ff' implied • Final state has both transverse and longitudinal polarizations H W- f W+ f' H W-

  25. Higgs Decays to W+ W-, ZZ • The action is with longitudinal gauge bosons (since they come from the EWSB) • Cross sections involving longitudinal gauge bosons grow with energy • H→WL+WL+ • As Higgs gets heavy, decays are longitudinal Exercise: Prove this

  26. Higgs decays to gauge bosons • H W+W- ffff has sharp threshold at 2 MW, but large branching ratio even for MH=130 GeV For any given MH, not all decay modes accessible

  27. Status of Theory for Higgs BRs • Bands show theory errors • Largest source of uncertainty is b quark mass Data points are e+e- at s=350 GeV with L=500 fb-1

  28. Total Higgs Width • Small MH, Higgs is narrower than detector resolution • As MH becomes large, width also increases • No clear resonance • For MH1.4 TeV, tot MH

  29. Higgs Searches at LEP2 • LEP2 searched for e+e-ZH • Rate turns on rapidly after threshold, peaks just above threshold, 3/s • Measure recoil mass of Higgs; result independent of Higgs decay pattern • Pe-=s/2(1,0,0,1) • Pe+=s/2(1,0,0,-1) • PZ=(EZ, pZ) • Momentum conservation: • (Pe-+Pe+-PZ)2=PH2=MH2 • s-2 s EZ+MZ2= MH2

  30. Higgs Limits From LEP2 e+e-→ZH LEP2 limit, MH > 114.1 GeV

  31. Higgs production at Hadron Colliders • Many possible production mechanisms; Importance depends on: • Size of production cross section • Size of branching ratios to observable channels • Size of background • Importance varies with Higgs mass • Need to see more than one channel to establish Higgs properties and verify that it is a Higgs boson

  32. Production Mechanisms in Hadron Colliders • Gluon fusion • Largest rate for all MH at LHC and Tevatron • Gluon-gluon initial state • Sensitive to top quark Yukawa t Largest contribution is top loop In SM, b-quark loops unimportant

  33. Gluon Fusion • Lowest order cross section: • q=4Mq2/MH2 • Light Quarks: F1/2(Mb/MH)2log(Mb/MH) • Heavy Quarks: F1/2 -4/3 • Rapid approach to heavy quark limit: Counts number of heavy fermions • NLO/NNLO corrections calculated in heavy top limit

  34. Gluon fusion, continued • Integrate parton level cross section with gluon parton distribution functions • z=MH2/S, S is hadronic center of mass energy • Rate depends on R, F

  35. NNLO, ggH Rates depend on renormalization scale, s(R), and factorization scale, g(F) Bands show .5MH < < 2 MH LO and NLO  dependence bands don’t overlap  dependence used as estimate of theoretical uncertainty Higher order corrections computed in large Mt limit

  36. Vector Boson Fusion • W+W-X is a real process: • Rate increases at large s:(1/ MW2 )log(s/MW2) • Integral of cross section over final state phase space has contribution from W boson propagator: • Outgoing jets are mostly forward and can be tagged Peaks at small  H k=W,Z momentum

  37. Vector Boson Fusion • Idea: Tag 2 high-pT jets with large rapidity gap in between • No color flow between tagged jets – suppressed hadronic activity in central region

  38. W(Z)-strahlung • W(Z)-strahlung (qqWH, ZH) important at Tevatron • Same couplings as vector boson fusion • Rate proportional to weak coupling • Theoretically very clean channel • NNLO QCD corrections: KQCD1.3-1.4 • Electroweak corrections known (-5%) • Small scale dependence (3-5%) • Small PDF uncertainties Improved scale dependence at NNLO

  39. Producing the Higgs at the Tevatron Tevatron Aside: Tevatron analyses now based on 3 fb -1 NNLO or NLO rates MH/2 <  < MH/4

  40. Higgs at the Tevatron • Largest rate, ggH, H bb, is overwhelmed by background (ggH)1 pb << (bb)

  41. Looking for the Higgs at the Tevatron • High mass: Look for HWWll • Large ggH production rate • Low Mass: Hbb, Huge QCD bb background • Use associated production with W or Z Analyses use more than 70 channels

  42. SM Higgs Searches at Tevatron 95% CL exclusion of SM Higgs at 170 GeV

  43. SM Higgs Searches at Tevatron Expected sensitivity of CDF/DØ combined with 3 fb-1: < 3.0xSM @ 115 GeV

  44. Production Mechanisms at LHC Bands show scale dependence All important channels calculated to NLO or NNLO

  45. Search Channels at the LHC ggHbb has huge QCD background: Must use rare decay modes of H • ggH • Small BR (10-3 – 10-4) • Only measurable for MH < 140 GeV • Largest Background: QCD continuum production of  • Also from -jet production, with jet faking , or fragmenting to 0 • Fit background from data

  46. H→ MH=120 GeV; L=100 fb-1 S/B = 2.8 to 4.3 

  47. Golden Channel: H→ZZ→4 leptons • Need excellent lepton ID • Below MH130 GeV, rate is too small for discovery

  48. H→ZZ→(4 leptons) CMS: Possible discovery with < 10 fb-1

  49. Heavy Higgs in 4-lepton Mode H  ZZ  l+l- l+l- • 200 GeV < MH < 600 GeV: • - Discovery in H  ZZ  l+l- l+l- • Background smaller than signal • Higgs width larger than experimental resolution (MH > 300 GeV) • Confirmation in H  ZZ  l+l- jj

  50. Heavy Higgs MH > 600 GeV: 4 lepton channel statistically limited Look for: H  ZZ  l+l-  H  ZZ  l+l- jj H  WW  l jj -150 times larger BR than 4 lepton channel

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