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Unveiling the Higgs Boson: Lecture Summary

Higgs boson, properties, collider physics, LHC, Fermilab, symmetry breaking, gauge bosons, mass

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Unveiling the Higgs Boson: Lecture Summary

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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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