Finding the Higgs boson

Transcription

1 Finding the Higgs boson Sally Dawson, BN XIII Mexican School of Particles and Fields ecture 1, Oct, 008 Properties of the Higgs boson Higgs production at the Tevatron and HC Discovery vs spectroscopy

2 Collider Physics Timeline First collisions in Spring, 009 Tevatron HC HC Upgrade IC e e 500 GeV, earliest possible date, 0x 15 billion $ s Planned shut-down in 010

3 arge Hadron Collider (HC) proton-proton collider at CERN (008) 14 TeV energy 7 mph slower than the speed of light cf. Fermilab ( 307 mph slower than the speed of light) Typical energy of quarks and gluons 1- TeV

4 CMS-TS Y 6.90 m m m m.950 m X Towards Center of HC Detectors of Unprecedented Scale Two large multipurpose detectors.864 m m 1.30 m CMS is 1,000 tons ( x s ATAS) Transverse View ϕ ATAS has 8 times the volume of CMS

5 Standard Model Synopsis Group: SU(3) x SU() x U(1) QCD Electroweak Gauge bosons: SU(3): G i, i=1 8 SU(): i, i=1,,3 U(1): B Gauge couplings: g s, g, g SU() Higgs doublet: Φ Gauge symmetry forbids gauge boson masses

6 The Problem of Mass hy are the and Z boson masses non-zero? U(1) gauge theory with spin-1gauge field, A 1 = 4 F ν F ν F ν = ν A A ν U(1) local gauge invariance: A ( x) A ( x) η( x)

7 The Problem of Masses Mass term for A would look like: = 1 4 F 1 ν ν F m A A Mass term violates local gauge invariance e understand why M A = 0 Gauge invariance is guiding principle

8 SM Higgs Mechanism Standard Model includes complex Higgs SU() doublet ith SU() x U(1) invariant scalar potential > 0, boring.. (Minimum at Φ=0, gauge bosons stay massless) = Φ = ϕ ϕ φ φ φ φ i i ( Φ) Φ Φ Φ = λ V

9 SM Higgs Mechanism If < 0, then spontaneous symmetry breaking V = Φ Minimum of potential at: Φ λ( Φ Φ) Choice of minimum breaks gauge symmetry hy is < 0? Φ = 1 0 v

10 More on SM Higgs Mechanism Couple Φ to SU() x U(1) gauge bosons ( i, i=1,,3; B ) Gauge boson mass terms from: σ B g i g i D V D D i i S ) ( ) ( ) ( ' = Φ Φ Φ = ( ) ( )... ) ( ) ( ) ( ) )( ( 0, ) ( 3 1 Φ Φ σ σ g B g g g v v g B g g B g v D D b b a a = Φ v 0 1 Higgs mechanism gives gauge bosons mass

11 More on SM Higgs Mechanism Massive gauge bosons: M =gv/ M Z = (g g' )v/ ± = ( 1 ) m / Z 0 = (g 3 -g'b )/ (g g' ) Orthogonal combination to Z is massless photon A 0 = (g' 3 gb )/ (g g' )

12 More on SM Higgs Mechanism eak mixing angle defined cosθ g = sinθ g g Z = - sin θ B cosθ 3 = g g g A = cos θ B sinθ 3 M =M Z cos θ Natural relationship in SM Provides stringent restriction on Beyond the SM models

13 Recap Generate mass for,z using Higgs mechanism Higgs VEV breaks SU() x U(1) U(1) em Single Higgs doublet is minimal case Before spontaneous symmetry breaking: Massless i, B, Complex Φ After spontaneous symmetry breaking: Massive ±, Z; massless γ; physical Higgs boson H Exercise: Count degrees of freedom

14 Muon decay Consider ν e ν e Fermi Theory: 1 1 i e ν γ 5 ν γ 5 GF gν u γ uν uν γ u e e ν e ig k E Theory: 1 1 γ5 ν 1 γ5 gν u γ uν u γ νe M ν e ν e u e G F = x 10-5 GeV - G g 1 F = = 8M v

15 Higgs Parameters G F measured precisely G F 1 = = v = ( G ) (46GeV ) 8M v F = Higgs potential has free parameters,, λ V = Φ Φ λ( Φ Φ) Trade, λ for v, M H V = g M 1 H M H 3 H H v arge M H strong Higgs self-coupling A priori, Higgs mass can be anything M 8v H H 4 v M H = = λ v λ

16 hat about Fermion Masses? Fermion mass term: = mψψ = m ( Ψ Ψ Ψ Ψ ) eft-handed fermions are SU() doublets Q u = d Scalar couplings to fermions: d = λdqφd R Effective Higgs-fermion coupling Mass term for down quark R h.c. 1 0 d = λd ( u, d ) d R v H R h. c. Forbidden by SU()xU(1) gauge invariance λ d = m d v

17 Fermion Masses, M u from Φ c =iσ Φ* (not allowed in SUSY) = λu QΦcuR hc Φ c φ 0 = φ λ u = m u v For 3 generations, α, β=1,,3 (flavor indices) Y = ( v H ) ( αβ α β αβ α β λ u u λ d d ) u R d R α, β h. c.

18 Fermion masses, 3 Unitary matrices diagonalize mass matrices u u α α R = U = V αβ u αβ u u u mβ mβ R d d α α R = U = V αβ d αβ d d d mβ mβ R 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 argest coupling is to heaviest fermion m f m f = ffh = ( f f R f R f )H v v Top-Higgs coupling plays special role? No Higgs coupling to neutrinos Higgs couples to gauge boson masses = gm gm Z cosθ H Z Z H... 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 (γ) or gluons (g) M H =v λ large M H is strong coupling regime

21 Higgs Decays H ff proportional to m f BR( H bb ) BR( H τ τ ) m m b N c τ Identifying b quarks important for Higgs searches For M H <M, decays to bb most important

22 Higgs Decays to Gluons H m t 4 d k 1 3 ( k m t ) m t g g Top quark contribution most important Doesn t decouple for large m t Decoupling theorem doesn t apply to particles which couple to mass (ie Higgs!) Decay sensitive to extra generations Γ( H gg) α sα 7π s θ M M 3 H

23 Higgs Decays to Photons Dominant contribution is loops Contribution from top is small 3 α M 16 Γ( H γγ ) π s M 9 θ 3 H top

24 Tree level decay Higgs Decays to /Z H 3 α M H 3 Γ( H ) = 1 x 1 x x 16s M 4 θ M x = 4 M H A = gmε ( p ) ε ( p ) - Below threshold, H * with branching ratio * ff' implied Final state has both transverse and longitudinal polarizations H - f f'

25 Higgs Decays to -, ZZ The action is with longitudinal gauge bosons (since they come from the ESB) Cross sections involving longitudinal gauge bosons grow with energy H As Higgs gets heavy, decays are longitudinal ( ),0 0,1, 1 ),0,0, ( i p E p T V V V ± = = ε r H M M g gm H A ) ( = ε ε ) ( ) ( V V T T x x V V H V V H = Γ Γ 4 H M M x = ( ) V V V V V M p E p M ε =,,0,0 1 r Exercise: Prove this

26 Higgs decays to gauge bosons H - ffff has sharp threshold at M, but large branching ratio even for M H =130 GeV For any given M H, not all decay modes accessible

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

28 Total Higgs idth Small M H, Higgs is narrower than detector resolution As M H becomes large, width also increases No clear resonance For M H 1.4 TeV, Γ tot M H Γ( H α ) 16sin θ M M M H 330GeV 1TeV 3 H 3

29 Higgs Searches at EP EP searched for e e - ZH Rate turns on rapidly after threshold, peaks just above threshold, σ β 3 /s Measure recoil mass of Higgs; result independent of Higgs decay pattern P e- = s/(1,0,0,1) P e = s/(1,0,0,-1) P Z =(E Z, p Z ) Momentum conservation: (P e- P e -P Z ) =P H =M H s- s E Z M Z = M H

30 Higgs imits From EP e e - ZH EP limit, M H > 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 argest rate for all M H at HC and Tevatron Gluon-gluon initial state Sensitive to top quark Yukawa λ t argest contribution is top loop In SM, b-quark loops unimportant

33 Gluon Fusion owest order cross section: τ q =4M q /M H ight Quarks: F 1/ (M b /M H ) log(m b /M H ) Heavy Quarks: F 1/ -4/3 α s ( R ) ˆ σ 0( gg H ) = F1/ ( ) ( M sˆ) τ q δ H 104πv q Rapid approach to heavy quark limit: Counts number of heavy fermions NO/NNO corrections calculated in heavy top limit

34 Gluon fusion, continued Integrate parton level cross section with gluon parton distribution functions dx z σ 0 ( pp H ) = ˆ σ 0z g( x, F ) g(, F ) x x z=m H /S, S is hadronic center of mass energy Rate depends on R, F 1 z

35 NNO, gg H Rates depend on renormalization scale, α s ( R ), and factorization scale, g( F ) Bands show.5m H < < M H O and NO dependence bands don t overlap dependence used as estimate of theoretical uncertainty σ K NO σ O Higher order corrections computed in large M t limit

36 Vector Boson Fusion - X is a real process: d σ pp s dz σ Rate increases at large s: σ (1/ M )log(s/m ) Integral of cross section over final state phase space has contribution from boson propagator: X ( ) = X ( zs) dz pp / dθ dθ k M ) (EE'(1 cosθ ) ( M ) Peaks at small θ Outgoing jets are mostly forward and can be tagged H k=,z momentum

37 Vector Boson Fusion Idea: Tag high-p T jets with large rapidity gap in between No color flow between tagged jets suppressed hadronic activity in central region

38 (Z)-strahlung (Z)-strahlung (qq H, ZH) important at Tevatron Same couplings as vector boson fusion Rate proportional to weak coupling Theoretically very clean channel NNO QCD corrections: K QCD Electroweak corrections known (-5%) Small scale dependence (3-5%) Small PDF uncertainties Improved scale dependence at NNO

39 Producing the Higgs at the Tevatron Tevatron Aside: Tevatron analyses now based on 3 fb -1 NNO or NO rates M H / < < M H /4

40 Higgs at the Tevatron argest rate, gg H, H bb, is overwhelmed by background σ(gg H) 1 pb << σ(bb)

41 ooking for the Higgs at the Tevatron High mass: ook for H lνlν arge gg H production rate ow Mass: H bb, Huge QCD bb background Use associated production with or Z Analyses use more than 70 channels

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

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