Elementary Particles II S Higgs: A Very Short Introduction Higgs Field, Higgs Boson, Production, Decays First Observation 1
Reminder - I Extend Abelian Higgs model to non-abelian gauge symmetry: ( x) + = 0 ( ) U() Gauge group = SU 1 SSB in the Standard odel : Add a doublet of complex, scalar fields: φ φ ( x) φ ( x) Assuming y 1 + Q φ ( x) =+ 1 ( x) = = 0 Q φ 0 L Y
Reminder - II SU () U (1) Gauge transformation of doublet: L g g ' φ φ ' = exp i α( x) τ+ yθ( x) I φ SU () U (1) Covariant derivative: L µ µ g µ g ' µ D = + i τ W + yb Additional term to EW lagrangian: µ LH Dµ D Take µ < 0, λ> 0 : Y Y ( ) = φ φ µ φφ λφφ µ v µ φ = = v= min λ λ Pick ground state (= vacuum) as 0 φ = v SSB of Electroweak gauge symmetry 0 v= 46 GeV 3
Reminder - III Introduce field deviation from vacuum: 1 σ+ iσ µ λ φ= = + λ η + λη σ + σ + η + η + σ + σ + η + η v+ + 1 4 4 1 V v 1 v 1 1 1 1 1 η1 iη 4λ 4 After properly 'rotating' to Unitary Gauge: 1 massive scalar: η1, m mh= λv Th η ± massive, charged vectors: W, m 0 1 massive, neutral vector:, F F W W g = ( g + g ') e Higgs ( ) ( ) µ Z mz= λ Relating model parameters to independently measured constants e, G,sin θ : W H g e W = = 77.5 GeV, Z= 88.4 8G 8G sin θ cosθ λ = =??? G F µ λ W F GeV W
Reminder - IV 5 Gauge terms of L in the unitary gauge, in terms of the physical fields: L B + L H 1 µν = Fµν( x) F ( x) Photon 4 1 W W µν 1 µ ± F µν ( x) F ( x) + mw Wµ W W boson 1 µν 1 µ 0 Zµν ( x) Z ( x) + mz Zµ Z Z boson 4 +( σ 1 )( µ σ ) mh Higgs boson σ µ H I I I + L + L + L Gauge-Higgs, Higgs self-, Gauge self-interactions BB HH HB
Reminder - V ( ) Fermion masses: Yukawa scalar coupling Describing interaction between Dirac and scalar fields: Example: Single lepton family * L R R L L R R LHL= g l ΨΦ l ψl + ψlφψ l g l l l l l ν ΨΦ ɶ ψ ν + ψ ν ΦΨ ɶ L φ b, Φ= ɶ * φ = 0 for massless neutrino In the unitary gauge: 1 1 LHL= mlψψσ l l mνψ l νψσ l νl v v Lepton masses in terms of model parameters: m g l l vg vg l νl =, mν = = 0 in the inimal Standard odel l individual constant ( ) 6 a
Reminder - VI Higgs vertexes: 7 Observe: Amplitude mass(fermions), mass (bosons)
About the Higgs Field - I Universal, constant field Lorentz scalar Same value in any frame 8 Higgs boson: Quantum excitation of the field Non-standard feature: Vacuum expectation value v 0 Some analogy to a spontaneously magnetized ferromagnet: 0 Actually, more similar to a superconductor: Quantum condensate of superconducting electrons (= Cooper pairs : The 'Higgs field' of superconductivity) State of minimal energy: Density 0 SSB of QED gauge symmetry Photon becoming massive inside the superconductor eissner effect, B 0 inside
About the Higgs Field - II 9 Energy difference between normal and s.c. state at two different temperatures 1 4 E= a( T) ψ + b( T) ψ +... From Landau theory of phase transitions ψ is the Cooper pair wave function ψ density of Cooper pairs Below T c, the minimum energy state ( vacuum ) occurs for ψ = ψ 0 0, phase undefined U(1) QED gauge invariance spontaneously broken Photon becomes massive B = 0 inside
About the Higgs Field - III ψ Higgs field of superconductivity: <ψ> 0 Permanent supercurrents Superconductive state: Higgs field = Wave function of Cooper pairs Not a fundamental field Composite field of fundamentals fermions (electrons) Why there is the composite? e-e effective interaction: Attractive (!) due to e lattice interaction Is the real Higgs field a genuine, fundamental field or a composite? Good question..no answer (yet): Take it as a fundamental field 10
Higgs Decays - I 11
Higgs Decays - II 1
Higgs Decays - III 13 3-body phase space factor 3-body phase space factor
Higgs Decays - IV 14 3-body phase space factor
H Width Entirely determined by Higgs mass: 15 (GeV) H =16 GeV Γ H 5 ev!
H Branching Ratios -I 16
H Branching Ratios -II 17
H Branching Ratios - III Selecting best decay channels for detection: Strongly dependent on (unknown) By taking < H W H 18 bb : Large BR > 50 %, good signature (secondary vertexes), lots of QCD background + τ τ γγ : Large BR 7 %,somewhat harder than bb (neutrinos) 3 : Tiny BR 10, small background, experimentally challenging gg : Large BR 5 %, jets, lots of QCD background ZZ*: Small BR 3 %,small background in the 4 leptons mode WW*: Large BR 0 %,sizeable QCD background in the 4 jets mode, harder than ZZ * in leptonic modes (neutrinos)
Detector Guidelines Go for: 19 Excellent muon tracking Excellent e.m. calorimetry Vertexing Large acceptance High momentum/energy resolution High vertex resolution No way of directly measuring H width for H W PDG (013) best estimate: = 15.9 GeV, σ 400 ev
agnetic Analysis & Accuracy 0 otion of a charged particle in a uniform magnetic field: Cylindrical helix coaxial to B p r= r : m, p : GeV, B : T 0.3B x θ L θ L 0.3BL x B sin = θ r L r r p x A s L r θ x C θ θ θ 0.3BL s= r r cos r 1 1 r = 4 8 8 p 0.3BL p 8s Take 3 measured points, with single point accuracy σ xa+ xb 1 3 Then: s= xb σs= σ + σ = σ σ p σs 3σ 3 σ8p 300 64σ p σ p = = = = 3.7 p s s 0.3BL 18 BL BL σ N 10, uniformly spaced points: 8.3 σ p p p BL N + 4 B= 4 T, L= m, p = 50 GeV : 0.3 4 4 1. s m m 1 cm 400 100 σ 100µ m σ p p σ p= 30GeV 4 30 10 = 0.3% 0.6% 0.6 σ 80eV σ 4tracks
Electromagnetic Calorimetry 1 σe E σ E= 50GeV σ 0.5%.7% 1 σ 130 ev S: Photon statistics, shower containment N: Electronic noise C: Intercalibration
Production - I 0 Start from H coupling to Fermions: Compare to coupling to Z : m f H coupling down by a factor as compared to Z m Leptons: Easier to handle W 0 + Feasible at e e colliders? m Tiny cross section, in view of factor 4 10 e W 11 + Better chance for a µµ collider mµ 1.6 10 ajor task, several unsolved issues about short muon lifetime vs. intensity W 6
Production - II 3 Quarks: Best bet is with b m b 3 Factor 3 10 encouraging W But: No b-quark beams, must rely on bb sea inside the nucleon b-quark partonic density small... Taking H production at small rapidity y 0, with a 7 TeV beam x 10 Incident flux of sea b-quarks very small
Production - III Shift to gauge bosons (Exclude massless photon), Top ore promising: W, Z, t mass very large + e e colliders 'Higgsstrahlung', 'Gauge boson fusion' 4
Production - IV 5 Top
Production - V 6 Higgs width Higgs Recoil method: First sensitivity to invisible decays e + Top Yukawa coupling νν HH Higgs selfcoupling: e -
Production - VI pp, pp colliders 7
Production - VII 8 Need to convolute with parton densities Results for LHC cross sections
Results 9 6-7 σ effect = Discovery