Lecture 17 - The Higgs Boson Spontaneous Symmetry Breaking The Higgs Mechanism Higgs Couplings to Fermions Electroweak Constraints on the Higgs Direct Searches for Higgs Bosons Higgs signatures at the LHC 1
Spontaneous Symmetry Breaking The ground state configuration of a system does not always display the full symmetry that might be expected. The symmetry is spontaneously broken, and is hidden. Everyday example: A circle of people are sitting at a dining table. The first person who picks up a napkin (with Left Hand or Right Hand), breaks rotational symmetry. Physics example: In a ferromagnet spins align in a random direction until an external magnetic field is applied which breaks rotational symmetry.
The Higgs Potential In electroweak theory the difference between the physical γ, W ±, Z 0 boson masses is created by spontaneous symmetry breaking of the Higgs field φ. The potential energy of the Higgs field is: V (φ) = µ φ φ + λ(φ φ) µ < 0 λ > 0 The Higgs is a scalar field that exists in a vacuum The potential is symmetric under rotations in φ space The free energy of a ferromagnet is related to its magnetization M: G = αm + βm 4 α < 0 β > 0 The magnetization exists in the absence of an external field The free energy is symmetric under rotations in space 3
Vacuum Expectation Value The Higgs potential has the shape of a mexican hat It has a minimum which is not at < φ >= 0 Known as the vacuum expectation value v v = µ λ = M W g = 46GeV This parameter defines the electroweak scale 4
The Standard Model Higgs Field The Higgs field is a weak isospin doublet with four components: φ = φ+ = 1 φ 1 + iφ φ 0 φ 3 + iφ 4 A fluctuation around the minimum v spontaneously breaks the rotational symmetry of the Higgs field. Choose direction of fluctuation so that vacuum Higgs field is: φ 0 = 1 0 v Breaking the symmetry eats three of the four φ components! 5
The Higgs Boson The fluctuation around the minimum v is written as: 1 φ(x) = φ 0 + h(x) φ 1 + iφ 1 φ 3 + iφ 4 The scalar field h(x) describes a physical Higgs boson Expanding the Higgs potential to second order in h : 0 v + h(x) V = V 0 + µ (vh + h ) + λ 4 (4v3 h + 6v h ) = V 0 + λv h The additional term from h gives the Higgs boson mass: M H = λv M H = µ This mass still has to be determined experimentally! 6
Vector Boson Masses Couplings of vacuum Higgs field φ 0 to electroweak bosons: ( ) g τ. W + g B φ 0 L H = 1 gw 3 + g B g(w 1 iw ) 0 8 g(w 1 + iw ) gw 3 + g B v In terms of the physical W and Z bosons this gives: ( gv ) W + W + v 8 Z0 Z 0 Z 0 = gw 3 + g B We identify these as vector boson mass terms: M W = vg M Z = v g + g Note that the coupling of photon A 0 = gw 3 + g B to φ 0 is zero! 7
Higgs Couplings to Fermions The scalar Higgs field φ couples fermion states of opposite helicity In the Lagrangian there are new fermion terms: L f = g f ( f L f R + f R f L )v + g f ( f L f R + f R f L )h The first term is treated as a fermion mass term: m f = g fv = gf M W sinθ W e The vacuum Higgs field v generates the fermion masses m f The second term is the fermion coupling to the Higgs boson h The coupling constant g f, describing the Higgs boson coupling to f f, is proportional to m f! 8
Upper Bound on Higgs Boson Mass The Higgs boson width Γ H is the sum of all its couplings: Γ(H f f) + Γ(H W + W ) + Γ(H Z 0 Z 0 ) + Γ(H HH) f The last term is from the Higgs self-couplings. For a very large Higgs mass M H v the self-coupling dominates To satisfy unitarity Γ H < M H : G F M 3 H < M H M H < 1 GF A more precise calculation gives M H < 1. TeV 9
m W [GeV] Precision Electroweak Bounds on Higgs Mass Higher order diagrams involving Higgs Bosons enter as corrections to Standard Model predictions for electroweak processes. 80.5 80.4 LEP1 and SLD LEP and Tevatron (prel.) 68% CL χ 6 5 4 3 Theory uncertainty α (5) α had = 0.0758±0.00035 0.0749±0.0001 incl. low Q data m Limit = 144 GeV 80.3 α m H [GeV] 114 300 1000 150 175 00 m t [GeV] Higgs mass M H = 85 +39 8 GeV 1 Excluded Preliminary 0 30 100 300 m H [GeV] M H < 144 GeV (90% C.L.) 10
Direct Search for Higgs at LEP (1989-1995) At the Z 0 peak look for associated production of a Higgs and a lepton pair from a virtual Z 0 (Higgsstrahlung) l + Z 0 Z 0 H 0 l No signal for a light Higgs with M H < 46 GeV (M Z /) 11
Direct Search for Higgs at LEP- (1996-001) e Z 0 e + H 0 Associated production e + e Z 0 H 0 at s 00 GeV A few candidates caused a lot of excitement in 001! Lower limit M H > 114 GeV (90%C.L.) 1
Higgs Production at Tevatron At the Tevatron Higgs searches use three different channels: Gluon-gluon fusion: gg H 0 W + W l + l ν ν Associated W-Higgs production: q q WH lνb b Associated Z-Higgs production: q q ZH llb b 95% CL Limit/SM 10 10 1 CDF II Preliminary WHlvbb 1.7/fb Expected WHlvbb ZHvvbb 1/fb Expected ZHvvbb ZHllbb 1/fb Expected ZHllbb HWWllvv 1.9/fb Expected HWWllvv CDF for 1-1.9/fb Expected CDF ± 1σ 10 140 160 180 00 Higgs Mass (GeV/c ) CDF limits compared to Standard Model (SM): No signal yet... < SM for M H 160 GeV Tevatron expects to rule out M H > 140 GeV and may observe a signal! 13
Higgs Production at LHC At the LHC W + W fusion will be a significant process: d u W H 0 W + u d Identify these events by: - forward-tagging of jets from protons - central production and decay of Higgs boson 14
Higgs Signatures at LHC M H > M Z. Coupling to ZZ is proportional to M Z. Large decay rate. Clear signature from ZZ l + l l + l. M H M W. Coupling to W + W is proportional to M W. Large decay rate. Clear signature in W + W to q qlν. M H 10 GeV. Largest coupling is to b b. There is a lot of background from QCD jets. Next largest coupling to τ + τ Difficult because of missing neutrinos. Also looking at small rate H γγ. First LHC data in 009/10. High mass Higgs found quickly. Low mass Higgs will take several years! 15
Simulated H γγ at CMS Simulated Higgs at ATLAS 16