Lecture 17 - The Higgs Boson

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1 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

2 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.

3 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

4 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

5 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

6 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

7 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

8 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

9 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

10 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 LEP1 and SLD LEP and Tevatron (prel.) 68% CL χ Theory uncertainty α (5) α had = ± ± incl. low Q data m Limit = 144 GeV 80.3 α m H [GeV] m t [GeV] Higgs mass M H = GeV 1 Excluded Preliminary m H [GeV] M H < 144 GeV (90% C.L.) 10

11 Direct Search for Higgs at LEP ( ) 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

12 Direct Search for Higgs at LEP- ( ) 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

13 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 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 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

14 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

15 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

16 Simulated H γγ at CMS Simulated Higgs at ATLAS 16

How To Find The Higgs Boson

How To Find The Higgs Boson Dezső Horváth: Search for Higgs bosons Balaton Summer School, Balatongyörök, 07.07.2009 p. 1/25 Search for Higgs bosons Balaton Summer School, Balatongyörök, 07.07.2009 Dezső Horváth MTA KFKI Research