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Lecture 16 – The Higgs Boson
12/3/10 1 Par:cle Physics Lecture 16 Steve Playfer
M-‐
Will it be produced at the LHC?
Spontaneous Symmetry Breaking • Start with a system that has an intrinsic symmetry
• By choosing a par:cular ground state configura:on of this system the symmetry is broken
• If the choice is arbitrary, i.e. no external agent is responsible for the choice, then the symmetry is “spontaneously” broken
12/3/10 Par:cle Physics Lecture 16 Steve Playfer 2
Everyday example: A circle of people are siUng at a dining table with napkins between them. The first person who picks up a napkin, either with their leV or right hand spontaneously breaks the L/R symmetry. All the others must do the same if everyone is to end up with a napkin.
Physics example: In a domain inside a ferromagnet all the spins align in a par:cular direc:on. If the choice of direc:on is random, the underlying theory has a rota:onal symmetry which is spontaneously broken. The presence of an external magne:c explicitly breaks the symmetry and defines a preferred direc:on.
The Higgs Poten:al
12/3/10 Par:cle Physics Lecture 16 Steve Playfer 3
A complex scalar field φ in a vacuum has real and imaginary parts φ1 and φ2
Poten:al Energy U has a “mexican hat” shape with a minimum at |φ| ≠ 0
U(φ) = µ2 φ† φ + λ (φ† φ )2 with µ2 < 0 and λ > 0
U(φ) is symmetric under rota:on of the complex phase of φ. Choice of par:cular phase spontaneously breaks this symmetry.
Free energy of a ferromagnet is: G = α|M|2 + β|M|4 with α < 0 and β > 0 This is symmetric under rota:on of the magne:sa:on vector M. Choice of par:cular direc:on spontaneously breaks this symmetry.
Standard Model Higgs Field
12/3/10 Par:cle Physics Lecture 16 Steve Playfer 4
Introduce a weak isospin doublet of complex scalar fields:
Three degrees of freedom are spontaneously broken. Two complex phases are set to zero, and an isospin rota:on removes φ+ to give a ground state:
From the Higgs poten:al the vacuum expecta:on value (vev) of this ground state is: v = √(2|µ|2/λ)
Introducing the Higgs Boson
12/3/10 Par:cle Physics Lecture 16 Steve Playfer 5
Consider a fluctua:on of the Higgs field about its minimum:
φ(x) = φ0 + h(x) =
Expand the Higgs poten:al to second order in h(x):
U(φ) = U0 + µ2 (2vh + h2) + λ (4v3h + 6v2h2) = U0 + λv2h2 2 4 A poten:al energy which is quadra:c in the field rela:ve to the minimum can be interpreted as a mass term in the Lagrangian: L = L0 + 1 m2 (φ ‒ φ0)2
2 The Standard Model has one scalar Higgs boson with a mass: MH
2 = 2 λv2 MH = √2 |µ| MH (or µ) is a free parameter (to be determined experimentally!)
Higgs Couplings to Vector Bosons
12/3/10 Par:cle Physics Lecture 16 Steve Playfer 6
In unbroken electroweak symmetry there is a weak isospin Higgs field coupling to the W1,2,3 and a hypercharge coupling to the B: g τ.W φ + g’ B φ 2 2
These give addi:onal terms in the Electroweak Lagrangian:
Note that by wri:ng the Higgs field as φ =φ0 and mixing the vector boson states we have now spontaneously broken electroweak symmetry
Expanding this expression gives terms: LH = (gv)2 W+W- + v2 Z0Z0
4 8
N.B. There is no term containing the photon A0 = gW3 + g’B The photon does not couple to the Higgs field and is massless!
The Electroweak Scale
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The Higgs field couplings in the Lagrangian can be iden:fied with vector boson mass terms: MW = vg MZ = v √(g2 +g’2) = MW 2 2 cosθW
By expanding the Higgs field about its minumum φ0 using φ = v + h it is also possible to obtain the trilinear gauge couplings HW+W-‐ and HZ0Z0
H→WW vertex = g MW H→ZZ vertex = g MZ
cosθW
From measured masses the “electroweak scale” is defined by v = 246 GeV This is the vacuum expecta:on value of the Higgs field v = √(2|µ|2/λ) Note that v is another free parameter of the Standard Model
Couplings of Higgs boson to WW and ZZ are propor:onal to their masses.
Higgs Couplings to Fermions
12/3/10 Par:cle Physics Lecture 16 Steve Playfer 8
The scalar Higgs field must couple to a leV and right-‐handed fermion-‐an:fermion pair. In the Electroweak Lagrangian there are addi:onal terms for these fermion interac:ons:
Lf = gf ( fL fR + fR fL ) v + gf ( fL fR + fR fL ) h
The first term is interpreted as a fermion mass term: mf = gf v
The vacuum Higgs field generates fermion masses propor:onal to the coupling strengths gf N.B. these are all s1ll free parameters in the Standard Model!
The second term describes the Higgs boson couplings to fermions H → f f
It predicts that the Higgs boson couplings should be propor:onal to the fermion masses mf
Precision Electroweak Bounds on MH
12/3/10 Par:cle Physics Lecture 16 Steve Playfer 9
Diagrams involving the Higgs boson give correc:ons to electroweak predic:ons which depend on MH
MH = 85+39-‐28 GeV MH < 144 GeV (90% C.L.)
MH > 114 GeV from searches at LEP2 Blue band
is χ2 from Electroweak fit
Searches for the Higgs at LEP
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LEP-‐1 at √s ∼ ΜΖ (1989-‐1995)
Higgsstrahlung with a ZZH vertex
No evidence for a light Higgs: MH > 46 GeV (~ MZ/2)
LEP-‐2 at √s ∼ 200GeV (1996-‐2001)
Associated ZH produc:on
No evidence for a light Higgs: MH > 114 GeV (~ √s – MZ)
virtual
real
virtual Z0
Higgs Produc:on at Hadron Colliders
• Gluon-‐gluon fusion gg → H Dominant mechanism at the LHC (can also have H t t final state)
• Quark-‐an:quark annihila:on and Higgsstrahlung qq → WH or ZH Associated produc:on with a vector boson
• Vector boson fusion WW→ H or ZZ→ H Known as “central” produc:on (underlying quark jets in final state) 12/3/10 Par:cle Physics Lecture 16 Steve Playfer 11
Higgs Produc:on Cross-‐Sec:ons at LHC
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Gluon fusion
Central produc:on
Associated produc:on
Higgs Decay Modes
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MH = 115 GeV
H → bb (~80%) H → τ+τ- (~8%) H → WW (~8%) H → cc (~3%) H → γγ (~0.2%)
MH = 144 GeV
H → WW (~60%) H → bb (~25%) H → ΖΖ (~8%)
Note that for MH < 2MW (2MZ) the vector bosons are virtual
Searches for Higgs at Tevatron
12/3/10 Par:cle Physics Lecture 16 Steve Playfer 14
Tevatron Higgs working group hup://tevphwg.fnal.gov
1
10
130 140 150 160 170 180 190 200
1
10
mH(GeV)R lim CDF + D0 Run II
L=4.8-5.4 fb-1 ExpectedObserved
Expected !1Expected !2
SM=1
Ra:os of sensi:vi:es are compared to Standard Model
The Tevatron begins to exclude a region around MH~2MW
January 2010
Associated WH/ZH produc:on with H → bb H → WW/ZZ
Higgs signals at LHC
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H → ΖΖ → e+e-µ+µ-
in ATLAS experiment H → γγ
in CMS experiment S:ll only simula:ons! Wait a few years…
Higgs Self-‐Couplings
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H0
H0
H0
Coupling is propor:onal to λv
H0
H0
H0
H0
Coupling is propor:onal to λ
Measurements of these determine parameter λ in Higgs poten:al Very hard to do at LHC … Probably requires ZHH produc:on at a √s ∼ 1TeV e+e- collider