lecture’16’–the’higgs’boson’’playfer/higgs.pdf · the’higgs’poten:al’...

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


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


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


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


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


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


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


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


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


Gluon fusion

Central produc:on

Associated produc:on

Higgs Decay Modes


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


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


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


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

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