Beyond Standard Model Higgs
Ling-Fong Li
Nov 2008
Ling-Fong Li ()
Nov 2008
1 / 15
Outline
1
2
3
Standard Model Higgs Particle
Beyond Standard Model Higgs
Higgs Particle as Partner of Guage Boson
Ling-Fong Li ()
Nov 2008
2 / 15
Standard Model Higgs Particle
Left-handed fermions
νe
e
liL =
qiL =
u0
d
L
νµ
µ
L
c0
s
L
ντ
τ
L
t0
b
liR = eR , µR , τ R
,
L
qiR = uR , cR , tR
,
L
Higgs Scalar
φ=
Ling-Fong Li ()
φ0
φ
,
1
hφi = p
2
v
0
,
v = 246 Gev
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Important roles of Higgs scalar:
1
Break the gauge symmetry: SU (2) U (1) ! U (1)em
Only h = Re φ0 left over after spontaneous symmetry breaking
Gauge boson masses ratio
ρ=
2
MW
=1
MZ2 cos2 θ W
This is a property of Higgs in doublet.
2
Give fermion masses
Yukawa coupling
_
LY = fij l iL ljR φ +
fermion mass matrices
v
mij = fij ,
2
Diagonalization of mij =) Yukawa coupling conserves ‡avor &
magnitude is proportional to fermio mass)favor heavy particles
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Higgs mass–not determined by theory and data indicates
mH > 114 Gev /c 2
Search for Higgs
LHC(Large Hadron Collider) : 7 Tev on 7 Tev proton machine
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Production at hadron machine:
(i )
Gluon fusion :
(ii )
V V fusion :
(iii )
Association with V
Decay of Higgs
Ling-Fong Li ()
pp ! gg ! H +
pp ! VV ! H +
,
pp ! qq 0 ! VH +
,
.
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2) Beyond Standard Model Higgs
Motivations for extra Higgs:
1
Neutrino mass(Majorana mass)–leptonic number violation
2
Supersymmetry
3
Spontaneous CP violation
4
Breaking of larger symmetries–
Left-Right model
Grand Uni…ed Theory(GUT)
Little Higgs
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Nov 2008
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Neutrino mass:
Leptons:
νa
la
laL =
2,
L
1
2
_
, laR
(1, 1) , φ =
φ0
φ
2,
1
2
leptonic bilinears:
la L lbR
c
la L lbL
c _
la R lbR
2,
1
2
,
(1, 1) + (3, 1) ,
(1, 2) ,
usual doublet with lepton number L=0
triplet and singlet, L=2
doubley charged singlet, L=2
To get neutrino masses, we need lepton number violation. This can be
achieved by trilinear coupling
φφh
where h is one of L=2 Higgs singlet or triplet.
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Example : Zee model— singlet charged Higgs h +one additional doublet φ2
Yukawa coupling
c
LY = fab la iL lbjL εij h + h..c.
Note that h has 2 units of lepton number. To generate leptons number we
need the trilinear coupling
Lφ = εij φ1i φ2j h + h.c.
Due to the antisymmetric nature of εij we need 2 doublets of Higgs. The
neutrino masses is generated through 1-loop diagram,
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Doubly charged singlet k ++ can give rise to neutrino masses
and also contribute to nuclear ββ decays,
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k ++ can also contribute to many ∆L = 2 processes similar to nuclear ββ
decays,
∆S = 0
Σ ! Σ+ e e
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∆S
Σ
Σ
Ξ
=1
! pe e
! pµ µ
! Σ+ e e
∆S = 2
Ξ ! pe e
Ξ ! pµ µ
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Supersymmetry:
Quarks:
qaL =
ua
da
1
6
2,
L
,
uaR
1,
2
3
,
daR
1,
1
3
quarks bilinear
q aL ubR
2,
1
2
φ† ,
q aL uaR
2,
1
2
φ
But in supersymmetry φ and φ† belongs to two di¤erent chiral multiplets
) two di¤erent doublets of Higgs–one gives masses to up-type of quarks
and the other to down-type of quarks
After spontaneous symmetry breaking, 5 scalar particles left-over, 3
neutral and 2 charged
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Nov 2008
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Spontaneous CP violation:(TD Lee 1973)
Two doublet of Higgs with vacuum expectation value
φ1 =
0
ρ1
,
φ2 =
0
ρ2 e i θ
The CP violation comes from the phase e i θ .
Problem: the Higgs couplings will not conserve ‡avors
Breaking larger symmetries:
Left-right symmetric model: spontaneous violation of parity
Grand uni…cation theory: uni…es strong, electroweak interactions
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Higgs scalar as partner of gauge …eld in higher dimension
Abelian case
Field tensor:
Fab = ∂a Ab
∂b Aa ,
Aa =
!
A0 , A, φ
The part which contains the scalar …eld φ is
Fµ4 = ∂µ φ
∂ 4 Aµ
There is no scalar …eld self interaction. This is true in any dimension.
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Non-Abelian case
(a) 5-dimension
Field tensor:
a
FCD
= ∂C AaD
∂D AaC + igf abc AbC AcD ,
AaC =
!a
Aa0 , A , φa
The part contains scalar …elds is
a
Fµ4
= ∂ µ φa
∂4 Aaµ + igf abc Abµ φc
= ∂µ φa + gf abc Abµ φc
covariant derivative
where Aaµ is assumed to be independent of x4 .
Again there is no self interaction of scalar …eld φa .
(b ) 6-dimension AaC =
!a
Aa0 , A , φa1 , φa2
a
F45
= ∂4 φa1
∂5 φa2 + gf abc φb1 φc2
Now we get scalar …elds self interaction,
a a45
F45
F
! g 2 f abc f ade φb1 φc2 φd1 φe2
The quadratic term can come from the ∂4 φa1
tensor.Ling-Fong Li ()
∂5 φa2 part of the …eld
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