Koji TSUMURA (NTU)
NCTS seminar
22 March 2011
Phenomenology in the Higgs Triplet Model (HTM) with the A_4 Symmetry
T. Fukuyama, H. Sugiyama and K.T.
Phys. Rev. D82 036004 (2010)
Outline
‡
Introduction
‡
Higgs Triplet Model (HTM)
‡
A4 symmetry
‡
HTM with A4
‡
Phenomenology
‡
Summary
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Neutrino
Neutrinos are massless in the SM
But, solar/atmospheric neutrino deficits are observed.
Æ … Massive neutrino?
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Neutrino oscillation
‡
Manifestly oscillating
Æ Massive
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Neutrino (a clear evidence of BSM)
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Introduction
‡
Massive neutrino can be mixed
Mass eigenstates
Flavor eigenstates
‡
Neutrino flavor oscillation
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Neutrino (MNS) mixing matrix
5
Tiny neutrino masses
‡
Oscillation data:
The sign can be determined by matter effects.
Absolute mass scale
or
“normal”
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“inverted”
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Large neutrino mixing
‡
Oscillation data:
Atmospheric (SK)
Reactor (CHOOZ)
Accelerator (K2K,T2K,MINOS)
Maximal mixing
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Small mixing
(not yet measured)
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Solar (SK,SNO)
Reactor (KamLAND)
Large mixing
7
Why are neutrino masses so important?
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Comparison with other fermions
‡
Extremely small mass Æ suggest new phys. Scale?
d
s
u
ν1
c
μ
e
t
τ
TeV
GeV
MeV
keV
eV
meV
μeV
‡
ν2 ν3
b
Large mixing Æ new phys. in lepton sector?
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Fundamental fermion?
‡
Majorana nature for neutral fermions
‡
Mass term can be written by left-handed field.
cf. Charged fermion mass term:
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Connections to new physics
‡
Dim.5 Weinberg op.
‡
Æ
Possible origin of neutrino Majorana mass in the eff. SM
Seesaw I, II and III (tree-level decomposition)
Φc (2)
Φ(2)
NR (1)
T (3)
Δ(3)
L(2)
Æ
Lc (2)
New source of mass scale other than EW vev
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Higgs Triplet Model:
A model for Majorana neutrino mass
‡
Motivations:
‡
‡
μ−
Rich LFV phenomenology
H −−
e−
e−
Interesting collider phenomenology
−
i
q̄
e+
∗
Z ,γ
∗
q
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+
i
H ++
H ++
H −−
−
j
+
k , νk
H −−, H −
γ
+
j
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Higgs Triplet Model (HTM)
‡
Adding a complex SU(2) triplet scalar with Y=2
Doubly charged Higgs boson
‡
Neutrino mass generation in HTM
L# = -2
Triplet scalar develops vev:
L# violation generates NGB?
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HTM potential
‡
Explicit L# breaking to avoid NGB (Majoron)
Triplet scalar develops vev:
Soft L# breaking parameter
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Possible realizations for tiny neutrino mass
‡
Possible realizations
‡ Heavy
triplet scalar (M) : often called type2-seesaw
‡ Small
Yukawa (h_ll)
‡ Small
L# breaking (μ): moderate (M & h_ll)
Æ h_ll can affect low energy LFV,
and triplet scalar can be discovered at the LHC
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HTM at the LHC
q̄
q
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∗
Z ,γ
∗
+
i
H ++
H ++
H −−
+
j
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Phenomenology of double charged Higgs bosons
‡
Pair produced by gauge int. @ LHC
3
10
10
n√
σ( κ
0
C
tro
√s =
1
4 Te
7T
eV
V
2T
-1
√s
=
LHC
s=
H −−
LH
va
q
1
10
Te
++
−−
Z ∗, γ ∗
2
10
H ++
κ ) [fb]
q̄
10
eV
-2
10
‡
200
400
mκ [GeV]
600
800
+
i
Clear leptonic decay signal
H ++
Decays of doubly charged Higgs bosons
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+
j
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Discovery pot. of triplet Higgs boson @ LHC
‡
Akeroyd, Chiang, JHEP11(2010)005
Discovery potential
Luminosity (fb -1)
102
4 lepton
10
≥ 3 lepton
1
10-1
200
300
400
500
600
700
800
mH ±± (GeV)
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LHC vs Low energy data
q̄
q
Z ∗, γ ∗
+
i
H ++
μ−
H ++
H −−
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e+
H −−
+
j
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e−
e−
−
i
−
j
+
k , νk
H −−, H −
γ
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Rich Higgs phenomenology in HTM
‡
Yukawa (h_ll) prop. to Neutrino mass
‡
Rich Higgs phenomenology
‡ H++
can be produced at LHC; M < 1 TeV
‡ H++
decays (Testable!!)
vs neutrino oscillation data
vs low energy LFV (Lepton flavor violation)
vs low energy L#V (Lepton number violation)
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A4 flavor symmetry
A4 group: alternating group for 4 letters
flavor sym.: Origin of fermion masses and mixings
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Why are we focusing on A4 symmetry?
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Large neutrino mixing
‡
Oscillation data:
Atmospheric (SK)
Reactor (CHOOZ)
Accelerator (K2K,T2K,MINOS)
Maximal mixing
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Small mixing
(not yet measured)
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Solar (SK,SNO)
Reactor (KamLAND)
Large mixing
23
Neutrino mixing
‡
Tri-Bi-Maximal mixing: good agreement with experiments.
Z3 symmetry
in charged lepton sector
Z2 symmetry
in neutrino sector
Z6, S3 also contain Z2 and Z3, but there is no irr. 3-rep. Æ A4
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A4 group (alternating group for 4 letters)
‡
even-permutation of 4 letters (12 elements)
‡
Elemental transposition S: S2 = I Æ Z2
‡
Elemental transposition T: T3 = I Æ Z3
others can be obtained from products of S and T, ex., ST, STS, …
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Irreducible representations of A4
‡
Transformations under A4
1-dim. rep. :
3-dim. rep. :
3-dim. rep. may be related for 3 generation of fermion family
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Computation rules
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A4HTM:
The minimal A4 symmetric extension of the Higgs triplet
model with soft A4 breaking terms
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A4HTM (particle contents)
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A4 Yukawa interaction for charged fermions
‡
Mass generation
‡
Developing aligned vev:
‡
Mass eigenvalues:
Structures are same for up and down quarks
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A4HTM potetial 1
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A4HTM potential 2
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A4HTM potential 3
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A4HTM potential 4
‡
Soft A4 breaking terms
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Quark mixing
‡
Unitary transf.
Z3 sym. in quark and charged lepton mixing
‡
Quark CKM mixing
Unit matrix at LO.
(or Quarks can be coupled with other Φ[1], next slide)
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Possible quark sector
‡
Effectively Type-X 2HDM
Quarks and leptons couple to other Higgs doublet
for leptons
for quarks
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Neutrino mixing
‡
Tri-Bi-Maximal mixing: good agreement with experiments.
Z3 symmetry
in charged lepton sector
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Z2 symmetry
in neutrino sector
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Triplet Yukawa interaction for neutrino masses
‡
2-3 maximal mixing is preferred in this basis
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Neutrino mixing
‡
Tri-Bi-Maximal mixing: good agreement with experiments.
Z3 symmetry
in charged lepton sector
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Z2 symmetry
in neutrino sector
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Neutrino masses and mixings under A4
‡
Diagonalize:
‡
A4 sym. + vev alignment Æ TriBiMaximal mixing
Good agreement with experiments.
‡
Note: TB-mixing can be obtained in model without δ[1],
but it is required to solve mass degeneracy of m1 & m3.
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Approximate symmetry in the broken phase
‡
Doublet vev is symmetric under T
A4 Æ Z3 sym
‡
Tiny Triplet vev is symmetric under S
A4 Æ Z2 sym
‡
EW precision obs. ρ:
Æ approx. Z3 symmetry
(slightly broken by triplet vev)
All the particle in A4HTM can be classified by approx. Z3 charge !!
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Z3 classification
‡
Singlets: by default
‡
Triplets
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Z3 charges for leptons
Z3
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A4
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Z3
A4
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Doubly charged Higgs bosons
‡
Mass eigenstates can be determined approximately
by neglecting tiny effects from triplet vev
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Doubly charged Higgs Yukawa interaction
Zeros are consequence of Z3 sym.
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BRs of doubly charged Higgs bosons
‡
A4HTM predicts unique Ratios of BRs.
+
i
H ++
+
j
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Lepton flavor violation
‡
A4HTM (approx. Z3 sym.) forbids specific LFV modes
In particular,
μ−
e+
H −−
e−
e−
Same for
‡
A4HTM predicts specific LFV tau decays
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(Triplet-like) Singly charged Higgs Yukawa interaction
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Decays of singly charged Higgs bosons
‡
Ratios of BRs
+
i
H+
νj
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Lepton flavor violation
‡
Natural suppression
−
i
−
j
+
k , νk
H −−, H −
γ
MEG preliminary result
presented @ ichep10
Discovery of μ Æ e γ excludes A4HTM
It can be excluded by coming MEG data
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Neutral Higgs phenomenology
‡
Only couple to neutrinos
‡
H0, A0 phenomenology may be poooooooor
νi
H 0 , A0
νj
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Summary
‡
‡
‡
HTM provides new source for neutrino mass.
A4 sym. can give large neutrino mixing and small
quark mixing even in HTM.
Remaining Z3 sym. plays an important role in A4HTM.
‡
Unique predictions of triplet Higgs decays
‡
Natural suppression of muon LFV
Thank you very much for your attention.
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Back up
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Lepton universality
‡
Charged Higgs contributes to leptonic decay
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Non-standard neutrino interactions
‡
Charged Higgs contributes to NSI
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Doublet like charged Higgs bosons
‡
Doublet-triplet mixing is suppressed by vev ratio
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