Higgs Bosons Phenomenology in the Higgs Triplet Model

phys.nthu.edu.tw

Higgs Bosons Phenomenology in the Higgs Triplet Model

Higgs Bosons Phenomenology

in the Higgs Triplet Model

Andrew Akeroyd

National Cheng Kung University, Tainan, Taiwan

• TeV scale mechanisms (“testable”) for neutrino mass generation

Higgs Triplet Model

• Production of H ±± and H ± at hadron colliders

• Decays H ±± → l ± l ± and H ± → l ± ν

• Testing HTM at the LHC

A.A, Mayumi Aoki (Kashiwa, ICRR), Phys.Rev.D72,035011 (2005)

A.A, Mayumi Aoki, Hiroaki Sugiyama (SISSA), arXiv:0712.4019[hep-ph]

Seminar at National Tsing Hua Univ, Hsinchu, 17 April 2008


Large Hadron Collider

• LHC (CERN) due to commence operation in summer 2008

• Proton-Proton collisions at √ s = 14 TeV

• Highest energy collider ever built

• ATLAS and CMS optimized for Higgs boson search

• New Physics discovery potential up to TeV scale


Neutrino Mass and Mixing

Strong evidence for neutrino masses and mixings

from both terrestrial and celestial sources

VMNS =



1 0 0

0 c23 s23

0 −s23 c23

⎞ ⎛


⎝ c13 0 s13e −iδ

0 1 0

−s13e iδ 0 c13

⎞ ⎛


⎝ c12 s12 0

−s12 c12 0

0 0 1

Mixing angles are being probed by oscillation experiments:

i) Atmospheric angle almost maximal: sin 2 2θ23 ∼ 1

ii) Solar angle close to maximal: sin 2 2θ12 ∼ 0.8

iii) Reactor angle not measured: sin 2 2θ13 < 0.16

θ23 and θ12 much larger than mixing angles in the

quark sector



Neutrino Mass

Oscillation experiments only sensitive to neutrino

mass differences:

i) ∆M 2 atm ∼ 10−3 eV 2 (= M)

ii) ∆M 2 sol ∼ 10−5 eV 2 (= m)

Other experiments constrain the absolute neutrino mass

• Neutrinoless double beta decay, Cosmological observations..

• Tritium beta decay (H 3 → He 3 + e − + νe): mνe < 2.2 eV

Much lighter than charged fermion masses (me = 0.5 MeV)


Neutrino mass hierarchies

Three possibilities to satisfy oscillation data:

1) Hierarchical ∼ (0, m, M).

2) Inverted hierarchical ∼ (M, M + m,0)

3) Quasi-degenerate ∼ (M, M, M)

m 3 2

m 2 2

m 1 2

0

m 2

atmospheric

~2×10 −3 eV 2

solar~8×10 −5 eV 2

ν e

ν μ

ν τ

? ?

solar~8×10 −5 eV 2

atmospheric

~2×10 −3 eV 2

m 2

m 2 2

m 1 2

m 3 2

0


Future measurements of Neutrino parameters

Present and Future neutrino experiments

(e.g. MINOS, OPERA, T2K, DoubleChooz, Daya Bay

Neutrino Factory...)

i) Measure ∆m 2 , θ12, θ23 with higher precision

ii) Possible first measurement of θ13, CP Phase

Mechanism of mass and mixing?

Models which can be probed at the Tevatron/LHC

are of immediate phenomenological interest


TeV scale models of neutrino mass generation

Many models for neutrino mass generation!

Models with a specific signature at High Energy Colliders

(Tevatron/LHC) are phenomenologically appealing

One such model is:

Higgs Triplet Model (HTM) Schechter/Valle 80, Cheng/Li 80

Distinctive signature:

H ±± with coupling to W, Z and leptons


Higgs Triplet Model (HTM)

SM Lagrangian with one SU(2) L I = 1, Y = 2 Higgs triplet

Higgs potential:

∆ =


⎝ δ+ / √ 2 δ ++

δ 0 −δ + / √ 2

V = m 2 (Φ † Φ) + λ1(Φ † Φ) 2 + M 2 Tr(∆ † ∆)

+λi (quarticterms) + 1 √ 2 µ(Φ T iτ2∆ † Φ) + h.c

Triplet vacuum expectation value:

< δ 0 >= v L ∼ µv 2 /M 2 (1 eV < v L < 8 GeV )



Higgs boson spectrum

The HTM has 7 Higgs bosons: H ±± , H ± , H 0 , A 0 , h 0

• H ± , H 0 , A 0 , h 0 are mixtures of doublet (φ) and triplet (δ) fields

• Mixing ∼ v L/v and v L


Neutrino mass in Higgs Triplet Model (HTM)

No additonal (heavy) neutrinos: L = hijψ T iL Ciτ2∆ψ jL + h.c

Neutrino mass from triplet-lepton-lepton coupling (hij):

hij

√ 2¯l c i P Lljδ ++ + (¯l c i P Lνj +¯l c j P Lνi)δ + − √ 2¯ν c i P Lνjδ 0

Light neutrinos receive a Majorana mass: Mν ∼ v Lhij

hij = 1 √ V

2vL PMNSdiag(m1, m2, m3)V T PMNS

(V PMNS = V †

l Vν; take V l = I and Vν = V PMNS)

+ h.c


Decays of H ±± :

Decay channels for H ±± and H ±

• Γ(H ±± → l ± i l± j ) ∼ h2 ij ; Γ(H±± → W ± W ± ) ∼ v 2 L

• hijv L = mν

Γ(H ±± → l ± l ± ) > Γ(H ±± → W ± W ± ) for v L < 10 −4 GeV

• H ±± → H ± W ∗ suppressed if m H ±± ∼ m H ±

Tevatron searches have only been performed for H ±± → l ± l ±

Decays of H ± :

• Γ(H ± → l ± ν) > Γ(H ± → W ± Z, tb) for v L < 10 −4 GeV

No Tevatron searches yet


BR(H ±± → W ± W ± ) and BR(H ±± → l ± i l± j

BR

1

0.8

0.6

0.4

0.2

0

10 -4

) against triplet vev) Han 07

v , (GeV)


Limits on hij

Presence of H ±± would lead to lepton flavour violating decays

Many limits exist for hij (assuming m H ±± < 1 TeV):

Cuypers/Davidson 98

• BR(µ → eee) < 10 −12 → hµehee < 10 −7 : 1988; no forthcoming experiment

• BR(τ → liljl k) < 10 −8 → hτih jk < 10 −4 Limits from ongoing B factories

• BR(µ → eγ) < 10 −11 →

i hµihei < 10 −6 sensitivity to BR> 10 −13 from 2008

All constraints can be respected with suitably chosen hij

Absolute values not so important for H ±± direct searches


Production of H ±± at Hadron Colliders

(Tevatron and LHC)


Production of H ±± at Tevatron

First searches at a Hadron collider in 2003 CDF,D0

L = i

∂ µ H −−

H ++

gW3Lµ + g ′


q

γ, Z

H ++

q H −−

+ h.c

• σ H ++ H −− is a simple function of m H ±± Raidal et al 96

• σ H ++ H −− has no dependence on hij


Search strategy

• H ±± decays via hij to same charge ee, µµ, ττ, eµ, eτ, µτ

• 4 leptons from pair produced H ++ H −−

• For e ± e ± ,e ± µ ± ,µ ± µ ± , sufficient to search for 2 or 3 leptons

of high momentum with two being of same charge

• Background almost negligible (≈ 1 event)

• Mass limits presented for BR(H ±± → l ± i l± j

in a given channel

) = 100%


Tevatron search (2003) for pp → H ++ H −− , H ±± → e ± e ± , e ± µ ± , µ ± µ ±

BR (pb)

×

Cross section

0.14

0.12

0.1

0.08

0.06

0.04

0.02

0

μμ


ee

Theory (L)

Theory (R)

80 90 100 110 120 130 140 150

H

± ±

Mass (GeV/c

2

)


)

ll’

Coupling (h

10

10

10

10

10

-1

-2

-3

-4

-5

Comparison of H ±± searches

L3, OPAL, DELPHI

ll’


±

±

H

μ

μ


± ±

L

H

O

D

OPAL Exclusion

Single

Production

CDF:

H

H

H

H

± ±

L

± ±

L

± ±

L

± ±

R

→ μμ

→ ee

→ eμ

→ μμ

90 100 110 120 130 140 150 160 170

± ±

2

H

± ±

H →

Strongest mass limits for any Higgs boson!

ee

Mass (GeV/c

)

CD


Tevatron search (2007) for pp → H ++ H −− , H ±± → µ ± µ ±

Cross section (fb)

2

10

10

LEP excl.

excl.

± ±

CDF HR

excl.

±

±

L

CDF H

-1

D0, L = 1.1 fb

Theory(L)

Theory(R)

Observed

Expected

±

1 σ

80 100 120 140 160 180 200

2

(GeV/c )

M ± ±

H

band


Current status of Tevatron searches

ee eµ µµ eτ µτ ττ

2l > 133 GeV > 113 GeV > 136 GeV x x x

3l > 150 GeV > 114 GeV > 112 GeV

4l > 114 GeV > 112 GeV

• > 150 GeV limit uses 1.1 fb −1

• Other limits use 0.24 fb −1 or 0.35 fb −1

• Run II has accumulated ∼ 3 fb −1

• Expect up to 8 fb −1 by 2009

• Sensitivity to m H ±± ∼ 250 GeV in ee, eµ, µµ channels


Single H ±± production via qq ′ → H ±± H ∓

Additional production mechanism for H ±±

L = ig


∂ µ H +

H −− −

∂ µ H −−

H +

W + µ

q ′

W ±

H ±±

q H ∓

+ h.c..

• σ H ±± H ∓ is a function of m H ±± and m H ± Dion et al 98, Gunion 98

• Similar magnitude to σ(pp → H ++ H −− ) for m H ±± ∼ m H ±


Impact of qq ′ → H ±± H ∓

Current searches are already sensitive to qq ′ → H ±± H ∓ !

• 2l search: sensitive to H ±± H ∓ irrespective of H ± decay

• 3l search: sensitive to H ±± H ∓ if H ± → l ± ν

→ Define inclusive single H ±± cross-section for 2l search:

σ H ±±= σ(pp → H ++ H −− ) + 2σ(pp → H ±± H ∓ )

Increases search potential of Tevatron in ee, eµ, µµ channels

Akeroyd,Aoki 05


Inclusive single H ±± production at Tevatron Akeroyd,Aoki 05

σ H ±± = σ(pp → H ++ H −− ) + 2σ(pp → H ++ H − )

σ H±± (fb)

350

300

250

200

150

100

50

H ++ H − − only

(a)

√s

=1.96 TeV

m H± =m H±± −20 GeV

m H± =m H±±

m H± =m H±± +20 GeV

0

100 110 120 130 140 150 160 170 180 190 200

m (GeV)

H±±


Inclusive single H ±± production at LHC Akeroyd,Aoki 05

σ H±± (fb)

100

10

1

0.1

0.01

H ++ H − − only

(a)

m = m −80GeV

H± H±±

m = m H± H±±

m = m +80GeV

H± H±±

√s

=14 TeV

200 300 400 500 600 700 800 900 1000

m H±± (GeV)


Summary for qq ′ → H ±± H ∓

• Cross-section can be as large as qq → H ++ H −−

• Can enhance H ±± discovery potential in 2l,3l channels

• (Best?) Production process for H ± of HTM at hadron colliders

• Not yet simulated (but see Han et al arXiv:0803.3450)


Branching ratio for H ±± → l ± l ± and

testing HTM at LHC

Akeroyd,Aoki,Sugiyama, arXiv:0712.4019[hep-ph]


Light H ±± at LHC

Simulations by Azuelos et al 05, Hebbeker et al 06, Hektor et al 07, Han et al 07

• Discovery for m H ±± < 400 GeV with 1 fb −1

• Precise measurements of BR(H ±± → l ± l ± ) possible for l = e, µ

• Sensitivity to BR(H ±± → l ± l ± ) ∼ 1% for l = e, µ

Large Event Numbers for H ±± :

m H ±± (GeV) N 4l (30 fb −1 ) N 4l (300 fb −1 ) N 2l (300 fb −1 )

200 1500 15000 42000

300 300 3000 8400

400 90 900 2500


BR(H ±± → l ± i l± j

Branching ratios of H ±± → l ± l ±

) depends on relative values of hij

Γ(H ±± → l ± i l± j ) ∼ mH ±±

|hij|

2


In HTM hij is directly related to neutrino mass matrix

hij = 1 √ V

2vL PMNSdiag(m1, m2, m3)V T PMNS

Prediction for BR(H ±± → l ± i l± j ) determined by: Chun,Lee,Park 03

• Neutrino mass hierarchy (normal, inverted)

• Neutrino oscillation parameters (masses, mixing angles)


Explicit expressions for hij

All hij are functions of nine parameters:

hee = 1

√ (m1c

2v∆

2 12c 2 13 + m2s 2 12c 2 13e iϕ1 + m3s 2 13e −2iδ e iϕ2 )

Five parameters are experimentally constrained:

∆m 2 21 ≡ m 2 2 − m 2 1 ≃ 7.9 × 10 −5 eV 2 , |∆m 2 31| ≡ |m 2 3 − m 2 1| ≃ 2.7 × 10 −3 eV 2 ,

sin 2 2θ12 ≃ 0.86 , sin 2 2θ23 ≃ 1 , sin 2 2θ13 < ∼

0.13 .

Main uncertainty in hij comes from:

• Absolute mass of lightest neutrino: 0 < m0 < 1eV

• Majorana phases 0 < φ1, φ2 < 2π

These three parameters are unconstrained by neutrino

oscillation data


Testing the HTM at LHC via precise measurements

of BR(H ±± → l ± l ± )

There are several models of neutrino mass generation with

possibly light H ±± → l ± l ± :

• Left-Right Symmetric Model : I = 1, Y = 2 triplet

Neutrino mass via seesaw mechanism, hij arbitrary

• Zee-Babu Model I = 0, Y = 4 singlet see also Chen et al 06

Radiative neutrino mass, hij partially correlated with

neutrino mass matrix

→ HTM predicts distinctive regions for BR(H ±± → l ± l ± )

which can be tested at LHC for m H ±± < 400 GeV


Dependence of BR(H ±± → l ± l ± ) on m0,φ1,φ2

• Neglect Majorana phases, φ1 = φ2 = 0 :

BR(H ±± → l ± l ± ) essentially determined by absolute

neutrino mass m0

• Include Majorana phases, φ1 = 0, φ2 = 0 :

Allowed regions for BR(H ±± → l ± l ± ) considerably larger

but still smaller than case of arbitrary hij

→ we quantify the prediction for BR(H ±± → l ± l ± ) in the HTM

(see also Garayoa et al,arXiv:0712.1453;Kadastik et al, 0712.3912;Han et al,0803.3450


BR(H ±± → l ± i l± j ) against lightest neutrino mass (m0): normal hierarchy


BR(H ±± → l ± i l± j ) against lightest neutrino mass (m0): inverted hierarchy


BR(H ±± → l ± i l± j ) against Majorana phase and m0 = 0: normal hierarchy

0.6

0.5

0.4

0.3

0.2

NH

μτ

μμ

m 0 = 0

0.1

ττ


0

0

ee

90


180

ϕ = ϕ − ϕ

rel 1 2

270 360


BR(H ±± → l ± i l± j ) against Majorana phase and m0 = 0: inverted hierarchy

0.6

0.5

0.4

0.3

0.2

0.1

μτ

ττ

IH



ee

m 0 = 0

μμ

0

0 90 180 270 360

ϕ

1


HTM prediction in the plane [BR(H ±± → e ± e ± ),BR(H ±± → e ± µ ± )]

BR eμ

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

normal, inverted

(a)

HTM

HTM, normal

HTM, inverted

BR ee +BR eμ = 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

BR ee


HTM prediction in the plane [BR(H ±± → e ± e ± ),BR(H ±± → µ ± µ ± )]

BR μμ

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

normal, inverted

(b)

HTM

HTM, normal

HTM, inverted

BR ee +BR μμ = 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

BR ee


HTM prediction in the plane [BR(H ±± → e ± µ ± ),BR(H ±± → µ ± µ ± )]

BR μμ

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

normal, inverted

(c)

HTM

HTM, normal

HTM, inverted

BR eμ +BR μμ = 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

BR eμ


HTM prediction in the plane [BR(H ±± → e ± e ± ),BR(H ±± → e ± µ ± )]

with/without CP violation from Majorana phases

true

BReμ 0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

(a)

CPV

90%CL

HTM

Case I

Case II

Case III

Case IV

BRtrue ee +BReμ true = 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

true

BRee


Prediction for BR(H ± → l ± ν)

H ± phenomenology important for testing HTM:

Han et al 0803.3450[hep-ph]

• Γ(H ± → l ± νi) ∼ m diagV T PMNS

• BR(H ± → l ± ν) =

i BR(H ± → l ± νi)

• BR(H ± → l ± ν) has no dependence on Majorana phases

• Robust prediction as function of lightest neutrino mass

• Increases importance of pp → H ±± H ∓ in HTM


HTM prediction for H ± → l ± ν: Inverted Hierarchy Han 08


Conclusions

Higgs Triplet Model generates neutrino mass hijv L

• H ±± → l ± l ± is a distinctive signal with BRs determined by hij

• LHC can produce thousands of H ±± → l ± l ± events

if m H ±± < 400 GeV

• HTM predicts specific regions for BR(H ±± → l ± l ± )

which can be tested at LHC

• Strong prediction for BR(H ± → l ± ν)

• H ± best produced via pp → W → H ±± H ∓

• Simulations of pp → W → H ±± H ∓ well-motivated

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