Phenomenology of Doubly Charged
Higgs Bosons at Hadron Colliders
Andrew Akeroyd
NExT Institute, SHEP, University of Southampton, UK
• Higgs Triplet Model (HTM) and doubly charged scalars (H ±± )
• Leptonic decay channels H ±± → ℓ±ℓ±
• Production of H ±± at hadron colliders
• Searches for H ±± at the Large Hadron Collider
Collaborators: Mayumi Aoki (Kanazawa, Japan), Hiroaki Sugiyama (Ritsumeikan, Japan),
Cheng-Wei Chiang (Nat.Cent.Univ, Taiwan), Naveen Gaur (Delhi, India), Stefano Moretti (Soton, UK)
Seminar at University of Sussex, 30 January 2012 (based on work from 2005 → 2012)
CERN Large Hadron Collider
• LHC is colliding protons at
√
s = 7 TeV(until 12/2012)
√
• From 2014 it will operate at s = 14 TeV
• Search for the SM Higgs boson of high priority
• Its search is receiving attention in the media
• Detectors ATLAS and CMS have collected 5 fb−1
• Sensitvity to the mass range 100 GeV < MH < 600 GeV
• The Higgs sector of the SM will be confirmed or falsified
within two years
LHC search for the Higgs Boson of the Standard Model
The mass range 115 GeV < MH < 128 GeV is not excluded (small excess?). Similar result from ATLAS
Electrically Charged Higgs Bosons (Scalars)
The Higgs boson of the Standard Model is a spinless, neutral
particle with a vacuum expectation value (v = 246 GeV, mf = hf v)
Still undiscovered If exists, how many Higgs bosons?
Classify Higgs bosons by their electric charge
• Neutral: h0 (SM 1967), H 0,A0 (2HDM 1973, MSSM 1980...)
• Singly Charged: H ± (2HDM, MSSM..)
• Doubly Charged: H ±± (this talk, twice the charge of e±)
These three types have received considerable theoretical/experimental attention
(Order of priority: neutral > singly charged > doubly charged)
Models with Doubly Charged Higgs Bosons, H ±±
Motivation → neutrino mass generation
Scalar triplets (isospin I = 1) and scalar singlets (I = 0)
• Higgs Triplet Model : I = 1,Y = 2 (tree-level mass for ν)
• LR Symmetric Model : I = 1,Y = 2 (tree-level mass for ν)
• Zee-Babu Model : I = 0,Y = 4 (radiative mass for ν)
All of these models are in textbooks (“classic models”)
I will discuss the Higgs Triplet Model
Konetschny/Kummer 77, Schechter/Valle 80, Cheng/Li 80
(recently I = 3/2 and I = 1/2 studied)
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
−s13 eiδ
0
1
0
s13 e−iδ
0
c13
c12
−s12
0
s12
c12
0
0
0
1
Mixing angles are being probed by oscillation experiments:
i) Atmospheric angle is close to maximal: sin2 θ23 ∼ 0.5
ii) Solar angle is sizeable, but not maximal: sin2 θ12 ∼ 0.3
iii) Reactor angle is not measured: sin2 θ13 < 0.03
2
2 ∼ 10−5eV 2
iv) Mass differences small: ∆Matm
∼ 10−3eV 2, ∆Msol
Higgs Triplet Model can accommodate these values
Higgs Triplet Model (HTM)
SM Lagrangian with one SU (2)L I = 1, Y = 2 Higgs triplet


√
++
+/ 2
δ
δ
√ 
∆=
0
+
δ
−δ / 2
2 >0
Higgs potential invariant under SU (2)L ⊗U (1)Y : m2 < 0, M∆
2 Tr(∆†∆)
V = m2(Φ†Φ) + λ1(Φ†Φ)2 + M∆
1
+λi (quartic terms) + √ µ(ΦT iτ2∆†Φ) + h.c
2
2
Triplet vacuum expectation value : < δ 0 >= v∆ ∼ µv 2/M∆
2 ∼ 1); ∆ has L# = 2 and so µ(ΦT iτ ∆† Φ) violates lepton number
< 5 GeV to keep ρ = (MZ2 cos2 θW )/MW
(v∆ ∼
2
Higgs boson spectrum
The HTM has 7 Higgs bosons: H ±±, H ±, H 0, A0, h0
• H ±± is purely triplet: H ±± ≡ δ ±±
• H ±, H 0, A0, h0 are mixtures of doublet (φ) and triplet (δ) fields
• Mixing ∼ v∆/v and small (v∆/v < 0.03)
• h0 plays role of SM Higgs boson (essentially I = 1/2 doublet)
• H ±, H 0, A0 are dominantly composed of triplet fields
• Masses of H ±±, H ±, H 0, A0 close to degenerate ∼ M∆
• For H ±±, H ± in range at LHC require M∆ < 1 TeV
2 /v 2 )
Masses of the Higgs bosons in the HTM as a function of µ (∼ v∆ M∆
The triplet scalars tend to be degenerate, and H ±± is the lightest for λ4 > 0 AGA/Chiang 10
Neutrino mass in Higgs Triplet Model (HTM)
T Ciτ ∆ψ
No additional (heavy) neutrinos: L = hij ψiL
2
jL + h.c
T = (ν , ℓ ); i = e, µ, τ
ψiL
i i
Neutrino mass from triplet Yukawa coupling, hij (complex and symmetric):
hij
√
2 ℓ̄ciPLℓj δ ++ + (ℓ̄ciPLνj + ℓ̄cj PLνi)δ + −
√
2 ν̄icPLνj δ 0 + h.c
Light neutrinos receive a Majorana mass: Mνij ∼ v∆hij
hij = √ 1
2v∆
T
VPMNS diag(m1, m2, m3)VPMNS
(mi=neutrino masses; VPMNS = Vℓ†Vν ; take Vℓ = I and Vν = VPMNS )
Decay channels for H ±± and H ±
Decays of H ±± :
• In HTM: hij v∆ ∼ Mνij (neutrino mass matrix)
±
2 ∼ 1/v 2 ; Γ(H ±± → W ±W ±) ∼ v 2
• Γ(H ±± → ℓ±
ℓ
)
∼
|h
|
ij
i j
∆
∆
Γ(H ±± → ℓ±ℓ±) > Γ(H ±± → W ±W ±) for v∆ < 10−4 GeV
Tevatron/LHC Searches have only been performed for H ±± → ℓ± ℓ±
Decays of H ± :
± → W ±Z, tb) for v < 10−4 GeV
• Γ(H ± → ℓ±
ν)
>
Γ(H
∆
i
Notably, if hij > helectron then necessarily v∆ < 10−4 GeV
±
± → ℓ±ν dominate
→ leptonic decays H ±± → ℓ±
and
H
ℓ
i j
i
P
±
BR(H ±± → ℓ±
i ℓj ) against triplet vev
BR
BR(H ±± → W ± W ± ) and
Han 07, Asaka/Hikasa 94
1
0.8
0.6
0.4
0.2
0
10
-4
,
v (GeV)
±
±± → W ± W ± ), assuming v
−4 GeV
I will only discuss the phenomenology of H ±± → ℓ±
∆ < 10
i ℓj (not H
Branching ratios of H ±± → ℓ±ℓ±
±
BR(H ±± → ℓ±
ℓ
i j ) determined by hij
Γ(H ±±
→
±
ℓ±
ℓ
i j )
(six decays ee, eµ, µµ, eτ, µτ, τ τ )
mH ±±
|hij |2
∼
8π
In HTM hij is directly related to the neutrino mass matrix
hij = √ 1
2v∆
T
VPMNS diag(m1, m2, m3)VPMNS
±
Prediction for BR(H ±± → ℓ±
ℓ
i j ) determined by: Chun,Lee,Park 03
• Neutrino mass matrix parameters (masses, angles, phases)
• Neutrino mass hierarchy: normal (m3 > m2 > m1) or inverted
HTM prediction in the plane [BR(H ±± → e±e± ),BR(H ±± → e± µ±)]
normal, inverted
0.7
HTM
HTM, normal
HTM, inverted
BRee+BReµ= 1
(a)
0.6
BReµ
0.5
0.4
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
BRee
White region is ruled out by neutrino oscillation data
AGA/Aoki/Sugiyama 07
Limits on hij
Presence of H ±± would lead to lepton-flavour-violating decays
Many limits exist for hij (assuming mH ±± < 1 TeV):
• BR(µ → eee) < 10−12 → |hµehee| < 10−7
Cuypers/Davidson 98
1988; no forthcoming experiment
• BR(τ → ℓiℓj ℓk ) < 10−8 → |hτ ihjk | < 10−4
Limits from ongoing B factories
• BR(µ → eγ) <
sensitivity to BR∼ 10−13 from 2012
10−11
→
P
i |hµihei |
< 10−6
All constraints can be respected with |hij | < 10−2 or 10−3
These decays provide valuable probes of virtual effects of H ±±
Production of H ±± at Hadron Colliders
(Tevatron and LHC)
Pair production of H ±± at Hadron Colliders
First searches at a hadron collider in 2003
µ
L=i ∂ H
−−
q
q
H
++
γ, Z
Tevatron: CDF,D0
′
gW3µ + g Bµ + h.c
H ++
H −−
• σH ++H −− is a simple function of mH ±±
• σH ++H −− has no dependence on hij
Barger 82, Gunion 89, Raidal 96
Single H ±± production via q ′q → H ±±H ∓
A mechanism not included in the Tevatron searches
L = ig
∂ µH + H −− − ∂ µH −− H + Wµ+ + h.c..
q′
q
W±
H ±±
H∓
• σH ±±H ∓ is a function of mH ±± and mH ±
Barger 82, Dion 98
• Similar magnitude to σ(pp → H ++H −−) for mH ±± ∼ mH ±
Inclusive single H ±± production at Tevatron
AGA,Aoki 05
Experimental search was sensitive to σH ±± = σ(pp → H ++ H −− ) + 2σ(pp → H ++ H −)
(a)
350
300
√ s =1.96 TeV
σH±± (fb)
250
mH±=mH±±−20 GeV
mH±=mH±±
200
150
mH±=mH±±+20 GeV
100
50
++
−−
H H
only
0
100 110 120 130 140 150 160 170 180 190 200
mH±± (GeV)
Mass limit mH ±± > 150 GeV at Tevatron would strengthen to mH ±± > 180 GeV
√
LHC cross sections at s = 7 TeV for qq → H ++H −− and qq ′ → H ±±H ∓
σ(qq ′ → H ±± H ∓ ) > σ(qq → H ++ H −− ) for mH ± = mH ±± and so should be included in searches
Importance of qq ′ → H ±±H ∓
• σ(qq ′ → H ±±H ∓) can be as large as σ(qq → H ++H −−)
• Increases the sensitivity to mH ±± in 2ℓ and 3ℓ search channels,
thus enhancing the discovery potential for H ±±
AGA,Aoki 05
• Received almost no theoretical attention from 1982 to 2005
• Not included in event generator Pythia , unlike qq → H ++H −−
• In
AGA/Chiang/Gaur 10
we created a CalcHEP file to generate events
for qq ′ → H ±±H ∓, which can then be used as input for Pythia
• This enabled the CMS collaboration to carry out a
search for qq ′ → H ±±H ∓
Strategy of search for H ±± by CMS collaboration (LHC)
• H ±± decays via hij to same charge ee, µµ, τ τ, eµ, eτ, µτ
• In the HTM, BR(H ±± → ℓ±ℓ±) depends mainly on
i) neutrino mass m1 and ii) Majorana phases φ1 and φ2
• Define four benchmark points for BR(H ±± → ℓ±ℓ±)
BP1 (normal hierarchy)
BP2 (inverted hierarchy)
BP3 (degenerate neutrinos)
BP4 (equal branching ratios)
ee
0
0.50
1/3
1/6
eµ
0.01
0
0
1/6
µµ
0.3
0.125
1/3
1/6
eτ
0.01
0
0
1/6
µτ
0.38
0.25
0
1/6
ττ
0.3
0.125
1/3
1/6
Search strategy for H ±± → ℓ±ℓ± and H ± → ℓ±ν at LHC
CMS search for H ±± is the first one to include both production
mechanisms qq → H ++H −− and qq ′ → H ±±H ∓
(CMS PAS HIG-11-007)
i) 4ℓ signature (ℓ+ℓ+ℓ−ℓ−):
• Backgrounds are negligible after all selection cuts
• Only H ++H −− contributes to the signal
ii) 3ℓ signature (ℓ±ℓ±ℓ∓):
• H ±±H ∓ contributes to the signal (assume mH ± = mH ±± )
• H ++H −− contributes if one lepton is missed
LHC (CMS collaboration) search for 3ℓ signature
After pre-selection cuts (signal for BP4)
After all selection cuts (signal for BP4)
Excluded cross sections from 3ℓ and 4ℓ search: ee and eµ channels
3ℓ (red) and 4ℓ (blue) have very similar sensitivity to mH ±± . When combined, give stronger limit on mH ±± .
Excluded cross sections from 3ℓ and 4ℓ search: eτ and µτ channels
4ℓ search (blue) has greater sensitivity to mH ±± than 3ℓ search
Mass limits on mH ±± from CMS search for H ±± → ℓ±ℓ±
Mass limit mH ±± > 300 GeV for BR(H ±± → ℓ±ℓ±) = 100% for ℓ = e, µ
Recent ATLAS search for H ±± → µ±µ±
arXiv:1201.1091
ATLAS has performed three searches for qq → H ++H −−
• Search in
arXiv:1201.1091
is only performed for H ±± → µ±µ±
• Uses 1.6 fb−1 of integrated luminosity (CMS used 0.98 fb−1)
• Signal is defined as two same-signed (µ±µ±)
• Differs from CMS search strategy ( ℓ±ℓ±ℓ∓ and ℓ+ℓ+ℓ−ℓ− )
• Number of signal events is linear (not quadratic)
in BR(H ±± → µ±µ±)→ can probe smaller values of BR
• Current search does not include qq ′ → H ±±H ∓
−−
BR(H±± → µ ±µ ±)
ATLAS
∫ Ldt = 1.6 fb
-1
10
1
0.9
s = 7 TeV
Observed 95% C.L. limit
Expected 95% C.L. limit
0.8
L
σ(pp → H++ H )× BR(H±± → µ± µ±) [fb]
ATLAS search for H ±± → µ±µ± with 1.6 fb−1 (CMS used 0.98 fb−1 )
Expected limit ± 1σ
0.7
0.6
0.5
1
R
10-1
100
0.4
Observed 95% C.L. upper limit
Expected 95% C.L. upper limit
Expected limit ± 1σ
Expected limit ± 2σ
++ −−
σ(pp → H HL ), BR(H±±→µ±µ±)=100%
L
L
++ −−
σ(pp → H HR ), BR(H±±→µ±µ±)=100%
150
250
∫ Ldt = 1.6 fb
-1
0.2
0.1
R
200
ATLAS
0.3
300
350
400
H±± mass [GeV]
0
100
s = 7 TeV
150
200
250
300
350
M(H±±) [GeV]
L
Limit mH ±± > 355 GeV; stronger than CMS bound for H ±± → µ±µ± (mH ±± > 313 GeV)
Status of searches for H ±± at LHC
The CMS collboration has performed the first search
(July 2011) for H ±± at the LHC
√
−1
at s = 7 TeV
• Used 0.98f b
(CMS PAS HIG-11-007)
• Both 4ℓ and 3ℓ signatures studied
• All six decay channels investigated: ee, eµ, µµ, eτ, µτ, τ τ
• For the first time qq ′ → H ±±H ∓ included in search for H ±±
• ATLAS
(Aug/Oct/Nov 2011)
have searched for 2ℓ, 3ℓ, 4ℓ
• Have not yet included qq ′ → H ±±H ∓ in the 2ℓ and 3ℓ searches
Case of non-degeneracy of triplet scalars
mH ±± < mH ± < mH 0,A0
Case of non-degeneracy of triplet scalars
The ongoing CMS searches assume mH ±± = mH ± = mH 0,A0
This is only true if λ4 = 0 in scalar potential term λ4 H †∆∆†H
• For λ4 > 0 one has mH ±± < mH ± < mH 0,A0
• The decay H ± → H ±±W ∗ would be open, and can have a
large branching ratio even for mH ± − mH ±± << mW
• q ′q → W ∗ → H ±±H ∓ then leads to H ++H −−W ∗
• Would increase sensitivity to mH ±± in 4ℓ searches
AGA/Sugiyama 11
BR(H ± → H ±±W ∗) as a function of (mH ± − mH ±± ) and v∆
mH±±= 200GeV, mh= 120GeV, m3 > m1=0.1eV
(a) mH±±= 200 GeV, v∆=100 eV, mh= 120GeV, m3 > m1=0.1 eV
109
1
108
0.8
H
0.6
±±
107
*
W
lν
BR=0.5
BR=0.9
BR=0.99
v∆ (eV)
H± decay branching ratios
AGA/Sugiyama 11
106
105
0.4
104
0.2
0
200
103
210
220
230 240
mH± (GeV)
250
260
270
102
200
210
220
230
240
mH± (GeV)
Large parameter space for BR(H ± → H ±±W ∗ ) > 50%
250
260
270
CMS sensitivity (with 0.98 fb−1) to mH ±± in ℓ+ℓ+ ℓ−ℓ− channel as function of mH ± − mH ±±
qq ′ → H ±± H ∓ with H ± → H ±± W ∗ increases sensitivity to mH ±± by as much as 50 GeV Senjanovic et al 11
Five-lepton/six-lepton signals and detection of H 0 and A0
Several cascade decays involving neutral triplet scalars
• BR(A0 → H ±W ∗) and BR(H 0 → H ±W ∗) can also be ∼ 100%
• q ′q → W ∗ → H ±H 0, H ±A0 leads to H ++H −−W ∗W ∗W ∗
• qq → Z ∗ → H 0A0 leads to H ++H −−W ∗W ∗W ∗W ∗
• W ∗ → ℓν (ℓ = e, µ) of particular interest
• Leads to 5ℓ and 6ℓ signatures with negligible background
• Would enable detection of H 0 and A0
• No search yet for 5ℓ and 6ℓ signatures
AGA/Moretti/Sugiyama 12
Cross sections for 5-lepton and 6-lepton signatures at LHC with
mH± (GeV)
300
10
320
√
mH± (GeV)
340
300
10
320
σ (fb)
σ (fb)
X5l
3
X5l
1
X5l
4
0.1
300
340
360
mA0,H0 (GeV)
380
1
6l(Total)
X6l
3
(a) s = (7 TeV)2
v∆ = 1000 eV
mH±± = 300 GeV
320
340
(a) s = (7 TeV)2
v∆ = 1000 eV
mH±± = 300 GeV
5l(Total)
1
s = 7 TeV
X6l
4
400
0.1
300
Maximum of 4 fb for 5ℓ and 0.6 fb for 6ℓ
320
340
360
mA0,H0 (GeV)
AGA/Moretti/Sugiyama 12
380
400
Conclusions
• Doubly charged Higgs bosons appear in the Higgs Triplet
Model of neutrino mass generation
• Neutrino mass generated at tree-level as hij v∆
• H ±± → ℓ±ℓ± is a distinctive signal
• Multi-lepton signals (2ℓ → 6ℓ) from qq → H ++H −− / q ′q → H ±±H ∓
• Searches
(2ℓ → 4ℓ)
are ongoing, with sensitivity mH ±± < 300 GeV
• The HTM also predicts a SM-like Higgs boson in most of
the parameter space of the scalar potential
• A large parameter space of the model will be probed
at the LHC