Table Of ContentA light triplet boson and Higgs-to-diphoton in supersymmetric type II
seesaw
Eung Jin Chun, and Pankaj Sharma
aKorea Institute for Advanced Study
Heogiro 85, Dongdaemun-gu, Seoul 130-722, Korea
Abstract
3
ThesupersymmetrictypeIIseesawmayleavealimitwhereatripletbosonalongwiththestandard
1
Higgs boson remains light. Working in this limit with small triplet vacuum expectation vlaues, we
0
2 explore how much such a light triplet boson can contribute to the Higgs boson decay to diphoton,
n and analyze the feasibility to observe it through same-sign di-lepton and tetra-lepton signals in
a the forthcoming LHC run after setting a LHC7 limit in a simplified parameter space of the triplet
J
vaccum expectation value and the doubly charged boson mass.
6
1
] 1. Introduction
h
p
- The origin of neutrino masses and mixing can be attributed to an SU(2)L triplet boson which
p
contains a doubly charged boson [1]. This scenario of type II seesaw can be readily probed at
e
h collidersbyobservingsame-signdi-leptonresonancescomingfromthedoublychargedbosondecay.
[
Furthermore, the observation of the flavor dependent branching ratios of the doubly charged boson
2 allows us to determine the neutrino mass pattern [2]-[8]. Such signals are being searched for at
v
the LHC and non-observation of them puts a strong bound on the mass or the di-lepton branching
7
3 ratio of the doubly charged boson [9, 10].
4 The doubly (and singly) charged boson in type II seesaw can make a sizable contribution to the
1
Standard Model (SM) Higgs boson decay to diphoton [11]-[19]. Thus, the type II seeasaw would
.
1
be a natural framework for the explanation of the current deviation of the Higgs-to-diphoton rate
0
observed by both ATLAS and CMS [20]. Whether or not the current anomaly disappears, more
3
1 precisemeasurementofthediphotonrateinthecomingyearswillplaceanadditionalrestrictionon
:
v the triplet boson mass and coupling to the SM Higgs boson. As was studied in Ref. [17], the scalar
i couplings of the triplet boson are tightly constrained by the EWPD, perturbativity and vacuum
X
stabilityconditionsandthusasizabledeviationoftheHiggs-to-diphotonratecanbearrangedonly
r
a by relatively light triplet boson. This implies that the LHC search for a doubly charged boson in
the small mass region remains important as it can hide from the current search by having a small
di-lepton branching fraction. This is also the case with the supersymmetric type II seesaw model
as will be discussed in this work.
In additional to clean same-sign di-lepton signals, the type II seesaw may exhibit a novel
signature of same-sign tetra-leptons which arises from triplet-antitriplet oscillation [21]. A pair
of neutral triplet and antitriplet produced from pp collision can evolve to a pair of two neutral
triplets or antitriplets which then decay to a pair of same-sign doubly charged bosons leading to
fourleptonsofthesamesigninthefinalstates. Observationofsucheventstogetherwithsame-sign
Preprint submitted to Elsevier December 11, 2013
di-leptons will be a clear confirmation of the existence of not only a doubly charged boson but also
the triplet state of the type II seesaw.
In this paper, we consider a supersymmetric version of the type II seesaw in a limit where light
degreesoffreedomconsistofoneofthetripletbosonsaswellastheusualSMHiggsbosonasinthe
non-supersymmetric model. Although fine-tuned, this would be a unique possibility for a triplet
boson to leave interesting phenomenological impacts in the supersymmetric type II seesaw. When
the triplet Yukawa couplings to leptons in the superpotential are taken to be small, which might
be indicated by the smallness of neutrino masses, the mass splitting among the triplet components
and their scalar couplings are determined by the gauge couplings through the D-term potential,
and thus generically smaller than in the non-supersymmetric model. We will show that a sizable
contributiontotheHiggsbosondecaytodiphotoncanoccurforaverylightdoublychargedboson.
Although the particle content in this scenario is the same as in the non-supersymmetric type II
seesaw, there appear more parameters relevant for the discussion of the neutrino mass generation
and the triplet decays. Taking this difference into account, we will analyze the LHC8 and LHC14
reach of same-sign di and tetra lepton signals in the parameter space of the doubly charged boson
mass and the ratio between the triplet and doublet vacuum expectation values.
2. Triplet boson spectrum and couplings
The supersymmetric type II seesaw model introduces a vector-like pair of SU(2) triplets:
L
∆ = (∆++,∆+,∆0) and ∆¯ = (∆¯0,∆¯−,∆¯−−) with Y = 1 and Y = −1, respectively. In the matrix
representation, they are written as
(cid:32)∆√+ ∆++(cid:33) (cid:32) ∆√¯− ∆¯0 (cid:33)
∆ = 2 , ∆¯ = 2 . (1)
∆0 −∆√+ ∆¯−− −∆√¯−
2 2
Then, the gauge-invariant superpotential contains
1 1 1
W = f LTiτ ∆L + λ HTiτ ∆H − λ HTiτ ∆¯H +µHTiτ H +MTr[∆∆¯]. (2)
2 ij i 2 j 2 1 1 2 1 2 2 2 2 2 1 2 2
Notice that the minimization of the scalar potential gives rise to non-trivial vacuum expectation
values of the triplets generating the neutrino mass matrix
Mν = f (cid:104)∆0(cid:105). (3)
ij ij
Non-vanishing triplet vacuum expectation values arise from the couplings λ , and thus the neu-
1,2
trino masses around 0.1 eV requires fλ ∼ 10−12. In this work, we will assume the smallness
1,2
of both couplings: f,λ (cid:28) 1. The scalar potential relevant for our discussion is presented in
1,2
Appendix.
Let us first calculate the Higgs triplet boson spectrum before considering the mixing mass
between the Higgs doublet and triplet bosons. Ignoring the contribution of the triplet vacuum
√ √
expectation values, (cid:104)∆0(cid:105) ≡ v / 2 and (cid:104)∆¯0(cid:105) ≡ v / 2, we get the mass matrix of the component
∆ ∆¯
∆a and ∆¯a¯:
(cid:18)M2 B (cid:19)
∆a M (4)
B M2
M ∆¯a¯
2
where B is a dimension-two soft mass, and a labels ++, + or 0. Here the diagonal components
M
are given by
c
M2 ≡ M2+m2 +d M2c + aλ2v2c2, (5)
∆a ∆ a Z 2β 4 1 0 β
c
M2 ≡ M2+m2 −d M2c + aλ2v2s2
∆¯a¯ ∆¯ a Z 2β 4 2 0 β
√
where (d ,d ,d ) = (1 − 2s2 ,−s2 ,−1), (c ,c ,c ) = (0,1,2), and (cid:104)H0(cid:105) ≡ v c / 2 and
++ √+ 0 W W ++ + 0 1 0 β
(cid:104)H0(cid:105) ≡ v s / 2. The triplet mass matrix can be diagonalized by the rotation:
2 0 β
∆a = c ∆a−s ∆a (6)
δa 1 δa 2
∆¯a∗ = s ∆a+c ∆a
δa 1 δa 2
where the rotation angle δa satisfies the relation t = 2B /(M2 −M2 ).
2δa M ∆a ∆¯a¯
Now taking the limit of vanishingly small λ ensuring tiny triplet vacuum expectation values,
1,2
we get the mass eigenvalues given by
1 (cid:104) (cid:113) (cid:105)
M2 = 2M2+m2 +m2 ∓ (m2 −m2 +2d M2c )2+4B2 , (7)
∆a1,2 2 ∆ ∆¯ ∆ ∆¯ a Z 2β M
and thus the mass splitting among the triplet components is controlled by the D term. In the
leading order of the D term contribution (assuming |m2 −m2 | (cid:29) M2), we get the relation
∆ ∆¯ Z
M2 −M2 = M2 −M2 = ∓(1−s2 )c c M2 (8)
∆0 ∆+ ∆+ ∆++ W 2δ 2β Z
1,2 1,2 1,2 1,2
where
m2 −m2
c ≡ − ∆ ∆¯ . (9)
2δ (cid:113)
(m2 −m2 )2+4B2
∆ ∆¯ M
In the same limit, the three rotation angles δa can be approximated by the angle δ (9): δa ≈ δ.
Thus, one can take M and δ ≈ δa as input parameters to determine the other masses M
∆++ ∆+,0
1,2 1,2
through the simple relation (8). This leads to the mass hierarchy
M < M < M < M < M < M (10)
∆++ ∆+ ∆0 ∆0 ∆+ ∆++
1 1 1 2 2 2
for c c < 0, which has a similar pattern as in the non-supersymmetric type II seessaw [2]. Here
2δ 2β
letusnotethatthelightertripletstatecanbemademuchlighterthantheheavierstateifthereisa
sizablecancellationbetweenthepositiveandnegativecontributionsinthemass-squaredeigenvalue
M2 . Such a fine-tuned limit (i.e., M (cid:28) M ) is assumed in the major part of this work.
∆1 ∆1 ∆2
From the minimization conditions of the scalar potential (A.1), one can calculate ξ ≡ v /v
∆ ∆ 0
and ξ ≡ v /v . Following the diagonalization matrix (6), it is convenient to split the ratio ξ
∆¯ ∆¯ 0 ∆
and ξ into ξ and ξ :
∆¯ 1 2
ξ = c ξ −s ξ , (11)
∆ δ0 1 δ0 2
ξ = s ξ +c ξ ,
∆¯ δ0 1 δ0 2
3
where ξ are given by
1,2
v[(λ s c2 +λ c s2)M +(λ c +λ s )µs +λ A c c2 +λ A s s2]
1 δ0 β 2 δ0 β 1 δ0 2 δ0 2β 1 1 δ0 β 2 2 δ0 β
ξ ≡ √ ,
1
2 2M2
∆0
1
v[(λ c c2 −λ s s2)M −(λ s −λ c )µs −λ A s c2 +λ A c s2]
1 δ0 β 2 δ0 β 1 δ0 2 δ0 2β 1 1 δ0 β 2 2 δ0 β
ξ ≡ √ .
2
2 2M2
∆0
2
Recall that the ρ parameter constraint, ρ − 1 (cid:46) 0.1%, puts a rough bound |ξ| (cid:46) 1%. We will
further assume |ξ| (cid:28) 0.01 for which the mixing between the Higgs doublet and triplet can be safely
ignored and thus the the triplet states ∆a can be taken as the full mass eigenstates to a good
1,2
approximation.
The doubly charged bosons have the Yukawa couplings to di-lepton and the gauge couplings to
di-W given by
L = √1 (cid:2)c f ¯lcP l +gξ M W−W−(cid:3)∆+++h.c. (12)
δ ij i L j 1 W 1
2
+ √1 (cid:2)−s f ¯lcP l +gξ M W−W−(cid:3)∆+++h.c..
δ ij i L j 2 W 2
2
There are also the scalar couplings to the (heavy) charged Higgs boson H± [see Appendix] which
will be ignored in our analysis. Thus, the light doubly charged boson ∆++ (lighter than H±) can
1
decay only to l+l+ and W+W+ depending on the corresponding couplings c f and ξ .
δ ij 1
Throughoutthiswork, wewilltakethedecouplinglimitoftheheavypseudo-scalarandcharged
√
bosons from the Higgs doublet and thus use the relation: H0 = c (v +h)/ 2, and H0 = s (v +
√ 1 β 0 2 β 0
h)/ 2. Another important aspect of the supersymmetric type II seesaw is that the doubly (singly)
charged boson couplings to the Standard Model Higgs boson h arises from the D-term potential:
(cid:20)g2−g(cid:48)2 g(cid:48)2 (cid:21)
V = c c v h (|∆++|2−|∆++|2)− (|∆+|2−|∆+|2) . (13)
D 2β 2δ 0 2 1 2 2 1 2
The effect of these couplings to one-loop diagrams for the Higgs boson decay to di-photon will be
discussed in the next section.
3. Higgs-to-diphoton rate
Including the contribution from the couplings (13), one obtains the following decay rate of the
Higgs boson to diphoton [22]:
(cid:12)
Γ(h → γγ) = G12F8α√22mπ3h3 (cid:12)(cid:12)(cid:12)(cid:12)(cid:88)NcQ2f gfhfAh1/2(xf)+gWh WAh1(xW) (14)
(cid:12) f
(cid:12)2
+gh [Bh(x )−Bh(x )]+4gh [Bh(x )−Bh(x )](cid:12)
∆+∆− 0 ∆+ 0 ∆+ ∆++∆−− 0 ∆++ 0 ∆++ (cid:12)
1 2 1 2
4
1
2 1.7 1.5
2.5 1.3
1.2
1.4
0.5 1.1
1.05
δ
s2 0 1
o
c
0.95
0.85
-0.5
0.9
-1
50 60 70 80 90 100 110 120
MΔ++
Figure 1: The R contours in the (M ,c ) plane for t = 10. The pink region in the below is disallowed by
γγ ∆++ 2δ β
positivity of the triplet masses. In the purple and gray regions on the left, BF(h→∆++∆−−) becomes larger than
30 % and 10 %, respectively.
where x = m2/4m2. The loop functions are defined by
i h i
Ah (x) = 2x−2[x+(x−1)f(x)] (15)
1/2
Ah(x) = −x−2[2x2+3x+3(2x−1)f(x)]
1
Bh(x) = −4x−1[x−f(x)]
0
√
arcsin2 x for x ≤ 1
where f(x) = (cid:104) √ (cid:105)2
−1 ln 1+√1−x−1 −iπ for x > 1
4 1− 1−x−1
The couplings appearing in (14) are as follows: gh = 1 for the top, gh = 1 for the W boson,
ff WW
and
M2 M2
gh = −c c t2 W and gh = c c (1−t2 ) W, (16)
∆+∆+ 2δ 2β W m2 ∆++∆++ 2δ 2β W m2
h h
for the singly and doubly charged triplet bosons, respectively. Notice that these couplings are
determined by the D-term potential and generically smaller than those coming from the scalar
potential in the non-supersymmetric type II seesaw model constrained by EWPD, perturvativity
and vacuum stability [17]. Furthermore, the light and heavy triplet bosons give opposite contri-
butions. Thus, a sizable deviation to the SM prediction on the diphoton rate can be obtained if
the heavy triplet boson decouples away and the light triplet boson becomes even lighter than the
Higgs boson. Furthermore, the contributions from ∆++ and ∆+ give a constructive interference
1 1
with the SM contribution (which is about −6.5) for c c < 0 corresponding to the mass hierarchy
2δ 2β
M++ < M+ < M0 . For these reasons we will consider the cases with M (cid:28) M , and c > 0
∆1 ∆1 ∆1 ∆1 ∆2 2δ
(with c < 0) to maximize the triplet boson contribution to the diphoton rate. Recall that, given
2β
c and M++, M is determined by M2 ≈ M2 −c c (1−s2 )M2 (8).
2δ ∆1 ∆+1 ∆+1 ∆+1+ 2β 2δ W Z
In Fig. 1, we plot the deviation of the diphoton rate from the SM value in the plane of M
∆++
and c . Here, R denotes the ratio between the Higgs-to-diphoton rates in the type II seesaw and
2δ γγ
5
in the SM: R ≡ Γ(h → γγ) /Γ(h → γγ) . Hereafter ∆ will be denoted by ∆ dropping the
γγ II SM 1
subscript. Ascanbeseen,onecanhaveasizableenhancementofthediphotonrateonlyinalimited
region of small M and large c . In this region, the Higgs coupling to the triplet boson becomes
∆++ 2δ
large enough to make the Higgs decay h → ∆++∆−− comparable to, e.g., the standard decay of
h → WW as both of them come from the gauge vertices. To see this effect, Fig. 1 also shows the
contour lines for which the branching fraction (BF) of the h → ∆++∆−− decay becomes 30 % and
10 %. Although consistent with the SM prediction, the current data [20] is not precise enough
to rule out such non-standard Higgs decays. Therefore, it would be interesting to contemplate
observing the doubly charged boson (and its companions) from the Higgs decay. The final states
from the Higgs decay consist of softer leptons and jets and thus would be distinguishable from
the conventional ones. The precise significance of observing such an exotic Higgs properly needs a
detailed simulation which we leave for a future work.
4. Same-sign di-/tetra-lepton signatures
The doubly charged boson in the type II seesaw is directly searched for by looking at same-sign
di-lepton resonances from the decay ∆±± → l±l±. No excess over the background expectation has
been observed so far and limits are placed on the doubly charged boson mass depending on the
branching ratio assumed for the di-lepton channel [9, 10].
When the doubly charged boson is lighter than the singly charged and neutral components
(c > 0), it decays to either di-leptons or di-W through the coupling in (12). The di-lepton decay
2δ
rates are then given by
|f |2
Γ ≡ Γ(∆++ → l+l+) = Sc2 ij M (17)
lilj i j δ 16π ∆++
where S = 2(1) for i (cid:54)= j(i = j). From the neutrino mass relation: Mν = f ξ v , one gets the
ij ij ∆ 0
total di-lepton rate [2]:
(cid:88) 1 c2m¯2
Γ ≡ Γ = δ ν M (18)
ll lilj 16π|ξ |2v2 ∆++
i,j ∆ 0
where m¯2 = (cid:80) m2 is the sum of three neutrino mass-squared eigenvalues. On the other hand,
ν i νi
the di-W decay ∆++ → W+W+, where one or both of W’s are off-shell for the range of M
∆++
considered in this work, depends on the parameter ξ , that is, Γ ∝ |ξ |2. In Fig. 2, the decay
1 WW 1
rates, Γ and Γ , of the doubly charged boson are presented taking ξ ≡ ξ /c = ξ = 10−5 for
WW ll ∆ δ 1
comparison.
The current neutrino oscillation data allow us to determine the neutrino mass matrix up to CP
phases and mass hierarchies. From the neutrino mass matrices for the normal (NH) and inverted
(IH) hierarchies [21], one can find the individual di-lepton decay rate Γ normalized by the total
lilj
leptonic decay rate Γ as
ll
Γ /Γ (%) ee eµ eτ µµ µτ ττ
lilj ll
NH 0.62 5.11 0.51 26.8 35.6 31.4 (19)
IH 47.1 1.27 1.35 11.7 23.7 14.9
The current LHC search limits on the doubly charged boson [9, 10] imply that the total leptonic
decay rate Γ is much smaller than Γ for the low mass region. For M = 70 GeV, for
ll WW ∆++
instance, the ATLAS limits on σ(pp → ∆++∆−−) × BF(ee,µµ) [10] put the upper bounds on
6
101
Δ++->W+W+
100 Δ++->l+l+
4
1
-1010-1 ξ=10-5
x
V)
e
G
n 10-2
Γ(i
10-3
10-4
50 60 70 80 90 100 110 120
MΔ++
Figure 2: The decay rates Γ and Γ of ∆++ for ξ≡ξ =ξ /c =10−5.
WW ll 1 ∆ δ
the branching fractions; BF(ee) < 0.5 % and BF(µµ) < 0.2 % given the production cross-section
σ(pp → ∆++∆−−) ≈ 2 pb at LHC7 [see Fig. 5]. Here the individual leptonic branching ratio is
given by BF(l l ) = Γ /(Γ +Γ ). Such limits on the di-leptonic branching fractions translate
i j lilj ll WW
into Γ /Γ (cid:46) 0.01 as can be seen in (19). From Fig. 2, one gets the relation
ll WW
Γ (cid:18)8×10−5(cid:19)2(cid:18)8×10−5(cid:19)2
ll
≈ 0.012 (20)
Γ ξ /c ξ
WW ∆ δ 1
for M = 70 GeV, and thus the ATLAS search excludes the region, e.g., ξ /c ,ξ (cid:46) 8×10−5.
∆++ ∆ δ 1
A general analysis in the parameter plane of (M , ξ) with ξ = ξ = ξ /c , is made in Fig. 3
∆++ 1 ∆ δ
which shows contours of branching fractions for the decays ∆±± → e±e±/µ±µ± in the case of the
normal (left) and inverted (right) hierarchies. The shaded regions are excluded by ATLAS search
for the same-sign di-leptons ee and µµ coming only from the pair production of pp → ∆++∆−−.
Theexclusionlinesareobtainedbysmoothingoutthefluctuatingmassdependenceoftheobserved
limits. Recall that the doubly charged boson search through the ee channel is excluded for the
mass range 70–110 GeV in the ATLAS analysis due to a large background coming from Z → e+e−.
As is clear from (19), the exclusion is dominated by the µµ channel in the NH case, whereas the
ee channel wherever applicable provides a little more stringent limit in the IH case. One can see
that BF(µµ) (cid:38)0.1% is excluded in the low mass region (M < 70 GeV) and the limit gets more
∆++
relaxed up to BF(µµ) ∼ 1 % for M ∼ 100 GeV, which correspond to the lower limits; ξ (cid:38) 10−4
∆++
and 10−5, respectively. There is still a lot of parameter space available for such a light doubly
charged boson to escape the current LHC search and waiting for further searches.
In order to get projections for the LHC8 and LHC14 reach, let us first calculate the production
cross-sections of various triplet pairs. The current search at CMS and ATLAS assumes degenerate
triplet bosons which is true for the limiting case of c = 0. However, a sizable mass splitting
2δ
among the triplet components appears generically for c (cid:54)= 0 as discussed in Section 2. In the case
2δ
of c > 0, in particular, ∆++ becomes lighter than ∆+,0 and thus not only the pair production
2δ
of pp → ∆++∆−− but also the gauge decays of, e.g., ∆0 → ∆+W− → ∆++W−W− after the
associated productions of pp → ∆±±∆∓,∆±∆0(†) and ∆0∆0† can contribute to the ∆++∆−− final
7
10-3 10-3
ATLAS-µµ ATLAS-ee ATLAS-µµ ATLAS-ee
µµ-0.1% µµ-0.1% ee-0.1%
µµ-1% ee-0.5% µµ-1% ee-1%
µµ-10% ee-0.1% µµ-10% ee-10%
10-4 10-4
ξ ξ
10-5 10-5
NNNNNNNooooooorrrrrrrmmmmmmmaaaaaaalllllll HHHHHHHiiiiiiieeeeeeerrrrrrraaaaaaarrrrrrrccccccchhhhhhhyyyyyyy IIIIIIIIInnnnnnnnnvvvvvvvvveeeeeeeeerrrrrrrrrttttttttteeeeeeeeeddddddddd HHHHHHHHHiiiiiiiiieeeeeeeeerrrrrrrrraaaaaaaaarrrrrrrrrccccccccchhhhhhhhhyyyyyyyyy
10-6 10-6
50 60 70 80 90 100 110 120 50 60 70 80 90 100 110 120
MΔ++ (in GeV) MΔ++ (in GeV)
Figure 3: BF(µµ) and BF(ee) in the (M , ξ) plane for NH (left) and IH-hierarchy (right), and the ATLAS
∆++
exclusion regions for ee- and µµ-channels.
state. To see how sizable are the gauge decay rates of the heavier triplet boson components, we
show Γ(∆0 → ∆+W−) for various values of c in Fig. 4. Comparing it with Fig. 2, one finds that
2δ
the gauge decay is many orders of magnitude higher than Γ or Γ for the parameter space of
ll WW
our interest, and thus one can infer that ∆+,0 will end up with producing ∆++ with almost 100%
branching ratios. We present in Figs. 5 and 6 various cross-sections of the triplet boson production
as functions of the doubly charged boson mass at LHC7, 8 and 14 for the two choices of c = 0.8
2δ
and0.2, respectively. Whilethepairproductionofpp → ∆++∆−− islargerthantheotherpairand
associated productions, the latter are larger for smaller c (and thus smaller mass gap between
2δ
the triplet components) and for larger M .
∆++
10-3
10-4 0.7
0.5 0.8
10-5 0.4 0.6
V)10-6 0.3
e
n G10-7 0.2
Γ (i10-8
10-9 0.1
10-10
10-11
50 60 70 80 90 100 110 120
MΔ++
Figure 4: The decay rate Γ(∆0 →∆+W−∗) as a function of M for different values of c =0.1−0.8.
∆++ 2δ
Combining all possible channels for the di-lepton production, we plot in Fig. 7 contour lines of
σ(pp → ∆++∆−− +X)×BF(∆++ → e+e+/µ+µ+) in the (M ,ξ) plane at LHC8 and LHC14
∆++
8
101 cos2δ=0.8 ΔΔΔ+++-+-ΔΔΔ-+-- 101 ΔΔΔ+++-+-ΔΔΔ-+-- 102 ΔΔΔ+++-+-ΔΔΔ-+--
b)Section (in p 100 Δ+Δ- Section (in pb) 100 cos2δ=0.8 Δ+Δ- Section (in pb) 110001 cos2δ=0.8 Δ+Δ-
Cross 10-1 Cross 10-1 Cross
10-1
10-2 10-2 10-2
50 60 70 80 90 100 110 120 50 60 70 80 90 100 110 120 50 60 70 80 90 100 110 120
MΔ++ (in GeV) MΔ++ (in GeV) MΔ++ (in GeV)
100 100
Δ+Δ0* Δ+Δ0* cos2δ=0.8 Δ+Δ0*
cos2δ=0.8 Δ-Δ0* cos2δ=0.8 Δ-Δ0* Δ-Δ0*
Δ0Δ0* Δ0Δ0* Δ0Δ0*
b)Section (in p10-1 Section (in pb)10-1 Section (in pb) 100
Cross Cross Cross 10-1
10-2 10-2 10-2
50 60 70 80 90 100 110 120 50 60 70 80 90 100 110 120 50 60 70 80 90 100 110 120
MΔ++ (in GeV) MΔ++ (in GeV) MΔ++ (in GeV)
Figure 5: All the pair and associated production cross-sections of triplets at 7 TeV (left), 8 TeV (middle) and 14
TeV (right) for c = 0.8.
2δ
together with the LHC7 exclusion lines for NH (left) and IH (right). The contours denote σ×BF
of 1 fb which can be reachable readily with minimal luminosity at LHC8 and LHC14. One can
find that the exclusion lines from LHC7 are almost same as in Fig. 3 for lower mass, but a bit
higherforheaviermassasFig.7includesmoredipleptonfinalstatescomingfromalltheassociated
production channels mentioned above. We also find that the figure for c = 0.8 changes very little
2δ
as ξ is insensitive to the change of σ×BF due to the scaling behavior of ξ ∝ 1/(σ×BF)1/4.
Apart from the well-studied same-sign di-lepton signals, there can appear also a novel phe-
nomenon of same-sign tetra-leptons indicating the neutral triplet–antitriplet oscillation [17]. For
this to occur, one needs a condition for the oscillation parameter
δM
x ≡ (cid:38) 1 (21)
Γ
∆0
where δM is the mass splitting between two real degrees of freedom of the neutral triplet boson,
and Γ (cid:39) Γ(∆0 → ∆+W−∗). Arising from the lepton number violating effect, δM is proportional
∆0
to ξ2 and thus can be comparable to the decay rate of Γ ≈ G2∆M5/π3 which is also quite
∆0 F
suppressed for a small mass gap ∆M ≡ M −M . Precise values of Γ are calculated in Fig. 4
∆0 ∆+ ∆0
as functions of M and c . Unlike in the non-supersymmetric type II seesaw, δM is a strongly
∆++ 2δ
model-dependent parameter in the supersymmetric version. Thus, we will parameterize its value
as
δM = aξ2M (22)
1 ∆0
where a is an order-one parameter depending on the other model parameters such as tanβ, the
couplingsλ andthemassesoftheheavypseudoscalarHiggsandtripletbosons, andsoon. Given
1,2
M ,c andξ = ξ = ξ /c , onecangetanestimateofxfrom(22)andΓ inFig.4. Forlarger
∆++ 2δ 1 ∆ δ ∆0
9
Δ++Δ-- Δ++Δ-- Δ++Δ--
101 ΔΔ+-+-ΔΔ+- 101 ΔΔ+-+-ΔΔ+- 102 ΔΔ+-+-ΔΔ+-
b)Section (in p 100 cos2δ=0.2 Δ+Δ- Section (in pb) 100 cos2δ=0.2 Δ+Δ- Section (in pb) 101 cos2δ=0.2 Δ+Δ-
Cross 10-1 Cross 10-1 Cross 100
10-1
10-2 10-2
50 60 70 80 90 100 110 120 50 60 70 80 90 100 110 120 50 60 70 80 90 100 110 120
MΔ++ (in GeV) MΔ++ (in GeV) MΔ++ (in GeV)
101 101
cos2δ=0.2 ΔΔ+-ΔΔ00** cos2δ=0.2 ΔΔ+-ΔΔ00** ΔΔ+-ΔΔ00**
Δ0Δ0* Δ0Δ0* 101 cos2δ=0.2 Δ0Δ0*
b)Section (in p 100 Section (in pb) 100 Section (in pb) 100
Cross 10-1 Cross 10-1 Cross 10-1
10-2 10-2 10-2
50 60 70 80 90 100 110 120 50 60 70 80 90 100 110 120 50 60 70 80 90 100 110 120
MΔ++ (in GeV) MΔ++ (in GeV) MΔ++ (in GeV)
Figure 6: All the pair and associated production cross-sections of triplets at 7 TeV (left), 8 TeV (middle) and 14
TeV (right) for c = 0.2.
2δ
c , one gets larger mass gap and thus more efficient decay of ∆0 → ∆+W−∗ suppressing the value
2δ
of x. Once the oscillation parameter is determined, one can calculate the production cross-sections
for the same-sign tetra-lepton final states from the following formula [17]:
(cid:40)
(cid:16) (cid:17) (cid:16) (cid:17)(cid:20) x2 (cid:21)
σ 4(cid:96)±+nW∓∗ = σ pp → ∆±∆0(†) BF(∆0(†) → ∆±W∓∗)
2(1+x2)
(cid:41)
(cid:16) (cid:17)(cid:20) 2+x2 x2 (cid:21)(cid:104) (cid:105)2
+ σ pp → ∆0∆0† BF(∆0(†) → ∆±W∓∗)
2(1+x2)2(1+x2)
(cid:104) (cid:105)2(cid:104) (cid:105)2
× BF(∆± → ∆±±W∓∗) BF(∆±± → (cid:96)±(cid:96)±) . (23)
i j
Letusnowdiscussifobservablesame-signtetra-leptonsignalscanbeobtainedintheparameter
region where a large enhancement of the Higgs-to-diphoton rate is obtained. To get an idea, let us
first take an example of M = 70 GeV and c = 0.8 which gives R = 1.7. From Fig. 4, one
∆++ 2δ γγ
finds Γ ≈ 10−4 GeV and thus the oscillation for this point is
∆0
(cid:18)8×10−5(cid:19)2
x ≈ 0.008a (24)
(70,0.8) ξ
1
inserting the value of ξ shown in (20). As the oscillation probability is proportional to a tiny
1
number x2, it is impossible to see same-sign tetra-lepton signals even at LHC14 for which the
neutral triplet boson cross-section is just around 1 pb as shown in Fig. 5. This feature remains
true for all the parameter region enhancing the diphoton rate by more than 50 %. Let us remark
that this conclusion can be invalidated if we relax the condition of a ∼ 1 and ξ ∼ ξ /c to allow
1 ∆ δ
a large deviation from this generic relation accepting a certain fine-tuning of parameters.
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