Table Of ContentFTPI–MINN–16/03
UMN–TH–3513/16
Testing the 2-TeV Resonance with Trileptons
Arindam Dasa, Natsumi Nagatab, Nobuchika Okadaa
6
1 aDepartment of Physics and Astronomy, University of Alabama,
0
Tuscaloosa, Alabama 35487, USA
2
bWilliam I. Fine Theoretical Physics Institute, School of Physics and Astronomy,
n
a University of Minnesota, Minneapolis, Minnesota 55455, USA
J
9
1
]
h Abstract
p
- The CMS collaboration has reported a 2.8σ excess in the search of the SU(2)
R
p
gauge bosons decaying through right-handed neutrinos into the two electron plus
e
h two jets (eejj) final states. This can be explained if the SU(2) charged gauge
R
[ bosons W± have a mass of around 2 TeV and a right-handed neutrino with a
R
1 mass of O(1) TeV mainly decays to electron. Indeed, recent results in several
v
other experiments, especially that from the ATLAS diboson resonance search, also
9
7 indicate signatures of such a 2 TeV gauge boson. However, a lack of the same-sign
0 electron events in the CMS eejj search challenges the interpretation of the right-
5
handed neutrino as a Majorana fermion. Taking this situation into account, in this
0
. paper, we consider a possibility of explaining the CMS eejj excess based on the
1
0 SU(2)L ⊗SU(2)R ⊗U(1)B−L gauge theory with pseudo-Dirac neutrinos. We find
6 that both the CMS excess events and the ATLAS diboson anomaly can actually
1
be explained in this framework without conflicting with the current experimental
:
v bounds. This setup in general allows sizable left-right mixing in both the charged
i
X gauge boson and neutrino sectors, which enables us to probe this model through
r the trilepton plus missing-energy search at the LHC. It turns out that the number
a
of events in this channel predicted in our model is in good agreement with that
observed by the CMS collaboration. We also discuss prospects for testing this
model at the LHC Run-II experiments.
1 Introduction
The CMS collaboration announced that they observed excess events in their search for
new massive charged gauge bosons (W±) associated with the the SU(2) gauge symmetry
R R
which decay into two leptons and dijet through heavy right-handed neutrinos [1]. The
excess was found in the invariant mass distribution of the two electrons and dijet (eejj)
final states around 2 TeV, whose significance is 2.8σ. This signal, if confirmed, certainly
implies the presence of TeV-scale new physics. Various models have been proposed so
far to interpret this CMS excess; see, e.g., Refs. [2–9]. Among them, models based on
the SU(2) ⊗SU(2) ⊗U(1) gauge theory [10] are the simplest and most promising
L R B−L
candidates, since they contain right-handed neutrinos and W± as their indispensable
R
ingredients. Indeed, such models have attracted a lot of attentions recently [5–9, 11] since
they can explain possible anomalies observed in other (totally independent) experiments,
such as a 3.4σ excess in the ATLAS diboson resonance search [12], an around 2σ excess
in the CMS dijet resonance search [13], and a 2.2σ excess in the W±h channel where W±
decays leptonically and the Higgs boson h decays into bb [14]. All of these results indicate
the presence of W± with a mass of around 2 TeV.
R
If such a TeV-scale W± exists, in the SU(2) ⊗ SU(2) ⊗ U(1) models, we also
R L R B−L
expect that there are right-handed neutrinos whose masses are of O(1) TeV. The presence
of these right-handed neutrinos is desirable since we can exploit them to explain the CMS
eejj excess events. An important caveat here is, however, that the CMS collaboration
observed only one same-sign electron event among all 14 eejj events [1]. This observation
disfavors the conventional SU(2) ⊗ SU(2) ⊗ U(1) model with an SU(2) triplet
L R B−L R
Higgs field; in this case, right-handed neutrinos are Majorana fermions, with which we
expect the same number of same-sign dilepton events as that of the opposite-sign ones.
In addition, TeV-scale right-handed Majorana neutrinos are stringently restricted by the
recent ATLAS [15] and CMS searches [16, 17] in the same-sign leptons plus dijet final
states. Therefore, it is required to extend this conventional model so that it evades the
above problems.
The inverse seesaw [18] mechanism offers a promising way to reconcile the difficulties.
In this mechanism, three singlet fermions are added to the neutrino sector on top of right-
handed neutrinos. Then, small lepton-number violation in the singlet mass terms results
in three light left-handed neutrinos as well as heavy pseudo-Dirac neutrinos. Since a neu-
trino which couples to W± is a pseudo-Dirac fermion, the lepton number is approximately
R
conserved in the process of W± decaying to the neutrino, which accounts for a lack of
R
same-sign electron events in the CMS eejj signals. Moreover, this mechanism has an ad-
vantage in explaining small neutrino masses with TeV-scale SU(2) ⊗SU(2) ⊗U(1)
L R B−L
symmetry. With such a low-scale symmetry-breaking of SU(2) , the ordinary type-I
R
seesaw mechanism [19] can yield small neutrino masses only with very small Yukawa cou-
plingsunlessaspecificmassstructureisassumed[20], whiletheinverseseesawmechanism
allows the couplings to be sizable. This feature is favorable when the model is considered
in the framework of grand unification [21] like SO(10) models [22].
In this paper, we consider an SU(2) ⊗SU(2) ⊗U(1) model that is extended to
L R B−L
1
accommodate the inverse seesaw mechanism. For recent work which considers a similar
model, see Ref. [6]. It is found that our model can actually realize the right number of
eejj signals observed in the CMS experiment [1]. A characteristic feature of our model
is that it allows sizable left-right mixing in both the charged gauge boson and neutrino
sectors. Indeed, such a significant W–W mixing is favored from the viewpoint of the
R
ATLAS diboson excess [12]. Moreover, the inverse seesaw mechanism allows a large left-
right neutrino mixing while keeping neutrino masses tiny. In the presence of the left-right
mixing, a heavy Dirac neutrino can decay into not only the two leptons plus two jets final
statesviaavirtualW exchange, butalsointoaleptonplusagauge/Higgsbosonchannels
R
via the left-right mixing. Such decay processes yield a trilepton plus missing energy
signature, which is regarded as the golden channel for probing heavy Dirac neutrinos at
the LHC [23–27]. We study the prediction of our model in this channel, and find that
the predicted number of events is in good agreement with the result given by the CMS
collaboration [28]. We further discuss the future prospects for testing this model at the
next stage of the LHC run.
This paper is organized as follows. In the next section, we first describe our model
which we consider in this work. In Sec. 3, we show the decay branching ratios of W and
R
heavy Dirac neutrinos. Then, we study the collider signatures of our model in Sec. 4.
Section 5 is devoted to conclusion and discussions.
2 Model
To begin with, we propose a model based on the SU(3) ⊗SU(2) ⊗SU(2) ⊗U(1)
C L R B−L
gauge symmetry which has the structure of the inverse seesaw mechanism [18] in the
neutrino sector. As in the Standard Model (SM), left-handed quarks and leptons form
SU(2) doublet fields:
L
(cid:32) (cid:33) (cid:32) (cid:33)
u ν
Q = Li , L = Li , (1)
Li d Li e
Li Li
where i = 1,2,3 denotes the generation index. On the other hand, right-handed fermions
are embedded into the SU(2) fundamental representation as
R
(cid:32) (cid:33) (cid:32) (cid:33)
u N
Q = Ri , L = Ri . (2)
Ri d Ri e
Ri Ri
In addition, we introduce three gauge-singlet fermions S , which lead to chiral partner
Li
fields of N as we see below.
Ri
The Higgs sector of this model contains two Higgs multiplets. One is an SU(2) ⊗
L
SU(2) bi-doublet scalar field with zero B − L charge, which breaks the electroweak
R
symmetry and thus plays a role of the SM Higgs field. We denote it by Φ and its vacuum
expectation value (VEV) by
(cid:32) (cid:33)
v 0
u
(cid:104)Φ(cid:105) = , (3)
0 v
d
2
(cid:112)
with v = v2 +v2 (cid:39) 174 GeV. Moreover, to break the SU(2) symmetry, we introduce
u d R
an SU(2) doublet Higgs field H with a B −L charge +1, whose VEV is given by
R R
(cid:32) (cid:33)
0
(cid:104)H (cid:105) = . (4)
R
v
R
This breaks SU(2) ⊗SU(2) ⊗U(1) to SU(2) ⊗U(1) .
L R B−L L Y
With these particle contents, the interaction terms are generically given as follows:
L =−yQQ ΦQ −yQQ Φ(cid:101)Q −yLL ΦL −yLL Φ(cid:101)L
int ij Ri Lj (cid:101)ij Ri Lj ij Ri Lj (cid:101)ij Ri Lj
1
−f L iσ H∗S − µ Sc S +h.c. , (5)
ij Ri 2 R Lj 2 ij Li Lj
where Φ(cid:101) ≡ σ Φ∗σ with σ (a = 1,2,3) being the Pauli matrices, and c indicates the
2 2 a
charge conjugation. Note that the Majorana mass terms for right-handed neutrinos N
Ri
are forbidden by the SU(2) gauge symmetry. After the above Higgs fields develop the
R
VEVs, these interaction terms lead to the mass terms of the fermions. Here we assume
that these Yukawa couplings and the VEVs are appropriately chosen so that the resultant
mass terms agree to the observed quark and lepton masses as well as the Cabibbo–
Kobayashi–Maskawa (CKM) matrix elements.1 The mass matrix of the neutrino sector
is written as
1
L = − ψcM ψ +h.c. , (6)
mass 2 i ij j
where ψ ≡ (ν ,Nc ,S ), and
i Li Ri Li
0 MD 0 (cid:32) (cid:33)
0 M
D
M = MT 0 MT ≡ , (7)
ij D N MT M
D N
0 M µ ij
N
ij
with
(cid:0) (cid:1)
MT = yLv +yLv ,
D ij ij u (cid:101)ij d
(cid:0) (cid:1)
MT = f v . (8)
N ij ij R
Notice that the Majorana mass terms for N are still not produced due to the choice
Ri
of the Higgs field that breaks the SU(2) symmetry.2 Here, we assume a hierarchical
R
1Note that the structure of the quark/lepton Yukawa couplings is the same as that of the generic
two-Higgs doublet model. Thus, we have more degrees of freedom for the Yukawa couplings than those
in, e.g., the type-IItwo-Higgs doubletmodel. These extra degrees offreedom are actually desirable since
wecanchoosetheYukawacouplingstoaccountfortheobservedfermionmassesandmixingeventhough
we take v /v = O(1); if we instead consider the type-II two-Higgs doublet model like structure, then
u d
v /v should be equal to m /m in order to explain the observed top-bottom mass ratio.
u d t b
2If we used an SU(2) triplet Higgs field with two unit of the B −L charge to break the SU(2)
R R
symmetry, then we would generically obtain Majorana mass terms for N .
Ri
3
structure among the mass parameters in the matrix, i.e., |µ | (cid:28) |(M ) | (cid:28) |(M ) |.
ij D ij N ij
The mass matrix M can be block diagonalized by means of a unitary matrix. We obtain
the mass matrix for light neutrinos as
M (cid:39) −M M−1MT (cid:39) M M−1µ(MT)−1MT , (9)
ν D N D D N N D
while the other two classes of mass eigenvalues are given by M ∓ µ/2. The latter can
N
be regarded as pseudo-Dirac neutrinos for |µ| (cid:28) M . Notice that small neutrino masses
N
are guaranteed by the smallness of |µ|, and these masses vanish in the limit of µ → 0.
In this limit, the theory recovers the lepton-number symmetry, which results in three
massless neutrinos and three heavy Dirac neutrinos. Since the µ term in Eq. (5) does
ij
not break any symmetry in our model, µ in principle can have arbitrary large value. We
ij
do not specify any mechanism to obtain a small µ in this paper, though there have been
several proposal to explain the smallness of µ by exploiting spontaneous breaking of the
lepton-number symmetry [29], extra dimensions [30], or generation of µ through radiative
corrections [31]. Finally, we note in passing that an extremely small |µ| allows the lepton
Yukawa couplings f to be sizable, which then indicates that the left-right mixing in the
ij
neutrino sector can also be significant.
The VEV of H gives masses to not only heavy neutrinos but also gauge bosons
R
associated with the broken symmetries. After the symmetry breaking, we have massive
charged and neutral gauge bosons, W± and Z , whose masses are given by
R R
(cid:113)
g2 +g2
m (cid:39) √gR v , m (cid:39) R√ B−Lv , (10)
WR 2 R ZR 2 R
respectively. Here, the SU(2) gauge coupling constant g and the B−L gauge coupling
R R
constant g are related to the U(1) gauge coupling constant g(cid:48) by
B−L Y
1 1 1
= + , (11)
g(cid:48)2 g2 g2
R B−L
which follows from
B −L
Y = T3 + , (12)
R 2
with Y, TA, and B −L denote the hypercharge, the SU(2) generators, and the B −L
R R
charge, respectively. From the relation (11), we find that there is a lower bound on the
value of g to keep the B−L coupling perturbative; for instance, g < 1 (4π) leads to
R B−L
g (cid:38) 0.39 (0.36).
R
As mentioned in Sec. 1, recently there have been various experimental observations
which indicate the presence of W± with a mass of around 2 TeV. Motivated by these
R
observations, throughout this paper, we assume m ∼ 2 TeV. In this case, we can
WR
predict the mass of Z as a function of g according to Eqs. (10) and (11). In Fig. 1, we
R R
plot m as a function of g . Here, we set m = 2 TeV. Currently, the most stringent
ZR R WR
limit on Z is given by the ATLAS collaboration using the 3.2 fb−1 data set at the center-
R √
of-mass energy of s = 13 TeV [32] (see also the CMS result [33]). According to the
4
5000
m =2TeV
WR
4500
4000
]
V
e
G
3500
[
R
Z
m
3000
2500
2000
0.4 0.5 0.6 0.7 0.8 0.9 1
g
R
Figure 1: Mass of Z , m , as a function of the SU(2) gauge coupling g . Here, we set
R ZR R R
m = 2 TeV.
WR
ATLAS result, the production cross section of Z times its branching fraction into two
R
leptons (cid:96)± ((cid:96) = e, µ), σ(Z )BR((cid:96)+(cid:96)−) should be less than about 1 fb, which gives a
R
lower limit on the Z mass of a several TeV. This limit can easily be avoided if one takes
R
g (cid:39) 0.4.
R
Since m ∼ 2 TeV means v = O(1) TeV, Eq. (8) tells us that heavy pseudo-Dirac
WR R
neutrinos also have masses of O(1) TeV. To explain the CMS excess, we take one of these
heavy neutrinos to have a mass lighter than m and the others to have masses heavier
WR
than m so that they do not participate in the decay of W . We denote the former by
WR R
N and the latter by N and N in what follows. In addition, we assume that N mainly
1 2 3 1
couples to electron; i.e., its couplings with µ and τ leptons are negligible. In this setup,
W decays into a pair of right-handed quarks, WZ, Wh, or a N plus an electron. In
R 1
the last case, the produced N subsequently decays into an electron plus quarks via the
1
exchange of a virtual W±. It can also decay into three leptons or a lepton plus two quarks
R
via the W±, Z, or the Higgs boson exchange if N has a sizable left-handed neutrino
1
component or W–W mixing is rather large. Relevant formulae for the decay processes
R
are summarized in the subsequent section.
Finally, we give a brief discussion about the constraint on W coming from flavor
R
physics. In this model, flavor-changing-neutral-current (FCNC) processes can be induced
by the exchange of W ,3 which are severely restricted from the low-energy precision flavor
R
measurements. Among them, the measurement of the K –K mass difference gives the
L S
3 As we discussed above, the structure of the Yukawa sector in our model is similar to that in the
generic two-Higgs-doublet model. Thus, FCNC processes may also be induced by the exchange of the
additional Higgs bosons in general. In this paper, we simply assume that the Yukawa couplings in our
modelareappropriatelyalignedsothatFCNCprocessesgeneratedbytheHiggsexchangearesufficiently
suppressed.
5
most stringent bound on m , which is roughly given by [34]
WR
(cid:18) (cid:19)
g (cid:16)g (cid:17)
m (cid:38) R ×2.5 TeV (cid:39) R ×1.5 TeV . (13)
WR g 0.4
L
Hence, W with a mass of around 2 TeV is still allowed by this bound when we take
R
g (cid:39) 0.4.
R
3 Decay Branching Fractions
Here, we first summarize formulae relevant to the calculation of the partial decay widths
of W± and N . As mentioned above, W decays into a pair of right-handed quarks, WZ,
R 1 R
Wh, or a N plus an electron. Among them, the WZ and Wh decay processes occur via
1
the mixing of W with W boson. Therefore, we begin with the discussion on the W–W
R R
mixing in our model. W mixes with W boson after the bi-doublet Higgs field Φ acquires
R
a VEV. The mass matrix of these gauge bosons is given by
(cid:32) gL2v2 −gLgRv2sin2β(cid:33)(cid:32)W+(cid:33)
L = (W− W−) 2 2 L , (14)
mass L R −gLgRv2sin2β gR2 {v2 +v2} W+
2 2 R R
where W± denote the SU(2) gauge bosons, and tanβ ≡ v /v . The mass matrix is
L L d u
diagonalized with an orthogonal matrix:
(cid:32) (cid:33) (cid:32) (cid:33)(cid:32) (cid:33)
W+ cosφW −sinφW W+
L = LR LR 1 . (15)
W+ sinφW cosφW W+
R LR LR 2
Here, W+ and W+ are the mass eigenstates of the charged gauge bosons. The corre-
1 2 √
sponding eigenvalues are m and m , respectively, with m (cid:39) g v/ 2 and m given
W WR W L WR
by Eq. (10). In what follows, we refer to the SU(2) -gauge-boson-like state W+ as W+.
L 1
Since the mixing angle φW turns out to be extremely small in our scenario, we denote
LR
W+ also by W+ unless otherwise noted. The mixing angle φW is then given by
2 R LR
2g g v2sin2β (cid:18)g (cid:19) m2
tan2φW = L R (cid:39) 2sin2β R W . (16)
LR g2v2 −(g2 −g2)v2 g m2
R R L R L WR
The couplings of W and W to fermions are given as follows:
R
g g
L =√L u(cid:0)cosφW W/ + −sinφW W/ +(cid:1)P d+ √R u(cid:0)sinφW W/ + +cosφW W/ +(cid:1)P d
WRff 2 LR LR R L 2 LR LR R R
g g
+√L ν(cid:0)cosφW W/ + −sinφW W/ +(cid:1)P e+ √R N (cid:0)sinφW W/ + +cosφW W/ +(cid:1)P e
LR LR R L 1 LR LR R R
2 2
+h.c. , (17)
6
where we suppress the flavor indices for simplicity. In the mass eigenbasis, the W –W–Z
R
interaction is given by
L =−ig sinφW cosφW (W+W−µ +W+ W−µ −W−W+µ −W− W+µ)Zν
WRWZ Z LR LR µν R Rµν µν R Rµν
−ig sinφW cosφW (W+W− +W+ W−)Zµν , (18)
Z LR LR µ Rν Rµ ν
(cid:112)
where V ≡ ∂ V −∂ V (V = W, W , or Z) and g ≡ g(cid:48)2 +g2. As for the W Wh
µν µ ν ν µ R Z L R
coupling, we have
1
L = − √ [(g2 −g2)sin2φW +2g g sin2βcos2φW ]vh(W−W+ +W−W+) .
WRWh 2 2 L R LR L R LR R R
(19)
NowweevaluatethepartialdecaywidthsofW . Forthefermionchannels, W → ff¯(cid:48),
R R
we have
g2
Γ(W+ → ud¯) = Γ(W+ → cs¯) = R m , (20)
R R 16π WR
g2 (cid:18) m2 (cid:19)(cid:18) m2 (cid:19)2
Γ(W+ → t¯b) = R m 1+ t 1− t , (21)
R 16π WR 2m2 m2
WR WR
g2 (cid:18) m2 (cid:19)(cid:18) m2 (cid:19)2
Γ(W+ → N e¯) = R m 1+ N1 1− N1 , (22)
R 1 48π WR 2m2 m2
WR WR
where we have neglected the small mixing factor φW . For the W → WZ decay process,
LR R
we have
g2 (cid:18) m2 +m2 (m2 −m2)2(cid:19)32
Γ(W+ → W+Z) = R sin2(2β)m 1−2 W Z + W Z
R 192π WR m2 m4
WR WR
(cid:18) m2 +m2 m4 +10m2 m2 +m4 (cid:19)
× 1+10 W Z + W W Z Z . (23)
m2 m4
WR WR
Here, notice that although the W –W–Z coupling in Eq. (18) is suppressed by the small
R
mixing angle φW , the partial decay width of the WZ channel does not suffer from this
LR
suppression. This is because the high-energy behavior of the longitudinal mode of W
R
gives an enhancement factor of ∼ (m /m )4 and this compensates the suppression
WR W
factor from the mixing angle. Finally, the W → Wh decay width is given by
R
g2 (cid:18) m2 +m2 (m2 −m2)2(cid:19)12
Γ(W+ → W+h) = R sin2(2β)m 1−2 W h + W h
R 192π WR m2 m4
WR WR
(cid:18) 10m2 −2m2 (m2 −m2)2(cid:19)
× 1+ W h + W h , (24)
m2 m4
WR WR
where we assume the decoupling limit for the Higgs bosons in our model. Notice that in
the large m limit,
WR
Γ(W+ → W+Z) (cid:39) Γ(W+ → W+h) , (25)
R R
7
holds. This is a consequence of the equivalence theorem.
As seen above, the lightest Dirac neutrino N is generated as a decay product of W .
1 R
The decay branching ratios of N highly depend on its mass and the left-right mixing in
1
both the gauge boson and neutrino sectors. When the mass of N is rather large and the
1
left-right mixing is very small, the three-body decay process via the virtual W+ exchange
R
is dominant. The three-body decay width into an electron plus a pair of the first/second
generation quarks is given by [4]
g4
Γ(N → qq(cid:48)e−) = R m F(x) , (26)
1 2048π3 N1
with x = m2 /m2 and
N1 WR
12 (cid:20) x x2 1−x (cid:21)
F(x) = 1− − + ln(1−x) . (27)
x 2 6 x
Here we neglect the quark and electron masses. For the N → bte− decay channel, we
1
have [9]
g4
Γ(N → bte−) = R m F (x,y) , (28)
1 2048π3 N1 t
where
12(cid:20) x x2 (cid:18) 3 3 (cid:19)
F (x,y) = (1−y)− (1−y2)− 1− y + y2 −y3
t
x 2 6 2 2
5x3y x4y2(1−y) x3y2
− (1−y2)+ − (4+x2y)lny
8 4 4
(cid:18) (cid:19) (cid:21)
1−x 1−x (cid:110) xy (cid:111)
(cid:2) (cid:3)
+ ln 1− 4+x+x2 −x3y2(1+x) , (29)
x 1−xy 4
with y ≡ m2/m2 (m is the top mass). Of course, F (x,y) → F(x) as y → 0. We note in
t N1 t t
passing that the functions F(x) and F (x,y) also appear in the calculation of the muon
t
decay width [35].
On the other hand, if m is relatively small and if φW or the mixing of N with left-
N1 LR 1
handed neutrinos ν , R , is sizable, then the two-body decay processes become dominant.
l l1
In what follows, we assume that only the R component can be sizable and the other
e1
flavor off-diagonal components, R and R , are always negligible for simplicity.4 The
µ1 τ1
4We here note that this assumption is consistent with the experimental data of neutrino oscillations,
as discussed in Ref. [25].
8
100 mWR =2TeV,mN1 =1TeV 100 mWR =2TeV,tanβ=1
jj jj
tb¯ tb¯
s s
atio 10−1 Ne¯ atio 10−1 Ne¯
r r
g g
n n
hi hi
c c W+Z,W+h
n n
Bra 10−2 W+Z,W+h Bra 10−2
10−3 10−3
1 10 0.1 1
tanβ m [TeV]
N1
(a) tanβ dependence (b) m dependence
N1
Figure 2: Branching ratios of the W+ decay as functions of tanβ and m in Figs. 2(a)
R N1
and 2(b), respectively. Here, we set m = 2 TeV. The red solid, black dashed, green
WR
dotted, and blue dash-dotted lines represent the branching fractions of the dijet, t¯b, N e+,
1
and W+Z and W+h channels, respectively. m is fixed to be 1 TeV in Fig. 2(a), while
N1
tanβ = 1 in Fig. 2(b).
relevant partial decay widths are then given as follows:
g2|R |2 +g2 sin2φW m3 (cid:18) m2 (cid:19)2(cid:18) m2 (cid:19)
Γ(N → e−W+) = L e1 R LR N1 1− W 1+2 W , (30)
1 64π m2 m2 m2
W N1 N1
g2|R |2m3 (cid:18) m2 (cid:19)2(cid:18) m2 (cid:19)
Γ(N → ν Z) = Z e1 N1 1− Z 1+2 Z , (31)
1 e 128π m2 m2 m2
Z N1 N1
g2|R |2m3 (cid:18) m2 (cid:19)2
Γ(N → ν h) = L e1 N1 1− h . (32)
1 e 128π m2 m2
W N1
By using the above formulae, we now evaluate the decay branching fractions of W
R
and N . First, we show the branching ratios of the W+ decay as functions of tanβ and
1 R
m in Figs. 2(a) and 2(b), respectively. Here, we set m = 2 TeV. The red solid, black
N1 WR
dashed, green dotted, and blue dash-dotted lines represent the branching fractions of the
dijet, t¯b, N e+, and W+Z and W+h channels, respectively. m is fixed to be 1 TeV in
1 N1
Fig. 2(a), while tanβ = 1 in Fig. 2(b). From these figures, we find that about 10% of W
R
decay into a pair of N and e+ when m (cid:46) 1 TeV. This decay branch hardly depends on
1 N1
tanβ. Such a sizable decay fraction allows the model to explain the CMS eejj excess, as
we will see below. The decay branch of WZ channel, on the other hand, strongly depends
on tanβ. In particular, this model can explain the ATLAS diboson anomaly [12] only if
tanβ is small; otherwise, the diboson decay mode is almost negligible.
9
