arXiv:1003.1468v2 [hep-ph] 27 Oct 2010
Neutrino Masses and a TeV Scale Seesaw Mechanism
Center for High Energy Physics, Peking university, Beijing 100871, China
A simple extension of the Standard Model providing TeV scale seesaw mechanism is presented.
Beside the Standard Model particles and right-handed Majorana neutrinos, the model contains a
singly charged scalar, an extra Higgs doublet and three vector like singly charged fermions. In our
model, Dirac neutrino mass matrix raises only at the loop level. Small but non-zero Majorana
neutrino masses come from integrating out heavy Majorana neutrinos, which can be at the TeV
scale. The phenomenologies of the model are investigated, including scalar mass spectrum, neutrino
masses and mixings, lepton flavor violations, heavy neutrino magnetic moments as well as possible
collider signatures of the model at the LHC.
∗Electronic address: email@example.com
The observation of neutrino oscillations [1–4] has revealed that neutrinos have small
but non-zero masses and lepton flavors are mixed, which can not be accommodated in the
Standard Model (SM) without introducing extra ingredients. As such, neutrino physics
offer an exciting window into new physics beyond the SM. Perhaps the most attractive
approach towards understanding the origin of small neutrino masses is using the dimension-
five weinberg operator :
Lbεbaφa+ h.c. , (1)
which comes from integrating out new superheavy particles.
A simple way to obtain the operator in Eq. (1) is through the Type-I seesaw mechanism
, in which three right-handed neutrinos with large Majorana masses are introduced to
the SM. Then three active neutrinos may acquire tiny Majorana masses through the Type-
I seesaw formula, i.e., the mass matrix of light neutrinos is given by Mν= −MDM−1
where MDis the Dirac mass matrix linking left-handed light neutrinos to right-handed heavy
neutrinos and MRis the mass matrix of heavy Majorana neutrinos. Actually, there are three
tree-level seesaw scenarios (namely type-I, Type-II  and Type-III  seesaw mechanisms)
and one loop-level seesaw scenario (namely Ma  model), which may lead to the effective
operator in Eq. (1).
Although seesaw mechanisms can work naturally to generate Majorana neutrino masses,
they lose direct testability on the experimental side. A direct test of seesaw mechanism would
involve the detection of these heavy seesaw particles at a collider and the measurement of
their Yukawa couplings with the electroweak doublets. In the canonical seesaw mechanism,
heavy seesaw particles turn out to be too heavy, i.e., 1014∼16GeV, to be experimentally
accessible. One straightforward way out is to lower the seesaw scale “by hand” down to the
TeV scale, an energy frontier to be explored by the Large Hadron Collider (LHC). However
this requires the structural cancellation between the Yukawa coupling texture and the heavy
Majorana mass matrix, i.e. MDM−1
D≈ 0 [10–15] at the tree level, and is thus unnatural!
To solve this unnaturalness problem, we propose a novel TeV-scale seesaw mechanism in
this paper. The model includes, in addition to the SM fields and right-handed Majorana
neutrinos, a charged scalar singlet, an extra Higgs doublet and three vector like singly
charged fermions. Due to Z2discrete flavor symmetry, right-handed Majorana neutrinos
don’t couple to left-handed lepton doublets, such that Dirac mass matrix only raises at the
loop level and is comparable with the charged lepton mass matrix. This drives down the
seesaw scale to the TeV, and thus the model is detectable at the LHC.
The paper is organized as follows: In section II, we describe our model. Section III is
devoted to investigate the phenomenologies of the model, including neutrino masses and
mixings, lepton flavor violations, transition magnetic moments of heavy Majorana neutrinos
as well as possible collider signatures. We conclude in Section IV. An alternative settings to
the model is presented in appendix A.
II. THE MODEL
In our model, we extend the SM by introducing three right-handed Majorana neutrinos
NR, three singly charged vector-like fermion SL,SR, an extra Higgs doublet Hn, a singly
charged scalar Φ as well as discrete Z2flavor symmetry. The Z2charges for these fields is
given in table I. Due to Z2symmetry, right-handed neutrinos don’t couple to SM Higgs.
TABLE I: Z2charges of particles.
fields ℓLeRNRSLSRH HnΦ
+1 +1 -1 -1 +1 +1 +1 +1
As a result the new lagrangian can be written as
LN= V (H,Hn,Φ) − ℓLYSHSR− SLMSSR− YNSLΦNR−1
RMRNR+ h.c. ,(2)
where YSand YNare new Yukawa couplings, MSand MRare mass matrices of S and NR,
respectively. Z2symmetry is explicitly broken by SLMSSRterm. It can be recovered by
adding an extra scalar singlet η, with Z2charge −1 and Yukawa coupling SLηSR. We will
not consider Yukawa couplings ℓLHneRand ℓLHnSR, which can be forbidden by another Z
symmetry. The following is the full Higgs potential:
V = −m2
1H†H − m2
3Φ†Φ + λ1(H†H)2+ λ2(H†
nHn) +?λnΦ(HTiσ2Hn) + h.c.?
+λ6(Φ†Φ)(H†H) + λ7(Φ†Φ)(H†
We define ?H? = v1/√2 and ?Hn? = v2/√2.
minimum, one finds that
After imposing the conditions of global
where λo= 1/2(λ3+ λ4).
In the basis (h−,h−
n,S−), we can derive the mass matrix for charged scalars:
2. MCcan be diagonalized by the 3×3 unitary transformation
V : V†MCV∗= diag(MG+,MH+,MS+). The mass eigenvalues for these charged scalars are
where ρ ≡ −2m2
MG+ = 0 ;
where B ≡ ρ − λ4(v2
matrix for CP-even scalars in the basis (h,hn)Tand CP-odd scalars in the basis (G,Gn)T:
2). Here G+is the SM goldstone boson. We also derive the mass
where λs= 1/2(λ4− λ5).
We also derive the masses for gauge bosons, which are M2
W = g2(v2
2)/4cos2θw, separately. Such that electroweak precision observable ρ ≡
Zcos2θw= 1 in our theory. Our scalar field sector is similar to that in Zee modelM2
. We present in appendix A a different setting to the particle contents, by replacing
scalar singlet with triplet.
In this section, we devote to investigate some phenomenological implications of our model.
We focus on (A) neutrino masses and mixings; (B)lepton flavor violations; (C) electromag-
netic properties and (D) collider signatures of heavy majorana neutrinos, which will be
deployed in the following:
A.Neutrino masses and lepton mixing martrix
In our model, there is no Dirac neutrino mass term at the tree level. However we can
derive a small Dirac neutrino mass matrix at the loop level. The relevant feynman diagram
is shown in Fig. 1.
FIG. 1: One-loop correction to the Dirac neutrino mass matrix.
A direct calculation results in
where the one loop function appearing in upper equation is given by
with βi= m2/m2
i. When m1= m2= m, F reduces to 1/2m2.
is the Dirac neutrino mass matrix linking the left and right hand neutrinos,Here Mloop
which only raises at the loop level in our model. If neutrinos are Dirac particles, then
Eq. (8) is just neutrino mass formula, whose predication must be consistent with present
neutrino oscillation data. In this paper, we assume that neutrinos are Majorana particles,
i.e., left-handed and right-handed neutrinos have different mass eigenvalues. Then three
active neutrino masses can be generated from seesaw mechanism. In this case, we can write
down the 6 × 6 neutrino mass matrix:
which can be diagonalized by the unitary transformation U†MU∗=?
M; or explicitly,