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arXiv:1003.1468v2 [hep-ph] 27 Oct 2010

Neutrino Masses and a TeV Scale Seesaw Mechanism

Wei Chao∗

Center for High Energy Physics, Peking university, Beijing 100871, China

Abstract

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: chaow@pku.edu.cn

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I.INTRODUCTION

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 [5]:

1

4κgfℓC

Lc

gεcdφdℓf

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

[6], 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

RMT

D,

neutrinos and MRis the mass matrix of heavy Majorana neutrinos. Actually, there are three

tree-level seesaw scenarios (namely type-I, Type-II [7] and Type-III [8] seesaw mechanisms)

and one loop-level seesaw scenario (namely Ma [9] 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

RMT

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

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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

Z2

+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

2NC

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

′

2

symmetry. The following is the full Higgs potential:

V = −m2

1H†H − m2

+λ3(H†H)(H†

2H†

nHn) +λ4

nHn− m2

4(H†Hn+ H†

3Φ†Φ + λ1(H†H)2+ λ2(H†

nH)2−λ5

nHn) +?λnΦ(HTiσ2Hn) + h.c.?

3

nHn)2

4(H†Hn− H†

nH)2

+λ6(Φ†Φ)(H†H) + λ7(Φ†Φ)(H†

. (3)

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We define ?H? = v1/√2 and ?Hn? = v2/√2.

minimum, one finds that

After imposing the conditions of global

v2

1=λ2m2

1− λom2

λ1λ2− λ2

2

o

;v2

2=λ1m2

2− λom2

λ1λ2− λ2

1

o

,(4)

where λo= 1/2(λ3+ λ4).

In the basis (h−,h−

n,S−), we can derive the mass matrix for charged scalars:

3+λ6v2

MC=

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

−λ4v2

λ4v1v2

√2λnv2

2

λ4v1v2

√2λnv2

−√2λnv1

ρ

−λ4v2

−√2λnv1

1

,

(5)

where ρ ≡ −2m2

1+λ7v2

then

MG+ = 0 ;

MH+ =

1

2

1

2

????B −

?

?

B2+ 4(v2

1+ v2

2)(ρλ4+ 2λ2

n)

????;

MS+ =

????B +

B2+ 4(v2

1+ v2

2)(ρλ4+ 2λ2

n)

????,(6)

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:

?2λ1v2

λov1v2

2λ2v2

2

1+ v2

2). Here G+is the SM goldstone boson. We also derive the mass

MN=

1

λov1v2

?

;MG=

?−λsv2

λsv1v2

2

λsv1v2

−λsv2

1

?

,(7)

where λs= 1/2(λ4− λ5).

We also derive the masses for gauge bosons, which are M2

W = g2(v2

1+ v2

2)/4 and

M2

Z= g2(v2

1+ 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

W/M2

[16]. We present in appendix A a different setting to the particle contents, by replacing

scalar singlet with triplet.

III.PHENOMENOLOGICAL ANALYSIS

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:

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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.

MS

ℓL

NR

SR

SL

H

Φ

Hn

FIG. 1: One-loop correction to the Dirac neutrino mass matrix.

A direct calculation results in

(MD)loop

ab

=λn?Hn?

32π2

(YS)ac(Y†

N)cbMScF?M2

H,M2

Φ,M2

Sc

?

,(8)

where the one loop function appearing in upper equation is given by

F(m2

1,m2

2,m2) =

1

m2

1− m2

2

?lnβ1

β1− 1−

lnβ2

β2− 1

?

,(9)

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

D

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:

M =

?

0Mloop

D

MloopT

D

MR

?

,(10)

which can be diagonalized by the unitary transformation U†MU∗=?

R

STMloopT

D

M; or explicitly,

0

ˆ MN

?V

?†?

0Mloop

D

MR

??VR

ST

?∗

=

?ˆ Mν

0

?

.(11)

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