Phenomenology in supersymmetric neutrinophilic Higgs model with sneutrino dark matter

Abstract

Abstract

We study a supersymmetric neutrinophilic Higgs model with large neutrino Yukawa couplings where neutrinos are Dirac particles and the lightest right-handed (RH) sneutrino is the lightest supersymmetric particle (LSP) as a dark matter candidate. Neutrinophilic Higgs bosons need to be rather heavy by the precise determination of the muon decay width and dark radiation constraints for large Yukawa couplings. From the Large Hadron Collider constraints, neutrinophilic Higgsino mass need to be heavier than several hundred GeV or close to the RH sneutrino LSP mass. The latter case is interesting because the muon anomalous magnetic dipole moment can be explained with a relatively large lightest neutrino mass, if RH sneutrino mixings are appropriately fine tuned in order to avoid stringent lepton flavor violation constraints. Dark matter is explained by asymmetric RH sneutrino dark matter in the favoured region by the muon anomalous magnetic dipole moment. In other regions, RH sneutrino could be an usual WIMP dark matter.

Published for SISSA by Springer

Received: June 9, 2014

Accepted: July 28, 2014

Published: September 11, 2014

Ki-Young Choi,a Osamu Setob and Chang Sub Shinc

aKorea Astronomy and Space Science Institute,

Daejon 305-348, Republic of Korea

bDepartment of Life Science and Technology, Hokkai-Gakuen University, Sapporo 062-8605, Japan

cNew High Energy Theory Center, Department of Physics and Astronomy, Rutgers University, Piscataway NJ 08854, U.S.A.

E-mail: mailto:[email protected]

Web End [email protected] , mailto:[email protected]

Web End [email protected] , mailto:[email protected]

Web End [email protected]

Abstract: We study a supersymmetric neutrinophilic Higgs model with large neutrino Yukawa couplings where neutrinos are Dirac particles and the lightest right-handed (RH) sneutrino is the lightest supersymmetric particle (LSP) as a dark matter candidate. Neutrinophilic Higgs bosons need to be rather heavy by the precise determination of the muon decay width and dark radiation constraints for large Yukawa couplings. From the Large Hadron Collider constraints, neutrinophilic Higgsino mass need to be heavier than several hundred GeV or close to the RH sneutrino LSP mass. The latter case is interesting because the muon anomalous magnetic dipole moment can be explained with a relatively large lightest neutrino mass, if RH sneutrino mixings are appropriately ne tuned in order to avoid stringent lepton avor violation constraints. Dark matter is explained by asymmetric RH sneutrino dark matter in the favoured region by the muon anomalous magnetic dipole moment. In other regions, RH sneutrino could be an usual WIMP dark matter.

Keywords: Supersymmetry Phenomenology

ArXiv ePrint: 1406.0228

Open Access, c

The Authors.

Article funded by SCOAP3. doi:http://dx.doi.org/10.1007/JHEP09(2014)068

Web End =10.1007/JHEP09(2014)068

Phenomenology in supersymmetric neutrinophilic Higgs model with sneutrino dark matter

JHEP09(2014)068

Contents

1 Introduction 2

2 Phenomenological constraints and implications 22.1 Neutrino mass and mixing 32.2 Muon decay width 42.2.1 Loop enhancement of e

e 5

e with (, ) 6= (, e) 6

2.2.3 R

Re 6

2.2.4 Total 72.3 Collider constraints 92.3.1 Constraints from LEP 102.3.2 LHC bound 102.4 Lepton avor violation ( e) 11

2.5 Anomalous magnetic dipole moment of muon 122.6 Compatibility in benchmarks 13

3 Cosmological constraints 153.1 Dark radiation 153.1.1 ll+ R

R 16

R 17

3.1.3 Decoupling condition 17

4 Dark matter 174.1 Relic density of dark matter 174.2 Dark matter scattering cross section with a nucleon 194.3 Indirect signal from sneutrino dark matter 204.4 Decay of cosmic neutrino background 20

5 Conclusion 21

A Formula for the muon g 2 22

B Auxiliary functions 22

L R

JHEP09(2014)068

2.2.2

3.1.2 L

1

1 Introduction

A scalar eld could be responsible for the breakdown of a large gauge symmetry and the generation of the masses of gauge bosons and fermions. In fact, a scalar boson discovered at the Large Hadron Collider (LHC) appears to be the Higgs boson in the standard model (SM) of particle physics [1, 2]. After the spontaneous symmetry breaking, the mass of each fermion, namely quarks and charged leptons, is given by the product of each Yukawa coupling constant and the vacuum expectation value (VEV) of the Higgs eld.

However, one might suspect a special mechanism for the generation of neutrino masses and a special reason for its smallness, because masses of neutrinos are very small compared with other SM fermions. One approach is the so-called seesaw mechanism with very heavy right-handed (RH) Majorana neutrinos, where the smallness of neutrino mass can be understood as a consequence of the high scale of RH neutrino mass [35].

Another approach is the neutrinophilic Higgs model [68]. In this model, neutrino has Dirac mass terms generated by another Higgs eld whose VEV is much smaller than that of the SM Higgs, where the smallness of neutrino mass is a consequence of the smallness of the other Higgs VEV. In this case, the neutrino Yukawa couplings can be much larger than those with only the SM Higgs eld if the Higgs VEV is small, because the neutrino mass is the product of the VEV of the neutrinophilic Higgs eld and the Yukawa couplings.

The large neutrino Yukawa couplings in the neutrinophilic Higgs model shows many interesting features, such as the possibility of the RH sneutrino as thermal dark matter (DM) [911] or the low scale thermal leptogenesis [1214]. In addition, the large Yukawa couplings have more implications in the avour structures and astrophysical phenomenon.

In this paper, we examine various phenomenological aspects of the large Yukawa interactions in the supersymmetric extended neutrinophilic Higgs model. Those include the anomalous magnetic moments of muon, lepton avour violation, experimental constraints on the couplings and the masses of new particles, and cosmological and astrophysical constraints including indirect detection signatures by asymmetric sneutrino DM through gamma ray and neutrinos.

In section 2, we consider the constraints on the Yukawa couplings from neutrino masses and mixings, the muon decay, collider searches, and lepton avour violation. Taking these constraints into account, we study the possibility to explain the muon anomalous magnetic moment in this model. In section 3, we consider the cosmological constraints from dark radiation, and in section 4 we study the possibility of the lightest RH sneutrino as DM and the astrophysical constraints on the models. We conclude our study in section 5. We provide some formulas in the appendices.

2 Phenomenological constraints and implications

In a supersymmetric model, the interaction is described by the term in superpotential

WN = (cR)i(y )i L H (2.1) where L is the lepton doublet of the Standard Model, Ri is a gauge singlet RH neutrino supereld and H is a scalar doublet in addition to the standard two Higgs doublets in

2

JHEP09(2014)068

the MSSM and i, = 1, 2, 3 denotes the generation index. In the so called neutrinophilic Higgs model with the neutrino Dirac mass given by a small VEV of neutrinophilic Higgs eld, hH0 i, neutrino Yukawa couplings can be as large as of the order of unity.

We consider the Yukawa interaction of Dirac neutrino and neutrinophilic Higgs as

L =

Ri(y )i L H + h.c. (2.2)

After the electroweak symmetry breaking, the neutrinophilic Higgs eld develops the VEV

hH0 i = v /2 and generates the neutrino mass. Since neutrinos are Dirac particles in this

model, their mass matrix is simply proportional to 3 3 neutrino Yukawa coupling matrix.

The neutrino mass matrix, or equivalently Yukawa interaction, is given by

L mass = Ri(m )i L + h.c. , (2.3)

with(m )i = (y )i v

2 , (2.4) here and hereafter we assume the Yukawa couplings are real, for simplicity. Therefore, the left- and right-handed neutrinos compose the four component Dirac mass eigenstates.

In a supersymmetric theory, there exists the Yukawa interaction of scalar RH neutrino with the same Yukawa coupling of eq. (2.2), given by

L = ~

Ri(y )i L PR + h.c. . (2.5)

Here, RH sneutrinos ~

Ri are dened as the superpartner of each Ri. If the lightest RH sneutrino is the lightest supersymmetric particle (LSP), it can be a good candidate for DM as shown in refs. [9, 10]. Throughout this paper, we consider this case of RH sneutrino DM and study the phenomenological constraints and implications.

2.1 Neutrino mass and mixing

Without loss of the generality, we can regard that the Ri is already mass eigenstate. The neutrino mass matrix is diagonalized with the Maki-Nakagawa-Sakata (MNS) matrix UMNS, which transfers LH neutrinos from mass eigenstates (L,i) to avor eigenstates (L, )

L, = (UMNS) iL,i,

diag(m1, m2, m3)ij = (m )i (UMNS) j . (2.6)

The neutrino oscillation data gives two independent mass squared di erences and three mixing angles [15],

m22 m21 7.5 105 eV2,

|m23 m21| 2.3 103 eV2, sin2 223 > 0.95 ,

sin2 212 0.857 , sin2 213 0.095 .

3

JHEP09(2014)068

(2.7)

Point 1: normal 2: normal 3: inverted 4: inverted m1,3 [eV] m1 = 0.0 m1 = 0.07 m3 = 0.05 m3 = 0.0

(y )i

0.0 0.0 0.0

0.14 0.13 0.16

0.22 1.0 1.0

0.96 0.57 0.36

0.65 0.62 0.77

0.22 1.0 1.0

1.0 0.59 0.37

0.68 0.65 0.80

0.14 0.62 0.62

1.0 0.59 0.37

0.68 0.65 0.80

0.0 0.0 0.0

Pm [eV] 0.06 0.23 0.19 0.10 v [eV] 0.05 0.08 0.08 0.05

Table 1. Neutrino Yukawa coupling matrix of the four benchmark 1, 2, 3 and 4 used in this work are shown. The resultant

Pm for a given input parameter m1 or m3 is also listed. v is a free parameter. The noted values of v are examples in the case that we normalize the largest element of Yukawa matrix to be 1.0.

The neutrino Yukawa couplings can be expressed in terms of these neutrino oscillation parameters as

(y )i = 2v diag(m1, m2, m3)ij(UMNS)1j

1 v

2m1 cos 12 m1 sin 12 m1 sin 12

2m2 sin 12 m2 cos 12 m2 cos 12

2m3 sin 13 m3 m3

JHEP09(2014)068

. (2.8)

Here, we neglect for simplicity any CP phase and take y to be real. In the second line, 23 /4 and sin 13 1 are used, while we use the full formula of MNS matrix in our

numerical calculation.

The upper bound on the sum of neutrino masses is provided by cosmological arguments. Since its value strongly depends on data set and a cosmological model used in the analysis, for reference, we here just quote one of less conservative values

Xm < 0.23 eV, (2.9)

from ref. [16].

In table 1, we list four benchmark points used in our analysis for a given lightest neutrino mass, m1 = 0, 0.07 eV for normal hierarchy (m1 < m2 < m3) and m3 = 0, 0.05 eV for inverted hierarchy (m3 < m1 < m2) of neutrino masses. To estimate Yukawa coupling constants, we have to x one extra free parameter v . Example value sets of y in table 1 are obtained under the assumption that the largest coupling is unity. The actual value can be somewhat larger or smaller by changing v .

2.2 Muon decay width

Muon decays into electron, electron-type anti-neutrino and muon-type neutrino, e

e

in the Standard Model. However, in the neutrinophilic Higgs model, the Yukawa interaction eq. (2.1) gives additional contribution to the SM prediction via one loop induced vertices and changes the muon decay width. Those come from box diagrams with a loop (R, H0

and H ) or (~

R,0 and ). Moreover, muon has additional decay mode into electron,

4

RH neutrino and anti-RH neutrino, through the H+ mediation. This new contribution can be severely constrained by the precise measurement of the decay rate and inverse decay rate of muon.

Now we are going to estimate those additional contributions to muon decay width. For this, we dene mass eigenstatesi from avour states Ri with an unitary matrix Sij as dened by

~

Ri = Sijj , (2.10)

Sij = R(12)R(23)R(13) , (2.11)

with R being a rotation matrix and the variables, 12, 23, 13, are the corresponding mixing angle. The Yukawa interaction eq. (2.5) becomes

L =

k(ST )ki(y )i L PR + h.c. , (2.12)

for the mass eigenstates. Thus, we denei (ST y )i for Yukawa couplings of the RH

sneutrino, lepton and Higgsino.

2.2.1 Loop enhancement of e

JHEP09(2014)068

e

First, let us estimate the decay width of the main decay mode. In the following, p1, p2, q1

and q2 are the momentum of incoming , outgoing e, and

e respectively. The amplitude

of W boson mediated process is given by

iM1 =(q1)

g2 2PLu(p1)

ig

M2W

2 PLv(q2) , (2.13)

where g2 is the SU(2) gauge coupling and MW is the W boson mass. That of RH neutrino and Higgs bosons loop shown in the left window of gure 1 is given by

iM2 Xi,j(q1)(y )i2 (y )iPLu(p1)(p2)(y )je (y )je2 PLv(q2)

(p2) g2

(2.14)

i4(4)2 F2(MH

, MH0

) + F2(MH

, MA0 )

g ,

with the auxiliary function F2(x), which is dened in the appendix. In this estimation of F2(x), we neglect O(M4) terms with M being the mass scale of new particles, those are

much smaller than the leading corrections of O(M2). That of RH sneutrino and Higgsino

loop shown in the right window of gure 1 is given by

iM3 (p2)PLu(p1)(q1) PLv(q2)g

Pi,j(ST y )2i(ST y )2jeF3(M , M0 , Mi, Mj )4(4)2 .(2.15)

i

5

Ri H0 H Rj

i0

j

e

e

Figure 1. The Feynman diagrams of muon decay to electron and left-handed neutrinos via one loop.

We obtain

(

ee) (SM)"

12

2M2W g22

Pi,j(y )2i(y )2je8(4)2 F2(MH

, MH0

)+F2(MH

, MA0 )

JHEP09(2014)068

+ 1

2

2M2W g22

Pi,j(ST y )2i(ST y )2jeF3(M , M0 , Mi, Mj ) 4(4)2

#

,

(2.16)

m5

1923

1

2v4 , (2.17)

with the auxiliary function F3(x, y, z, w), which is given in the appendix. Here m is the muon mass and v 246 GeV is the VEV of the SM Higgs eld and we keep only the leading

order loop corrections, namely the interference between tree and one loop.

2.2.2

e with (, ) 6= (, e)

Due to the lepton avor violating neutrino Yukawa coupling, the avor of the nal state neutrino can be di erent from muon-type and anti-electron-type. However, this decay mode has only loop induced new contribution and is suppressed compared to the other contribution to the decay which has the interference term between tree-level and loop induced term. Thus, this mode is negligible.

2.2.3 R

(SM) =

Re

This decay mode with RH neutrinos in the nal state is induced by the tree level process mediated by the neutrinophilic charged Higgs boson [17]. A worth noting feature is that this is not a V A interaction but a scalar interaction. The amplitude of the process

Ri

Rje mediated by H shown in the gure 2 is given by

iMH =(q1)(y )iPLu(p1)

i M2H+

(p2)(y )ejPRv(q2) (2.18)

4GF

2 gSLL(q1)PLu(p1)(p2)PRv(q2) . (2.19)

Here, we normalise the e ective coupling with GF , the Fermi constant measured in the experiment, and we introduce a new parameter gSLL dened by [18]

gSLL

(y )i(y )je

M2H+

24GF . (2.20)

6

Ri

H

Rj

e

Figure 2. The Feynman diagrams of muon decay to electron and right-handed neutrinos.

The partial width is estimated as

( Ri

Rje) =

JHEP09(2014)068

Pi,j

|(y )i(y )ej|2

64M4H+

m5

1922 . (2.21)

As we will see later, it turns out that this decay mode has to be highly suppressed due to the well consistency with the SM. Thus, in fact, this would not be signicant for muon decay contribution.

2.2.4 Total

From eqs. (2.17) and (2.21), the nal total decay width of muon is given by

(SM)

"1

Pi,j(y )2i(y )2ej8(4)2 v2 F2(MH

, MH0

)+F2(MH

, MA0 )

v2

+

Pi,j(ST y )2i(ST y )2jeF3(M , M0 , Mi, Mj ) 16(4)2

(2.22)

+ v4

Pi,j(y )2i(y )2ej 32M4H+

#

.

By comparing Fermi constant GF measured from muon decay width and other SM quantities, the consistency of the SM can be tested [19, 20]. If we express the Fermi coupling constant with a parameter which stands for a correction due to new physics by

GF = g22

42M2

W (1 )

, (2.23)

the new physics contribution is constrained to be [21]

= 0 0.0006 . (2.24)

The last term in eq. (2.22) comes from the non-(V A) interaction via H+ mediation.

The muon decay experiments can not measure helicity of produced neutrinos, but the inverse decay of muon, + e + missing, well conrms the V A form interaction and

leave a small room for scalar interaction as [22]

|gSLL|2 < 0.475 (90% C.L.) . (2.25)

With eq. (2.20), we nd the constraint on the H+ mass and Yukawa couplings.

7

0

-1

-2

4 [RParen2]

Log 10[LParen2]y

JHEP09(2014)068

-3

-4

-5

200 400 600 800 1000

MH[LParen1]GeV[RParen1]

Figure 3. Constraints on charged Higgs boson mass from the muon decay property. The brown (green) shaded region is excluded by too large gSLL ( ).

First, let us consider the constraints on charged Higgs boson from muon decay in the decoupling limit of Higgsino of the second term. Then the rst term in eq. (2.22) gives dominant contribution to and the third term to gSLL. The constraints on charged Higgs mass and Yukawa coupling is shown in gure 3, where for simplicity we take M = M0

.

For Yukawa couplings of the order of unity, the mass of charged Higgs must be heavier than around 600 GeV.1 The cosmological consideration of dark radiation imposes the further stringent lower bound on the masses of those extra Higgs bosons, as we will see later in section 3.

Next, we need to consider the decoupling limit of very heavy Higgs boson as found just above, the the dominant correction comes from the second term in eq. (2.22) from the sneutrino and chargino loop, namely

2

8

v2F3(M , M0

, Mi, Mj )16(4)2 . (2.26)

In gure 4, we show the contour plot of 2 for O(1) Yukawa couplings in the plane of (M , Mi) with Mi = Mj in the left window, and that in the plane of (Mi/M , Mj /M )

with M = 100 GeV in the right window. We can see that the charged Higgsino need to be heavier than a few hundreds GeV for degenerate sneutrino case, Mj Mi, or two of RH sneutrinos need to be several times heavier than chargino with 100 GeV mass and only one RH neutrino can be light.

1Neutrinophilic Higgs bosons with mass O(100) GeV is possible for y < O(0.01) [2325].

6

140 0.003

0.006

50 100 150 200 250 300

0.0006

5

120

4

100

0.0006

0.0012

M N [LParen1]GeV[RParen1]

M N j

M H

3

80

0.0012

60

2

40

1

JHEP09(2014)068

0.006

0 0.2 0.4 0.6 0.8 1.0

20

MH [LParen1]GeV[RParen1]

MNi

MH

Figure 4. Contours of 2 of eq. (2.26) in the plane of (M , Mi ) with M~ i = Mj in the left window, and in the plane of (Mj /M , Mj /M ) with M = 100 GeV in the right window.

The region 2 [lessorsimilar] 0.0012 is preferred.

2.3 Collider constraints

In our model, the neutrinophilic Higgsinos (0 ,+ ) are SU(2) doublet and can be light enough to be produced at the on-shell from pp or e+e collisions, and subsequently decay to leptons (li) and lightest sneutrino (DM), which similar to the production of Wino/Zino and subsequent decay to the lightest neutralino in the minimal supersymmetric standard model (MSSM). However, the collider constraints on our model with the RH sneutrino LSP is slightly di erent from the current searches on SUSY based on the neutralino LSP.

The production channels of the neutrinophilic Higgsinos are s-channel Z0/ boson exchange for e+e, pp collisions, t-channel exchange for e+e collision, and s-channel W exchange for pp collision. They subsequently decay to leptons (li) and the lightest sneutrino (DM),

+

il+i ,0

i

j ,

~

H+ (

(2.27)

i l+i

j 0 ) or l+ieDM (

jkDM) for i 6= DM ,

where i is the mass eigenstate of neutrino, and we assume thatDM is the lightest RH sneutrino as dark matter. For a case where those particle are too heavy to be produced at the on-shell, the production cross section is kinematically very suppressed. For cases that RH sneutrinos are light but degenerate, only three-body decay is possible via virtual Higgsino ( ) and the energy of the produced lepton is much suppressed.

The corresponding diagrams are given in gure 5. The nal decay products are multi leptons plus a large missing energy byDM,

e+e(qq) l+ilj + missing E + (n l+l) , u d l+i + missing E + (n l+l) ,

(2.28)

9

e+

e

e+

e

g

q

+

+

j ( Nj)

k(~

k)

l (~

l)

i (Ni)

q

l+j ( Nj)

j(~l

+j )

0

0

Z/

Z/

i )

li (Ni)

i (~l

q

q

e+

e+

e

l+j ( Nj)

li ( Ni)

j(~l

+j ) d

u

j (Nj)

JHEP09(2014)068

+

k (~

k)

W +

0

+

+

i(~l

+i )

i (~l

i )

l+i ( Ni)

Figure 5. The neutrinophilic Higgsinos ( ) production and its sequent decay into RH sneutrino. s are produced by the s-channel of Z0/, t-channel of, and s-channel of W exchanges.

with n being an integer, or mono photon plus a large missing energy byDM,

e+e(qq) + missing E . (2.29)

2.3.1 Constraints from LEP

As far as the LEP bound on chargino is concerned, if the mass of the Higgsinos are greater than the threshold energy scale for e+e collision (s/2 104 GeV), it is natural to expect

that the constraints are relaxed drastically. Thus, we take m [greaterorsimilar] 103.5 GeV [26] as the kinematical lower bound to avoid the LEP searches for direct production of charginos.

For the direct production ofi, the t-channel exchange for e+e collision is dominant as in gure 6.

e+e + missing E . (2.30)

In this case, the result of monophoton searches for the MSSM neutralino e+e ~

01 ~

01

can be used to constrain the mass and couplings of the RH sneutrino to electrons [27]. In this analysis, using the e ective operator

e/ , the cuto scale should be greater than about 330 GeV for the fermion dark matter mass m~ < 80 GeV as shown in gure 7.

2.3.2 LHC bound

The current 8 TeV LHC gives lower bound on the charged Higgsino mass of 550 GeV, leaving the degenerate region with M M < 50 GeV unconstrained from the chargino

decay into light leptons, namely e or . For the decay into lepton, the bound is relaxed and requires M [greaterorsimilar] 350 GeV and M [greaterorsimilar] 150 GeV [28].

10

e+

e

e+

DM

DM

e+

e+

e

DM

DM

e+

DM

DM

+

+

+

e

DMDM. Since the produced RH sneutrinos are the lightest superpartners,DM, the only observable signal is photon.

[LParen1] e[RParen1] [LParen1]e [RParen1] L2

[LParen1]L = 330 GeV[RParen1]

Figure 6. Feynman diagrams for e+e

JHEP09(2014)068

3.5 10-11

3. 10-11

ddE[LParen1]GeV-1 [RParen1]

2.5 10-11

y N

2. 10-11

DM H PLe + h.c.

[LParen1]y = 0.65, MH = 110 GeV[RParen1]

[LParen1]y = 0.7, MH = 110 GeV[RParen1]

MDM = 10 GeV

1.5 10-11

1. 10-11

5. 10-12

0 0.0 0.2 0.4 0.6 0.8 1.0

EEbeam

Figure 7. Production rate (d/dE ) with respect to E /Ebeam for (e+e plus DM pair) in

two models. Red dashed line corresponds to the model studied in ref. [27]. The studied process is (e+e

) from the interaction term (

e)()/ 2. Depending on the dark matter mass MDM, the the lower limit of is di erent. The DELPHI(LEP) monophoton search for MDM = 10 GeV

gives the lower bound on 330 GeV. The second model is ours. The event is (e+e

e e)

from the interaction term yDM

PLe + h.c.. We take m = 110 GeV, and the cases with two Yukawa couplings (y = 0.65, 0.7) are presented (blue and magenta). Ebeam is taken as 100 GeV,

which is the average value for the LEP search. We nd that our model parameters (y and m ) are constrained by the LEP search as did in ref. [27], i.e. the region above the red dashed line is ruled out.

2.4 Lepton avor violation ( e)

The o -diagonal components of Yukawa couplings (y )i in eq. (2.2) induce lepton avor violating (LFV) decay of leptons. The general e ective operator can be written as

M= eui(p q)

imj q (A2)ij + imj q 5(A3)ij

uj(p) , (2.31)

with = i2[, ]. The decay rate of lj li is given by

(lj li) =

e28 m5lj |(A2)ij|2 + |(A3)ij|2

. (2.32)

11

H H Ri

lj liFigure 8. The Feynman diagrams for the lepton avor violation corresponding to eq. (2.31).

For the muon decay, e, the branching ratio is given by

Br( e) =

i

lj li

JHEP09(2014)068

963

G2F |

(A2)12|2 + |(A3)12|2

. (2.33)

The present bounds on the branching ratios of the LFV decays are [29, 30]

Br( e) < 5.7 1013 (90% C.L.) ,

Br( e) < 3.3 108 (90% C.L.) ,

Br( ) < 4.4 108 (90% C.L.) .

(2.34)

For our model with Yukawa interactions in eq. (2.2), from the diagrams given in gure 8, we obtain

(A2)

1 322

Xl(ST y )l (ST y )l M2~H

F

M2~Nl

M2~H

!

Xk (y )k (y )k 48M2H

!,

(2.35)

with F (x) being an auxiliary function. The experimental limits (2.34) give strong bounds on Yukawa couplings as well as masses of mediated particle, Mk , M and MH

, as we

(A3) = 0 ,

will show. In fact, for O(100) GeV masses of sneutrinos and the neutrinophilic chargino, we

nd the LFV decaying branching ratios are of O(106), those are very large compared with

current bounds (2.34). Since Yukawa couplings are xed from the neutrino mass and are of the order of unity, the charged Higgs must be heavier than around 10 TeV in the second term. On the other hand, for the rst term, we have a possibility that one of sneutrinos and charged Higgsinos are relatively light in the case that = ST y are suitably aligned by appropriate sneutrino mixings ij in such a way that the avor-violating processes are suppressed enough. Such mixing angles can be found by requiring some o -diagonal components of = ST y to be almost vanishing.

2.5 Anomalous magnetic dipole moment of muon

The muon anomalous magnetic dipole moment has 3.3 discrepancy between experimental data and the SM prediction as [31, 32]

a(EXP) a(SM) = (26.1 8.0) 1010. (2.36)

12

Thus, this discrepancy has been regarded as a hint and provided a motivation to investigate new physics beyond the standard model of particle physics.

A2 and A3 in eq. (2.31) contribute to the magnetic and electric dipole moment, respectively. The resultant electric and magnetic dipole moment of lj lepton are given as

dlj = mlj(A3)jj , (2.37)

alj =

(g 2)lj

2 = 2m2lj(A2)jj . (2.38)

The additional contribution to the induced magnetic moment of muon in the supersym-metric neutrinophilic Higggs model with large Yukawa couplings is given by

a = 2m2 1

322Xl(ST y )l(ST y )l

M2~H

F M2~ l

!, (2.39)

where we assumed Yukawa couplings are real and the negligible charged Higgs boson contribution is omitted. We might expect a large g 2 of the muon for light sneutrinos and

the light -like chargino because Yukawa coupling constants are O(1). However, as men

tioned above, the experimental limits on the lepton avor violation in eq. (2.34) are very stringent and we need a special mixing of sneutrinos.

2.6 Compatibility in benchmarks

As mentioned previous subsections, LFV constraints are very stringent. Indeed, for cases of vanishing lightest neutrino mass m1 as in benchmark point 1 and 3 in table 1, we could not nd viable parameter sets. Thus, here we mention viable parameter sets based on the benchmark point 2 and 3 in the table 1.

At rst, for the benchmark 2, we nd that LFV constraints are avoided with the sneutrino mixing angles (12, 23, 13) (0.75, 0.68, 0.20), and the resultant is given by

= ST y

1.18 0.06 0

0 1.28 0 0.05 0.24 1.31

JHEP09(2014)068

M2~H

. (2.40)

Then, the mass of the lightest RH sneutrino2 can be 10100 GeV without inducing a large LFV, while the mass of the other two1 and3 need to be O(110) TeV. Notice

that with the denition of S by eq. (2.10), we take the mass ordering of RH neutrinos as M2 < M1 < M3. With this choice of sneutrino mixing angles, the muon decay width constraint discussed section 2.2 is avoided. Here, we can see that the coupling between the lightest RH sneutrino (2) and the electron is negligibly small. This small coupling automatically suppresses the LEP mono-photon constraint from eq. (2.30).

In gure 9, we show the viable sneutrino mixing angles from the constrains on the LFV processes for the benchmark 2. In those plots, we xed one mixing angle 12 = 0.75,

the neutrinophilic Higgsino mass M = 110 GeV, and the lightest sneutrino mass M2 =60 GeV. Heavy sneutrino masses, (M1, N3) are taken from around TeV to 10 TeV. As the gures show, the constraint from e is most serious, and very small regions are

13

1.2

1.2

1.1

1.1

1.0

1.0

0.9

0.9

23

23

0.8

0.8

0.7

0.7

0.6

0.6

JHEP09(2014)068

0.5

0.5

-0.6-0.4-0.2 0.0 0.2 0.4 0.6

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

13

13

1.2

1.2

1.1

1.1

1.0

1.0

0.9

0.9

23

23

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

-0.6-0.4-0.2 0.0 0.2 0.4 0.6

-0.6-0.4-0.2 0.0 0.2 0.4 0.6

13

13

Figure 9. Allowed parameter space in the plane of the sneutrino mixing angles (13, 23) from

the constraints on LFV for the benchmark 2. For all plots, we xed M = 110 GeV, M2 =60 GeV and 12 = 0.75. Top left corresponds to (M1 , M3 ) = (7 TeV, 10 TeV). Top right,(7 TeV, 1 TeV). Bottom left, (1 TeV, 7 TeV). Bottom right, (0.5 TeV, 1 TeV). The black region is

Br( e) < 5.7 1013, the red region is Br( ) < 4.4 108, and the green region is

Br( e) < 3.3 108. The blue region denotes a > 109.

allowed. Including the constrains from , we nd that the value of 23 should be

around 0.68, which corresponds to (ST y )2e 0. The constraints do not restrict the value

of 13 much for the case with two heavy sneutrino masses. In the allowed parameter space, the sizable a can be obtained as denoted by the blue colored region.

In gure 10, we show the viable parameter space for the benchmark 2 with contours of the contribution to the muon anomalous magnetic moment from eq. (2.39) in the plane of the mass of neutrinophilic Higgsino and the RH sneutrino mass M2, which is the lightest supersymmetric particle. Here, we use M1 = 7 TeV and M3 = 10 TeV for reference.

The region of Red and Orange color respectively show 1 and 2 range of eq. (2.36). The

14

140

120

MN > MH

100

M N [LParen1]GeV[RParen1]

80

JHEP09(2014)068

60

40

LHC

20

50 100 150 200

MH[LParen1]GeV[RParen1]

Figure 10. The viable parameter space for the benchmark 2 with tuned sneutrino mixing angles so that LFV processes are su ciently suppressed. Contours show the contribution to the muon anomalous magnetic moment from eq. (2.39) in the plane of the mass of neutrinophilic Higgsino and the RH sneutrino mass M . 1 and 2 region of eq. (2.36) is shown with Red and Orange color respectively. In the blue region, M > M is realized. The yellow region, where the mass splitting between sneutrino and chargino is too large, is constrained by the LHC results.

blue region corresponds m2 > m . The yellow region, where the mass splitting between sneutrino and chargino is too large, is constrained by the LHC results.

For the benchmark 3, if the sneutrino mixing angles are (12, 23, 13) (0.75, 0.93, 0.02), the resultant is given by

= ST y

. (2.41)

Then, the mass of the lightest RH sneutrino2 can be 10100 GeV without inducing a large LFV, while the mass of the other two1 and3 need to be O(110) TeV. In gure 11,

we show the viable region with M1 = 7 TeV and M3 = 8 TeV. Again, we take the mass ordering of RH sneutrinos as M2 < M1 < M3.

3 Cosmological constraints

3.1 Dark radiation

RH component of neutrinos could contribute to the additional relativistic degrees of freedom in the early Universe, which is constrained by big bang nucleosysthesis and cosmic

15

1.20 0 0.25

0 1.02 0 0.21 0.33 1.05

140

120

MN > MH

100

M N [LParen1]GeV[RParen1]

80

JHEP09(2014)068

60

40

LHC

20

50 100 150 200

MH[LParen1]GeV[RParen1]

Figure 11. Same as gure 10 for the benchmark 3.

microwave background radiation observation as Ne [lessorsimilar] 0.57. In our model, RH neutrinos

could be in thermal equilibrium due to the scatterings with charged leptons (left-handed neutrinos) through neutrinophilic charged (neutral) Higgs bosons via the Yukawa interaction in eq. (2.2).

In order to suppress Ne enough, RH neutrinos should have decoupled from the thermal bath much before the quark-hadron phase transition which takes place at the cosmic temperature Tc 200 MeV.

3.1.1 ll+ R

R

The scatterings between charged lepton and RH neutrinos are mediated by the neutrinophilic charged Higgs boson H . We obtain

Z |M|2

s212 , (3.1)

with s being the energy at the center of mass frame. Taking thermal average, we nd

hvi |

dLIPS

1 8 |

y y |2

M4H+

y y |2 32M4H+

T 2. (3.2)

16

3.1.2 L

L R

R

Similarly, the thermal scattering cross section between left-handed and right-handed components of neutrinos via H0 and A0 is estimated as

hvi |

y y |2 32

1 4

1 M2H0

+ 1

M2A0

!2T 2. (3.3)

3.1.3 Decoupling condition

The decoupling condition of RH neutrino at the quark-hadron transition epoch is expressed as

hvin|TQH < H|TQH , (3.4)

which is rewritten as

|y y |2 M4H+

+|y y |24

JHEP09(2014)068

1 M2H0

+ 1

M2A0

!2<

rg906443(3)T 3QHMP= 1 (3.3 TeV)4

0.1 GeV TQH

3. (3.5)

Therefore the neutrinophilic Higgs must be heavier than around 3 TeV for order of unity Yukawa couplings. We note that the similar bound has already been obtained but H0

and A0 contributions were missing in refs. [11, 23, 24]. Here we have re-estimated and corrected it.

4 Dark matter

The lightest RH sneutrino is stable when R-parity is preserved and can be a good candidate for dark matter. The possibility in the neutrinophilic Higgs model was suggested in refs. [9, 10] by two of the present authors. In this section we generalise the previous results considering the benchmark points in the previous section and examine the cosmological and astrophysical phenomenon.

4.1 Relic density of dark matter

Due to the large Yukawa coupling in eq. (2.2), the RH sneutrino interacts with fermions and Higgsinos e ciently so that they could be in the thermal equilibrium at high temperature. In the rapidly expanding early Universe, those RH sneutrinos decouple from the thermal plasma and the comoving abundance is conserved after that. The relic density of WIMPs is determined by the annihilation cross section which determines the freeze-out temperature of DM. However, for complex elds, there might be the non-vanishing DM asymmetry. With a large DM asymmetry, the nal relic density of DM may depend on the annihilation cross section and the DM asymmetry [3339]. This is the case for light RH sneutrino DM in our scenario.

The annihilation cross section of RH sneutrino DM is dominantly determined by the annihilations into the leptons, that is given in partial wave expansion method by [9, 10]

hviff =

Xf

y4 16

m2f

(M2~N + M2~H )2

+ y4

8

M2~N (M2~N + M2~H )2

T M

+ . . .

!. (4.1)

17

There is another subdominant contribution from the induced annihilation into photons,

hvi2 = |

M|22 32M2~N

2em

83

y4 (A2 + 2)2 M4~l

4 M2~N

, (4.2)

where we used the approximation of MH = MH

= M~l for simplicity and the soft term

L = y A

~LH + h.c.. In fact, it gives small subdominant contribution to determine the relics density of DM in our consideration with y4 (A2 + 2)2 M4~l.

Since the RH sneutrinos were in the thermal equilibrium, the asymmetry could be generated from non-zero baryon asymmetry during the sphaleron process. The asymmetry of RH sneutrinos will depend on the specic model of baryogenesis, mass spectrum and the electroweak phase transition. In the simple case, the leptonic asymmetry is expected to be the order of baryon asymmetry, as 1010 [11]. In this paper, in order to see the asymmetry dependence, we treat it as a free parameter taking a value of a certain range.

For the WIMP with a non-vanishing asymmetry, the resulting relic density can be estimated by [40, 41]

DMh2 = 2.8 108

JHEP09(2014)068

mDM

GeV (YDM + YDM) . (4.3)

Here

YDM + YDM =

C1 exp[CJ[xF ]]

+ C

exp[CJ[xF ]] 1

, (4.4)

with

= 4

rg90MP mDM , (4.5)

J[xF ] =

Z

hvix2dx , (4.6) x = mDM/T , (4.7)

where xF (xF ) denotes the value of x at the freeze out time of (anti-)dark matter particle. The asymmetry of dark matter is given by

C = nDM nDMs . (4.8)

In the gure 12 we show the contour plot of the corresponding DM asymmetry to give the correct relic density of DM. For a given asymmetries C = (5 1011, 1011, 5

1012, 3 1012, 1012), the required amount of DM is obtained on the corresponding

(thick solid, solid, dashed, dotted, solid) lines in the plane of DM mass and Higgsino mass.

For a smaller Higgsino mass, the annihilation cross section is large enough to annihilate the DM-anti DM pairs and only the asymmetry remains. In this case, the abundance is determined by the asymmetry and the relic density is proportional to the DM mass and the asymmetry. We can see this for the Higgsino mass between 80 GeV and 140 GeV, where the contour lines are parallel and horizontal, and the mass of dark matter is inversely proportional to the asymmetry. For large Higgsino mass, the annihilation cross section is too small to annihilate all anti DM. In this case, the relic density is determined by the

18

140

120

100

M N [LParen1]GeV[RParen1]

80

60

JHEP09(2014)068

40

20

0

50 100 150 200

MH[LParen1]GeV[RParen1]

Figure 12. The contour plot of the DM asymmetry C = (5 1011, 1011, 5 1012, 3 1012,

1012) with (thick solid, solid, dashed, dotted, solid lines) given in eq. (4.8), to give correct relic density for DM in the plane of its mass and Higgsino mass.

annihilation cross section as the usual WIMP, being independent from the asymmetry. That can be seen, in the gure, around Higgsino mass larger than 150 GeV and RH sneutrino mass smaller than 60 GeV, where contour lines are not horizontal.

Compared to gure 10 and 11, the region compatible to explain the muon anomalous magnetic moment corresponds to Higgsino mass between 40 GeV and 120 GeV and the DM relic density is dominantly determined by the DM asymmetry larger than around C = 5 1012.

4.2 Dark matter scattering cross section with a nucleon

An elastic scattering of RH sneutrino with nuclei may induce a signal in the direct detection experiments. The most relevant process for our sneutrino DM is through the Z-boson exchange even this is not LH but RH [9, 10], in contrast with most of other RH sneutrino DM models where the Higgs bosons exchange is dominant [4250]. The DM-DM-Z vertex is induced by one-loop digram involving neutrinophilic Higgs boson. Because of the Z-boson exchange, DM mostly scatters with only neutrons rather than protons. In gure 13, we show the scattering cross section with a neutron for (ST y )A /MH = 0.1, 1, 2, 10 from the bottom to the top, and the current bounds by direct detection experiments, especially, the LUX experiment [51] with the black thick line. The experimental bound shown in the gure is re-estimated for our DM which scatters o with only neutrons. Here A is the trilinear soft coupling dened after eq. (4.2).

19

10-41

n _[LParen2]cm2 [RParen2]

10-43

10-45

JHEP09(2014)068

10-47

10 20 50 100 200 500 1000

mDM[LParen1]GeV[RParen1]

Figure 13. The scattering cross section between the lightest RH sneutrino and a neutron for (ST y )A /MH = 0.5, 1, 2, 10 from the bottom to the top. The current LUX bound on it is also shown with the black thick line.

4.3 Indirect signal from sneutrino dark matter

For the asymmetric DM, their annihilation in the galaxy is negligible. However, they can scatter o the cosmic rays and produce secondary particles such as gamma-ray or neutrinos [52]. Since we are considering the large Yukawa couplings, the indirect signature might be very promising or even harmful. However, in our benchmark point 2 and 3, the Yukawa coupling between the lightest RH sneutrino (N2) and the electron is quite negligible as a consequence of suppressing LFV and therefore the indirect signature is also very suppressed.

For symmetric DM case with the heavy , the DM annihilation signal can be seen most likely as a gamma-ray line because annihilation into a fermion pair is helicity suppressed [9].

4.4 Decay of cosmic neutrino background

As the muon can decay to the electron through the charged neutrinophilic Higgs(ino), and sneutrino loops, the heavier neutrino can decay to the lighter one through similar diagrams. Assuming that the mass of lighter one is much smaller than that of the heavier one, the decay rate of neutrino is

(j i + ) =

e24 m5 j |(A 2)ij|2 + |(A 3)ij|2

, (4.9)

where

(A 2)ij

1 322

X

(y )i (y )j

M2~H

F

M2~l

M2~H

!

X (y )i (y )j 48M2H

,

(4.10)

(A 3)ij = 0 .

20

Although the GIM mechanism is not applied, so there is no suppression by the mass of charged leptons, the suppression by small neutrino mass as 5th powers is enough to satisfy the present constraint on the life-time of the neutrinos, which is

> 1012 yrs , (4.11)

from the analysis of the cosmic infrared background [53].

5 Conclusion

We have studied an extended supersymmetric model where neutrinos are Dirac particle and those masses are given by large neutrino Yukawa couplings and a small VEV of the neutrinophilic Higgs eld. Provided the lightest RH sneutrino is LSP as the dark matter candidate, we have examined various aspects of the model with Dirac Yukawa couplings of the order of unity.

By only considering the muon decay width, it turns out that the neutrinophilic Higgs bosons must be heavier than several hundreds GeV and some supersymmetric particles among RH sneutrinos and neutrinophilic Higgsino need to be heavier than several hundreds GeV. In fact, we have found that the neutrinophilic Higgsino and one of the RH sneutrino can be relatively light of the order of 100 GeV if the other two RH neutrinos are heavy enough. The current collider experiment, most importantly the LHC, constraints require a viable parameter space; is heavy enough, or the mass di erence of and the lightest

RH sneutrino is smaller than about 50 GeV, according to ref. [28]. The LEP constrains the

DM e coupling to be less than about 0.6.

For general mixing of RH sneutrinos, due to the large avor mixings of neutrino sector, the lepton avor violating processes induced through neutrino Yukawa interactions are also typically as large as 106 in the decay branching ratio, with new particles of O(100) GeV

mass. Only with appropriately tuned RH sneutrino mixings, we can avoid the LFVs.With the chosen parameters, we found that the deviation of the muon g 2 can be

explained with a relatively large lightest neutrino mass around m1 0.05 eV and the lightest RH sneutrino and Higgsino mass, M = 10100 GeV and M = 60160 GeV respectively. In other words, if the muon g 2 is explained in this model, then m1 can not

be so small. As a result of tuned RH sneutrino mixings, the

DM e coupling is

almost vanishing, which means the LEP data does not signicantly constrain this model and the international linear collider also would not be able to produce a mono-photon signal, while the

DM coupling is about unity. A muon collider can easily test

this model if it will be indeed constructed, as the Fermilab plans [54].In this muon g 2 favored parameter region, the DM relic density is explained by RH

sneutrino with the asymmetry of C 5 1012. If we do not mind the deviation of the

muon g 2, RH sneutrino dark matter could be an usual WIMP with heavier

.

Acknowledgments

K.-Y.C. appreciates Asia Pacic Center for Theoretical Physics for the support to the Topical Research Program. K.-Y.C. was supported by the Basic Science Research Program

21

JHEP09(2014)068

through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology Grant No. 2011-0011083. O.S. was supported in part by the Grant-in-Aid for Scientic Research on Innovative Areas No. 26105514 from the Ministry of Education, Culture, Sports, Science and Technology in Japan. C.S.S. is supported in part by DOE grants doe-sc0010008, DOE-ARRA-SC0003883, and DOE-DE-SC0007897.

A Formula for the muon g 2

For the Lagrangian

L =

L(v + ia5)f S + h.c. , (A.1)

where f is charged fermion, the anomalous magnetic dipole moment of the charged lepton L with charge Q is given by [55, 56]

aL = mL 82

Z

1 (|v|2 + |a|2)z(1 z)2mL + (|v|2 |a|2)(1 z)2mfz(1 z)m2L + (1 z)m2f + zm2s

. (A.2)

For neutrinophilic Higgs model with Lagrangian

L = y

LPR + h.c. (A.3)

we obtain

JHEP09(2014)068

aL = |y|2m2L 162

Z

1

0 dz

z(1 z)2 z(1 z)m2L + (1 z)m2f + zm2s

(A.4)

|

y|2m2L 162m2f

Z

1

0 dz

z(1 z)2

1 z + z(m2s/m2f)

.

B Auxiliary functions

F (x) = Z

1 z(1 z)2

0 (1 z) + zx= 1 6x + 3x2 + 2x3 6x2 ln(x)

6(x 1)4

, (B.1)

F2(x, y) = 1

ln

x2 y2

, (B.2)

F3(x, y, z, w) = x4(z2 w2) log(x2) + w4(x2 z2) log(w2) + z4(w2 x2) log(z2)

(x2 y2)(z2 w2)(x2 z2)(x2 w2)

x2 y2

y4(z2 w2) log(y2) + w4(y2 z2) log(w2) + z4(w2 y2) log(z2)

(x2 y2)(z2 w2)(z2 y2)(w2 y2)

.

(B.3)

Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

22

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