PDF Phenomenology of SUSY neutrinophilic Higgs GUT - TWCU

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Phenomenology of

SUSY neutrinophilic Higgs GUT

Kunio KANETA (Osaka Univ.)

in collaboration with N. Haba (Osaka Univ.)

Y. Shimizu (Tohoku Univ.) 14 Mar. 2012 @Kobe Univ.

workshop “Beyond the Standard Model and The Origin Of Higgs”

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Contents

1. Introduction

2. Gauge Coupling Uniﬁcation

3. Flavor Violating processes

4. Summary

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1. Introduction

(4)

1. Introduction

☆ Introduction to νHDM Question:

Why neutrino masses are tiny comparing to other fermions?

m_ν_e/m_e _∼^< 10⁻⁵, . . . e.g)

models provide why is tiny A lot of explanations (models):

For example,

m

_ν

∼ y

_ν

� φ � y

_ν

models provide what is origin of m_ν ∼ y_ν² �φ��φ�

M

let us consider another possibility

with

“neutrinophilic Higgs doublet model (νHDM)”

m

_ν

∼ y

_ν

� φ

_ν

�

�φ_ν� ∼ 0.1 eV

☆

(5)

How can get tiny VEV?

☆ Higgs potential

V = ! m

_"²

| " |

²

+ m

_"²_#

| "

_#

|

²

+ m

₃²

( "

^†

"

_#

+ "

_#^†

" ) + $

₁

2 | " |

⁴

+ $

₂

2 | "

_#

|

⁴

+ $

₃

| " |

²

| "

_#

|

²

+ $

₄

("

^†

"

_#

)("

_#^†

") + $

₅

2 [("

^†

"

_#

)

²

+ ("

_#^†

")

²

]

| m₃² | ! m_!² ,m_!²_"

☆Higgs potential:

NH, M.Hirotsu Eur. Phys. J. C69, 481 (2010).

fields Z₂-charge

SM fields (SM Higgs: Φ) ^＋

ν_R_{: N} ^ー

νHiggs doublet:Φ_ν ^ー

☆ Z₂ sym. (which distinguishes Φ_ν from Φ )

☆Yukawa interactions:

L_Yukawa = y_uQ!U + y_dQ!D + y_eL!E + y_"L!_"N +M N^cN

!"#$%&%$'(&

)$*+#$,$&%$'(&

wanted vacuum is

〈Φ〉~100 GeV ≫ 〈Φ_ν〉~0.1 eV/y_ν(Dirac) or 0.1 MeV/y_ν (Majorana)

E. Ma (2001, 2006), E. Ma and M. Raidal (2001), N. H. and K. Tsumura (2010), N. H. and O. Seto (2010)

F. Wang, W. Wang and J. M. Yang (2006), S. Gabriel and S. Nandi (2007), G. Marshall, M. McCaskey, M. Sher (2010), S. M.

Davidson and H. E. Logan (2009, 2010),

with symmetryZ₂

(to distinguish from )

φ

_ν

φ

N.Haba, M.Hirotsu, Eur.Phys.J. C69, 481 (2010)

1. Introduction

φ

_ν

(6)

☆ Higgs potential

V = ! m

_"²

| " |

²

+ m

_"²_#

| "

_#

|

²

+ m

₃²

( "

^†

"

_#

+ "

_#^†

" ) + $

₁

2 | " |

⁴

+ $

₂

2 | "

_#

|

⁴

+ $

₃

| " |

²

| "

_#

|

²

+ $

₄

("

^†

"

_#

)("

_#^†

") + $

₅

2 [("

^†

"

_#

)

²

+ ("

_#^†

")

²

]

| m₃² | ! m_!² ,m_!²_"

☆Higgs potential:

fields Z₂-charge

SM fields (SM Higgs: Φ) ^＋

ν_R_{: N} ^ー

νHiggs doublet:Φ_ν ^ー

☆ Z₂ sym. (which distinguishes Φ_ν from Φ )

☆Yukawa interactions:

L_Yukawa = y_uQ!U + y_dQ!D + y_eL!E + y_"L!_"N +M N^cN

!"#$%&%$'(&

)$*+#$,$&%$'(&

wanted vacuum is

〈Φ〉~100 GeV ≫ 〈Φ_ν〉~0.1 eV/y_ν(Dirac) or 0.1 MeV/y_ν (Majorana)

E. Ma (2001, 2006), E. Ma and M. Raidal (2001), N. H. and K. Tsumura (2010), N. H. and O. Seto (2010)

F. Wang, W. Wang and J. M. Yang (2006), S. Gabriel and S. Nandi (2007), G. Marshall, M. McCaskey, M. Sher (2010), S. M.

Davidson and H. E. Logan (2009, 2010),

with symmetryZ₂

(to distinguish from )

φ

_ν

φ

soft symmetry breaking mass parameterZ₂

1. Introduction

φ

_ν

(7)

V = !m_"² | " |² +m_"²_# | "_# |² +m₃²("^†"_# + "_#^†")+ $₁

2 | " |⁴ + $₂

2 | "_# |⁴ +$₃ | " |²| "_# |² +$₄("^†"_# )("_#^†") + $₅

2 [("^†"_# )² + ("_#^†")²]

| m₃² | ! m_!² ,m_!²_"

dV

d! = 0 " #!$ = 2m_!²

%₁

V

!"#

• !

☆Higgs potential:

☆ Higgs potential

1. Introduction

φ

_ν

(8)

| m₃² | ! m_!² ,m_!²_"

V

!"#

•

V = !m_"² | " |² +m_"²_# | "_# |² +m₃²("^†"_# + "_#^†") + $₁

2 | " |⁴ + $₂

2 | "_# |⁴ +$₃ ^| " |²| "_# |² +$₄⁽"^†"_# )("_#^†") + $₅

2 [("^†"_# )² + ("_#^†")²]

!"_#$

!_"

• •

dV

d! = 0 " #!$ = 2m_!²

%₁

☆Higgs potential:

dV

d!_" = 0 # $!_"% ! m₃²$!%

m_!²_"

!

☆ Higgs potential

� φ

_ν

� � � φ �

1. Introduction

φ

_ν

large & tiny^m²_φ_ν

m

²₃

“see-saw”

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☆ SUSY SU(5) GUT embedded νHDM

by the way, there is a fascinating relation among 3 scales ...

TeV

²

∼ m

_ν

× M

_GUT

Energy 10¹⁶ GeV

TeV 0.1 eV

an accident? or indicating new physics?

1. Introduction

N.Haba, Europhys.Lett., 96 (2011) 21001

(10)

TeV

²

∼ m

_ν

× M

_GUT

Energy 10¹⁶ GeV

TeV 0.1 eV

as a positive stance

m

_ν

∼ TeV

²

/M

_GUT

1. Introduction

(11)

TeV

²

∼ m

_ν

× M

_GUT

Energy 10¹⁶ GeV

TeV 0.1 eV

as a positive stance

m

_ν

∼ TeV

²

/M

_GUT

1. Introduction

�H_ν⁽�)� ∼ ρ⁽^�⁾�H_u(d)�/M

O(1) TeV

M

_GUT

SUSY

dynamically realized

W

_h

= µH

_u

H

_d

+ M H

_ν

H

_ν^�

+ ρH

_u

H

_ν^�

+ ρ

^�

H

_ν

H

_d

(12)

TeV

²

∼ m

_ν

× M

_GUT

Energy 10¹⁶ GeV

TeV 0.1 eV

1. Introduction

O(1) TeV

M

_GUT

SUSY SU(5) GUT

W

_h^GUT

= M

₀

trΣ

²

+ λtrΣ

³

+ 5Σ¯5 − M

₁

5¯5 + 5

_ν

Σ¯5

_ν^�

− M

₂

5

_ν

¯5

_ν^�

(similar model: R.Kitano, PLB539, 102 (2002))

W

_h

= µH

_u

H

_d

+ M H

_ν

H

_ν^�

+ ρH

_u

H

_ν^�

+ ρ

^�

H

_ν

H

_d

(13)

TeV

²

∼ m

_ν

× M

_GUT

Energy 10¹⁶ GeV

TeV 0.1 eV

1. Introduction

O(1) TeV

M

_GUT

SUSY SU(5) GUT

W

_h^GUT

= M

₀

trΣ

²

+ λtrΣ

³

+ 5Σ¯5 − M

₁

5¯5 + 5

_ν

Σ¯5

_ν^�

− M

₂

5

_ν

¯5

_ν^�

W

_h

= µH

_u

H

_d

+ M H

_ν

H

_ν^�

+ ρH

_u

H

_ν^�

+ ρ

^�

H

_ν

H

_d

(14)

TeV

²

∼ m

_ν

× M

_GUT

Energy 10¹⁶ GeV

TeV 0.1 eV

1. Introduction

O(1) TeV

M

_GUT

SUSY SU(5) GUT

W

_h^GUT

= M

₀

trΣ

²

+ λtrΣ

³

+ 5Σ¯5 − M

₁

5¯5 + 5

_ν

Σ¯5

_ν^�

− M

₂

5

_ν

¯5

_ν^�

W

_h

= µH

_u

H

_d

+ M H

_ν

H

_ν^�

+ ρH

_u

H

_ν^�

+ ρ

^�

H

_ν

H

_d

(15)

TeV

²

∼ m

_ν

× M

_GUT

Energy 10¹⁶ GeV

TeV 0.1 eV

1. Introduction

O(1) TeV

M

_GUT

SUSY SU(5) GUT

W

_h^GUT

= M

₀

trΣ

²

+ λtrΣ

³

+ 5Σ¯5 − M

₁

5¯5 + 5

_ν

Σ¯5

_ν^�

− M

₂

5

_ν

¯5

_ν^�

non-renormalizable term contributions (e.g. Giudice-Masiero mech.)

and can be SUSY scale

W

_h

= µH

_u

H

_d

+ M H

_ν

H

_ν^�

+ ρH

_u

H

_ν^�

+ ρ

^�

H

_ν

H

_d

ρ ρ

^�

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2. Gauge Coupling Uniﬁcation

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2. Gauge coupling uniﬁcation

☆ minimal SU(5) GUT

・For gauge coupling uniﬁcation (GCU)

( threshold correction)

・For avoiding proton decay

it is diﬃcult to take satisfying parameters ...

GeV

m

_T

∼ 5 × 10

¹⁴

m

_T

> 2 × 10

¹⁶

T

: color triplet Higgs let us remember the mass of color-triplet Higgs

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☆ SUSY neutrinophilic Higgs GUT matter sector superpotential

i, j : family

W = 1

4 f

_u_ij

10

_i

10

_j

H + √

2f

_d_ij

10

_i

¯5

_j

H ¯ + f

_ν_ij

1

_i

¯5

_j

Φ

_ν

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☆ SUSY neutrinophilic Higgs GUT matter sector superpotential

2. Gauge coupling uniﬁcation

i, j : family

( diagonalizes )

V

_D

m

_ν

¯5 = { (V

_D

)

_ij

D ¯

_j

, (V

_D

)

_ij

L

_j

} 10 = { Q

_i

, U

_i

, (V

_KM

)

_ij

E ¯

_j

}

in MSSM ﬁelds

W = 1

4 f

_u_ij

10

_i

10

_j

H + √

2f

_d_ij

10

_i

¯5

_j

H ¯ + f

_ν_ij

1

_i

¯5

_j

Φ

_ν

1 = { N ¯

_i

}

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☆ SUSY neutrinophilic Higgs GUT

i, j : family

Φ

_ν

= { T

_ν

, H

_ν

}

matter sector superpotential

in MSSM ﬁelds

H = { T, H

_u

}

^H^¯ ⁼ {T , H¯ _d}

W = f

_u_i

Q

_i

U

_i

H

_u

+ (V

_KM^∗

)

_ij

f

_d_j

Q

_i

D

_j

H

_d

+ f

_d_i

E

_i

L

_i

H

_d

− f

_ν_i

V

_Dij

N

_i

L

_j

H

_ν

+ f

_u_j

(V

_KM

)

_ji

E

_i

U

_j

T − 1

2 f

_u_i

Q

_i

Q

_i

T

+ (V

_KM^∗

)

_ij

f

_d_j

U

_i

D

_j

T ¯ − (V

_KM^∗

)

_ij

f

_d_j

Q

_i

L

_j

T ¯ + f

_ν_i

V

_Dij

N

_i

D

_j

T

_ν

W = 1

4 f

_u_ij

10

_i

10

_j

H + √

2f

_d_ij

10

_i

¯5

_j

H ¯ + f

_ν_ij

1

_i

¯5

_j

Φ

_ν

(21)

W = f_u_iQ_iU_iH_u + (V_KM^∗ )_ijf_d_jQ_iD_jH_d + f_d_iE_iL_iH_d − f_ν_iV_DijN_iL_jH_ν + f_u_j(V_KM)_jiE_iU_jT − 1

2f_u_iQ_iQ_iT

+ (V_KM^∗ )_ijf_d_jU_iD_jT¯ − (V_KM^∗ )_ijf_d_jQ_iL_jT¯ + f_ν_iV_DijN_iD_jT_ν

(22)

avoiding proton decay

2. Gauge coupling uniﬁcation

(e.g.)

τ(p → K⁺ν¯_e) _∼^> 10³³ (years)

Q

Q Q ˜ Q L ˜

L

W ,˜ Z,˜ B˜

T ˜ m

_T

> 2 × 10

¹⁶ ^GeV

2f_u_iQ_iQ_iT

(23)

nothing to do with proton decay

however, contributes running.

T

_ν

α

_s

m

_T_ν

∼ 5 × 10

¹⁴

GeV

^and

compatible with GCU and proton-stability m_T_ν ∼ 5 × 10¹⁴ GeV ^for GCU

m

_T

> 2 × 10

¹⁶

GeV

2f_u_iQ_iQ_iT

(24)

3. Flavor Violating processes

(25)

2f_u_iQ_iQ_iT

(26)

L

_i

L

_j

N

_k

f_ν_kV_Dki f_ν_kV_Dkj

N

_k

D

_i

D

_j

M_P M_T_ν

below the GUT scale directly related with neutrino mixing ﬂavor oﬀ-diagonal components for slepton and down-type squark

(δm²_L)_ij � − f_ν²_k

8π²(V_D^∗)_ki(V_D)_kj(3m²₀ + a²₀) log (δm²_D)_ij � − f_ν²_k

8π²(V_D^∗)_ki(V_D)_kj(3m²₀ + a²₀) log

2f_u_iQ_iQ_iT

H

_ν

T

_ν

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3. Flavor Violating processes

comparison with SU(5) + right-handed neutrinos (Majorana)

☆ SUSY SU(5) GUT with

N

_R

W = 1

4 f

_u_ij

10

_i

10

_j

H + √

2f

_d_ij

10

_i

¯5

_j

H ¯ + f

_ν_ij

1

_i

¯5

_j

Φ

_ν

W = 1

4 f

_u_ij

10

_i

10

_j

H + √

2f

_d_ij

10

_i

¯5

_j

H ¯ + f

_ν_ij

1

_i

¯5

_j

H + M

_ij

1

_i

1

_j

(28)

N

_R

2f_u_iQ_iQ_iT

W = f_u_iQ_iU_iH_u + (V_KM^∗ )_ijf_d_jQ_iD_jH_d + f_d_iE_iL_iH_d − f_ν_iV_DijN_iL_jH_u + f_u_j(V_KM)_jiE_iU_jT − 1

2f_u_iQ_iQ_iT + 1

2M_ijN_iN_j

+ (V_KM^∗ )_ijf_d_jU_iD_jT¯ − (V_KM^∗ )_ijf_d_jQ_iL_jT¯ + f_ν_iV_DijN_iD_jT

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3. Flavor Violating processes

N

_R

M_P M_T_ν

L_i L_j

N_k

D

_i ^Dj

N_k

f_ν_kV_Dki fν_kVDkj

M

_P

M

_N M_P M_T_ν

( diagonalizes MV_M N)

(δm²_L)_ij � − f_ν²_k

8π²(V_D^∗)_ki(V_D)_kj(3m²₀ + a²₀) log (δm²_D)_ij � −f_ν²_k

8π²(V_D^∗)_ki(V_D)_kj(3m²₀ + a²₀) log

M

_P

M

_T

(δm²_L)_ij � −f_ν_kf_ν_m

8π² (V_D^∗)_ki(V_M^∗ )_lk(V_M)_lm(V_D)_mj(3m²₀ + a²₀) log

(δm²_D)_ij � −f_ν_kf_ν_m

(M_T > M_GUT)

W = f_u_iQ_iU_iH_u + (V_KM^∗ )_ijf_d_jQ_iD_jH_d +f_d_iE_iL_iH_d −f_ν_iV_DijN_iL_jH_ν +f_u_j(V_KM)_jiE_iU_jT − 1

2f_u_iQ_iQ_iT

+ (V_KM^∗ )_ijf_d_jU_iD_jT¯ − (V_KM^∗ )_ijf_d_jQ_iL_jT¯ +f_ν_iV_DijN_iD_jT_ν

W = f_u_iQ_iU_iH_u + (V_KM^∗ )_ijf_d_jQ_iD_jH_d +f_d_iE_iL_iH_d −f_ν_iV_DijN_iL_jH_u +f_u_j(V_KM)_jiE_iU_jT − 1

2f_u_iQ_iQ_iT + 1

2M_ijN_iN_j

+ (V_KM^∗ )_ijf_d_jU_iD_jT¯ −(V_KM^∗ )_ijf_d_jQ_iL_jT¯ + f_ν_iV_DijN_iD_jT

H

_u

T

(30)

3. Flavor Violating processes

N

_R

M_P M_T_ν

M

_P

M

_N

M_P M_T_ν

・In SUSY SU(5) with , if mass matrix is ,

in SUSY νH GUT is larger than that of SUSY SU(5) with

N

_R

( > 6 %)

・Predictability is improved in SUSY neutrinophilic Higgs GUT because neutrinos have only Dirac mass.

⇨ Let us focus on , andµ → eγ, τ → µγ

b → sγ

N

_R

(δm²_L)_ij � − f_ν²_k

8π²(V_D^∗)_ki(V_D)_kj(3m²₀ + a²₀) log

(δm²_D)ij � −f_ν²_k

8π²(V_D^∗)ki(VD)kj(3m²₀ + a²₀) log

(δm²_L)_ij � −f_ν_kf_ν_m

(δm²_D)_ij � −f_ν_kf_ν_m

M

_P

M

_T

(M_T > M_GUT)

N

_R

M

_ij

= M

_i

δ

_ij

(δm²_D)_ij

(31)

3. Flavor Violating processes

Br(b → sγ) − Br(µ → eγ)

☆

large θ13 region becomes restricted in

µ → eγ

m_1/2 (GeV)

500 600 700

Preliminary

800

(32)

Br(b → sγ) − Br(τ → µγ)

☆

(When θ13 becomes large, )Br(τ → µγ)/Br(µ → eγ) ∼ 10

m_1/2 (GeV)

500 600 700

Preliminary

800

(33)

3. Summary

・tiny neutrino mass can be realized by introducing

We discussed GCU and Flavor Violation in SUSY neutrinophilic Higgs GUT

(neutrino Yukawa can be of order 1) In SUSY neutrinophilic Higgs GUT,

In νHDM

・gauge coupling uniﬁcation and proton decay can be compatible because can be lighter than GUT scale.

・LFV and are correlated with each other,

and can be larger than SUSY SU(5) + right-handed neutrino.

b → sγ

work in progress

other B physics

φ

_ν

T

_ν

・Flavor violating processes are directly related with MNS matrix.

Br(b → sγ)

・If ~ GUT and ~ SUSY scale, ~ 0.1 eV.

M

_φ_ν

m

₃

m

_ν

/y

_ν

= � φ

_ν

�