Neutrino mass generation, lepton number violation from ...icts.ustc.edu.cn/cs2014/0508/RadiativeNeutrinoMass_140508.pdf♣ the absolutely neutrino mass and the hierarchy of the mass

8th May 2014兩岸粒子物理與宇宙學研討會

Neutrino mass generation, lepton number violation from scalar multiplet

Lu-Hsing TsaiLu-Hsing Tsai National Tsing Hua University (NTHU)


Outline

☆ Motivation

☆ Neutrino mass Model Building

☆ Implication for H→ 2γ

☆ Conclusion


What we know about neutrinos ……

♣ Neutrino oscillations imply the nonzero mass active neutrinos

12 13 12 13 13 1

12 23 12 23 13 12 23 12 23 13 23 13 2

12 23 12 23 13 12 23 12 23 13 23 13 3

CP

CP CP

CP CP

ie

i i

i i

c c s c s e

s c c s s e c c s s s e s c

s s c c s e c s s c s e c c

d

d dm

d dt

n nn nn n

-æ öæ ö æ öç ÷ç ÷ ç ÷= - - -ç ÷ç ÷ ç ÷

ç ÷ ç ÷ç ÷- - -è ø è øè ø

Capozzi, et. al. (2013)


♣ The masses of neutrinos are observed from neutrino oscillation experiments.

0.44eVii

m <å WMAP9+eCMB+BAO+H0

tritium decay , Troitsk (2011)2.05eVii

m <å

Normal Hierarchy

Inverted Hierarchy

♣ the absolutely neutrino mass and the hierarchy of the mass spectrum are still unknown

0.23eVii

m <å (95%), Planck+WMAP+highL+BAO


♣ Generally, Majorana neutrino is generated with imposing such gauge singlet chiral component.

Majorana Phases α21, α32

Lepton numberSymmetry breaking ΛL

Majorana Mass 2

cL L

mn n n

2| |ei ii

m V mbb< >= å The effective masses of neutrinoless double beta decay is a function of Majorana mass and phases

♣ The simplest way to have neutrino mass is to add right-handed neutrinos into SM and lead to Dirac neutrino

Δ L=QLY νH N R+h.c. , mν=v

√2Y ν


♣ The tiny neutrino masses can be explained in terms of lepton number (L) symmetry which is broken at the scale ΛL

L

HHLLmn µ L

Three types of seesaw models

H< >H< >

LnLn

RN RN

type-I (-III)

R : (1,0)N 0( (3,0) : , )R R R±S S S

2

, DD R

R

mm m M

Mn ; =

type-II

: (3, 1)T +

2

2ab abT

vm g

Mnm < >;

H< >

Ln

H< >

Ln

0T

m

abg

Y: ( , ) Re presentation of dimensions in SU(2) , and hypercharges y in U(1)Lx y xy º


Zee model Zee-Babu model

Loop induced neutrino mass

2( )

h.c.

c cR RL L f i Ls l Yl

s s

s

m

+ ++

- - ++

= - - F

- F +2 1 1 2 2

1 2

( ) ( )

h.c.

cL RL L f i Ls L Y H Y H l

sH H

sm= - - +

+ +

klinjn

s-1,2H

1,2H

kl

1,2H

injn

s-m

s-

--F

HH

These model has too many Yukawa couplings undetermined.

2ˆˆ Tl l

vm fmYm f

mnf

mµ


Zee-Babu model has too many Yukawa couplings undetermined.

Tree-level neutrino mass generation has fine-tuning problem on the Yukawa coupling or vacuum expectation value

Does there exist any radiative neutrino mass model in which Yukawa coupling can be unique determined by experiments?


Model Building

If only new scalar multiplets are allowed, one of the below three possible Yukawa couplings should be required:

, :(2,1/2)

, : (1 , 2)

, : (1 , 4)

, : (3, 2)

ab La Rb

cab La Lb

cab Ra Rb

cab La Lb

h L l

f L L s s

y l l

g L L T T

c c

F F Zee-Babu Model

Type-II seesaw

Zee-model

Zee-model, Zee-Babu Model

We pick out Φ to form the sole Yukawa coupling beyond the SMChian-Shu Chen, Chao-Qiang Geng, Da Huang, LHT (2012)


A SU(2)L scalar multiplet ξ: ( n ,2 ) inspired by H→γγ excess is imposed into the model

Notice that the trilinear term is required can help to determine the form of ξ

1m xxF%

' ' ' ' ' '

' ' ' ... ' ' '...

...

...... 0

ii jj kk ijk i j k

i i j j k k ijk i j k

xx e e e x x

e e e x x

=

= - =

For n = 2, 4, 6,….. , the trilinear term vanishes

We have a class of choice n = 1, 3, 5, 7, 9, … ,

n : arbitrary positive integer , , ,........( , , ,... 1, 2)i j k i j kx x= =

ij ije e= -


A global symmetry (lepton number) exist in the model, which is broken spontaneously.

The Majoron arising from gauge multiplet is ruled out by experiments.

Another multiplet is required to make the model with explicit lepton number breaking

For example, for the case ξ: ( 5 ,2 ) , Imposing a scalar Δ: ( 3 ,0 ) to form

ΔξH*H* . Combing with ξξΦ and Yukawa coupling => L is broken

explicitly.

* *

*

: : 1, : 2

: :+1

: : 1

: 1

cR R Rl l l

H H

H H

xx x

x

F + F -F

D D -

D D ¹ -


injn

sm

s

F

HH

Neutrino Mass Generation

The broken lepton number symmetry implies that the neutrino must be Majorana

The neutrino mass in this model is generated through two loop diagram, which magnitudes are proportional to the mixing angle between ξ and Φ

Zee-Babu model

injn

F

HH

Xx

W W


Neutrino Mass

2 242 2

2 2 2 241 1 2 2

6 1 1( ) sin 2 [ log log ]

2(4 )W W

ab a b abP P P P

M Mgm m m v y

M M M Mn x bp

æ ö æ ö-ç ÷ ç ÷

è ø è ø;

A similar model with triplet ξ(3,2) requires to forbid the tree level Yukawa coupling explicitly

1

2 21 2

sin 2P P

v

M Mxm

b µ-

%

P1,2

: The mass eigenstates of doubly charged scalars

P1=cosβξ+sinβΦ

P2=−sinβξ+cosβΦ


♣ The neutrinoless double beta decay (0νββ) in this model can be larger than before.

Re

d

d

u

u

ReXFxW

W

vxeeyLe

d

d

u

u

LeXmn

W

W

4

4 2

( )~ ee

W

mgA

m pn

n < >

1 2

4

2 24

9 4

4 2

1 1~ sin 2

16 2

( )10 ~

16 2

P eeP PW

ee

W

gA y v

M Mm

mg

m p

x

n

qæ ö

-ç ÷ç ÷è ø

< >7/ 10PA An-<

2 20.01GeVp< >=

25 2 9 2

1,2 1,22 2 2

from neutrino mass relation

( ) ( ) 10 10ee ee

ee P Pe

m mpy v M M

p m pn n

x< >

< > < >; ;


♣ From the preserving of the perturbability of yab , the inverted hierarchy of neutrino is disfavor.

♣ The ratios of lepton violating process (LFV) can be predicted directly without any assumption between the Yukawa coupling.

*Br( e )

Br( e )Rtm

t gm g®

=®

PMNS PMNSˆ( ) [ ( ) ]Tab ab ab abm U m U yn n= µ

13expBr( e ) 5.7 10 (90% C. L.)m g -® < ´

(MEG, 2013)

Br (μ→3e)exp<1.0×10−12

Br (τ→e γ)exp

*=

Γ(τ→e γ)exp

Γ(τ→e ν ν)exp

<10−8


0.24 0.250.24 0.181.65 ( ) ( )m + +- -= stat syst

Implication for H→γγ

( ) ( )

( ) ( )SM SM

pp h h

pp h h

s ggms gg

® ®º

® ®Br

Br

8 TeV: /SM @ 125.0 GeV = 0.55 +0.29-0.27

7+8 TeV: /SM @ 125.0 GeV = 0.78 +0.28

-0.26

7 TeV: /SM @ 125.0 GeV = 1.69 +0.65-0.59

CMS-HIG-13-001ATLAS-CONF-2013-012

q

t

t

H

W,Zq

q'

W,Z

g

g

g

g

t̄

t̄

t

tHH

q'

q q'

W,Z

W,Z

H


H

gW

g

H

W

g

g

H

t

g

g

2 32 2

1/2 13( ) | 3 ( ) ( ) |

128 2F H

f f Wf

G mH Q A A

agg t tp

G ® = +å2

1 1/2( ) 8.3 , 3 ( ) 1.8W t tA Q At t-; ;

H→γγ in SM

τt=mt

2

mH2 , τW=

mW2

mH2


H

gW

g

H

W

g

g

H

t

g

g

2 32 2

1/2 13( ) | 3 ( ) ( ) |

128 2F H

f f Wf

G mH Q A A

agg t tp

G ® = +å2

1 1/2( ) 8.3 , 3 ( ) 1.8W t tA Q At t-; ;Imposing the charged particles beyond SM

H→γγ in SM

H

S

g

g

H

S

g

g

τt=mt

2

mH2 , τW=

mW2

mH2


Implication for LHC (I)

♣ Charged scalar multiplet ξ in the loop could contribute to the H→γγ significantly

♣ There seems to have more than 1.5 times excess of H→γγ than SM from ATLAS

Γ(H→γ γ)=GF α2mH

3

128√2π3 |∑ f

3Q f2 A1/2(τ f )+A1(τW )+∑I 3

( I 3+1)2 v2

μξ

mξ2 A0( τξ)|

2

−n−1

2≤ I 3≤

n−12

Γ(H→Z γ)=GF ααZ mH

3

64√2π3 |∑ f

3Q f2 A1/2

Z(τ f ,λ f )+A1

Z(τW ,λW )

+∑I 3

( I 3+1)( I 3−sW2 Y

2)v2

μξ

mξ2 A0

Z(τξ ,λξ) |

2


♣ Combing the effects on H→γγ and H→Zγ can help to identify different models

The correlation among H→γγ and H→Zγ is strongly dependent on theGauge representation of charged scalars.

scalar loop contribution by ξ :(5,2)


Implication for LHC (II)

ξ1111=ξ+++ ,ξ1112=1

√4ξ++ ,ξ1122=

1

√6ξ+ ,ξ1222=

1

√4ξ0 ,ξ2222=ξ-

Δ11=−Δ+ ,Δ12=

1

√2Δ

0 ,Δ22=Δ-


♣ The existence of triply charged scalar can be tested in the future

6 2 5

3 6

3( 3 ) 0.13MeV

512W

W

g v mW

mx xx

p+++ +G ® ; ;

x +++ x ++

W +

W +

W +

The mixing of doubly charged scalars would give the final state of left-handed same sign dilepton

x +++ x ++

W +

X

++F

cRe

cRe

x +++ x ++

W +

W +

cLe

n

n

cLeW +

2( ( , ) ') 10 pbpp W Zs g xx -® ® <


Summary

♣ We build a class of models in SM gauge group to radiatively generate neutrino mass. Yukawa coupling constants can locate within a reasonable region.

♣ The form of Yukawa coupling is fixed by neutrino oscillation data, which can be test from lepton violating processes.

♣ The higher charged scalar multiplet can contribute to H→γγ

significantly. The doubly and triply charged scalars could also be test in the future.


Backup


Motivation: Higgs discovery and Neutrino mixing angle θ13

♣ The 125GeV Higgs-like particle have been found at ~7σ

Eleni Mountricha (ATLAS)

h gg®

*h ZZ®


Spin-0+ boson is favored over spin-2.

Eleni Mountricha (ATLAS)


Neutrinoless double beta decay (ν0ββ) experiment could help to determine the Dirac or Majorana nature of neutrinos

PDG (2012)

The effective mass <m> depends also on Majorana phases α21 ,α31


The doubly charged mixing matrix between ξ and Φ is given by

2 2 2

2 2 2

2 2 2

1 3,

4 41 1

2 23 1

4 4

m m m

m m m

m m m

x x x

x x x

x x x

++ +++ -

+ +++ -

+ +++ -

= +

= +

= +

The mass spectrum of the 5-plet

0

0

2 2 2 2 2

2 2 2 2 2

orm m m m m

m m m m m

x x x x x

x x x x x

+++ ++ + -

+++ ++ + -

> > > >

< < < <

2 2 2~ (100GeV)m mx D=

To insure the mixing with other multiplet small


Collider signature for pp →e-(+)e-(+) +X

1 2

24 2 2

24 2 2

12 2 1

1 1( ' ') ~ sin 2

(4 )

10 GeV (10 fb)

ee

P P

g y vqq e e q q d

M Mxs q l

p± ±

- -

æ ö® -ç ÷ç ÷

è ø<

ò

cRe

d

d

u

u

cRe

X++Fx ++W +

W +

collision

decay


Neutrino mass generation, lepton number violation from ...icts.ustc.edu.cn/cs2014/0508/RadiativeNeutrinoMass_140508.pdf♣ the absolutely neutrino mass and the hierarchy of the mass

Documents