Neutrino mass generation, lepton number violation from...
Transcript of Neutrino mass generation, lepton number violation from...
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)
8th May 2014兩岸粒子物理與宇宙學研討會
Outline
☆ Motivation
☆ Neutrino mass Model Building
☆ Implication for H→ 2γ
☆ Conclusion
8th May 2014兩岸粒子物理與宇宙學研討會
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)
8th May 2014兩岸粒子物理與宇宙學研討會
♣ 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
8th May 2014兩岸粒子物理與宇宙學研討會
♣ 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
8th May 2014兩岸粒子物理與宇宙學研討會
♣ 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
8th May 2014兩岸粒子物理與宇宙學研討會
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
8th May 2014兩岸粒子物理與宇宙學研討會
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?
8th May 2014兩岸粒子物理與宇宙學研討會
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)
8th May 2014兩岸粒子物理與宇宙學研討會
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= -
8th May 2014兩岸粒子物理與宇宙學研討會
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 -
8th May 2014兩岸粒子物理與宇宙學研討會
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
8th May 2014兩岸粒子物理與宇宙學研討會
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
8th May 2014兩岸粒子物理與宇宙學研討會
♣ 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< >
< > < >; ;
8th May 2014兩岸粒子物理與宇宙學研討會
♣ 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
8th May 2014兩岸粒子物理與宇宙學研討會
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
8th May 2014兩岸粒子物理與宇宙學研討會
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
8th May 2014兩岸粒子物理與宇宙學研討會
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
8th May 2014兩岸粒子物理與宇宙學研討會
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
8th May 2014兩岸粒子物理與宇宙學研討會
♣ 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)
8th May 2014兩岸粒子物理與宇宙學研討會
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-
8th May 2014兩岸粒子物理與宇宙學研討會
♣ 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 -® ® <
8th May 2014兩岸粒子物理與宇宙學研討會
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.
8th May 2014兩岸粒子物理與宇宙學研討會
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®
8th May 2014兩岸粒子物理與宇宙學研討會
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
8th May 2014兩岸粒子物理與宇宙學研討會
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
8th May 2014兩岸粒子物理與宇宙學研討會
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