Minimal Texture of the neutrino mass matrix and CP...
Transcript of Minimal Texture of the neutrino mass matrix and CP...
Yusuke Shimizu (Hiroshima U.)
Setouchi Summer Institute 2016 @Hiroshima International Plaza
Minimal Texture of the neutrino mass matrix and CP violation
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2nd Sep. 2016
Collaboration:
Morimitsu Tanimoto (Niigata U.), Tsutomu Yanagida (Kavli IPMU)
Masataka Fukugita (Kavli IPMU), Yuya Kaneta (Niigata U.),
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- NOvA experiment @Neutrino 2016
1. Introduction
2. Minimal texture and CP violation
3. Summary
- Neutrino oscillation and lepton mixing
3
Plan of my talk
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1. Introduction
Particle First Second Third Mixing matrix
Quark
✓ud
◆
L
✓cs
◆
L
✓tb
◆
L
CKM matrix
ucR ccR tcR (Cabibbo-Kobayashi-Maskawa)
dcR scR bcR
Lepton
✓⌫ee
◆
L
✓⌫µµ
◆
L
✓⌫⌧⌧
◆
L
PMNS matrix
ecR µcR ⌧ cR (Pontecorvo-Maki-Nakagawa-Sakata)
Masses of elementary particles are different each generation.
Lepton flavor mixing is quite different from quark one.
- Generation Mysteries
- Neutrino oscillation and lepton mixing
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Neutrino flavor, mass eigenstates and time evolution
|⌫↵i =X
i
U↵j |⌫ji, |⌫↵(t)i =X
i
U↵j |⌫jie�iEjt
We consider 2 generations|⌫e(t)i = cos ✓|⌫1ie�iE1t
+ sin ✓|⌫2ie�iE2t
|⌫µ(t)i = � sin ✓|⌫1ie�iE1t+ cos ✓|⌫2ie�iE2t
Transition probability of ⌫e ! ⌫µ
P (⌫e ! ⌫µ; t) = |h⌫µ|⌫e(t)i|2 = sin2 2✓ sin2E2 � E1
2t
' sin2 2✓ sin2�m2L
4E, �m2 = m2
2 �m21
Ej =q
p2 +m2j ' p+
m2j
2E
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m1 < m2 < m3
m3 < m1 < m2
m1 ⇠ m2 ⇠ m3
Neutrino mass squared differences
Neutrino mass hierarchy
- Normal hierarchy (NH)
- Inverted hierarchy (IH)
- Quasi-degenerated (QD)
Fermions get masses through the Higgs mechanism
�m2
sol
⌘ m2
2
�m2
1
,���m2
atm
�� ⌘��m2
3
�m2
1
��
LY = y ̄LH R ! yhHi ̄L R = mf ̄L R
In the SM, neutrinos are massless since there are no right-handed neutrinos
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Seesaw mechanismMinkowski '77; Gell-Mann, Ramond, Slansky; Yanagida; Glashow; Mohapatra, Senjanovic '79
U ⌘
0
@1 0 00 c23 s230 �s23 c23
1
A
0
@c13 0 s13e�i�CP
0 1 0�s13ei�CP 0 c13
1
A
0
@c12 s12 0�s12 c12 00 0 1
1
A
0
@ei↵ 0 00 ei� 00 0 1
1
A
=
0
@c12c13 s12c13 s13e�i�CP
�s12c23 � c12s23s13ei�CP c12c23 � s12s23s13ei�CP s23c13s12s23 � c12c23s13ei�CP �c12s23 � s12c23s13ei�CP c23c13
1
A
0
@ei↵ 0 00 ei� 00 0 1
1
A
�CP ↵ �
- Adding three right-handed Majorana neutrinos
Lepton flavor mixing matrix (PMNS matrix)
- If , left-handed Majorana neutrinos get non-zero and small masses
MN >> MD
- is Dirac phase and , are Majorana phases
M =
✓0 MD
MTD MN
◆diagonalized���������! M =
✓M⌫ 00 MM
◆
M⌫ ' MDM�1N MT
D
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Experimental situations
- Reactor neutrino experiments indicate non-zero✓13
Experimental result by Daya Bay
sin2 2✓13 = 0.084± 0.005
Consistent with RENO, Double Chooz, and T2K experiments
Global fit of the neutrino oscillationM. C. Gonzalez-Garcia, M. Maltoni, T. Schwetz, JHEP 1411 (2014) 052
parameter best fit 1� 3�sin2 ✓
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0.304 0.292-0.317 0.270-0.344
sin2 ✓23
0.4520.579
0.424-0.5040.542-0.604
0.382-0.6430.389-0.644
sin2 ✓13
0.02180.0219
0.0208-0.02280.0209-0.0230
0.0186-0.02500.0188-0.0251
�m2
sol
[10�5eV2] 7.50 7.33-7.69 7.02-8.09���m2
atm
�� [10�3eV2]2.4572.449
2.410-2.5042.401-2.496
2.317-2.6072.307-2.590
�CP
[�]306254
236-345192-317
0-360
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- Deference of mixing matrices
Lepton mixing: PMNS mixing matrix
Quark mixing: CKM mixing matrix (PDG 2014)
|UPMNS| '
0
@0.825 0.545 0.1480.462 0.587 0.6650.326 0.598 0.732
1
A
The lepton mixing is large except for reactor angle ✓13
sin ✓13 ' 0.148
|VCKM| '
0
@0.974 0.225 0.003550.225 0.973 0.04140.00886 0.0405 0.999
1
A
The quark mixing is small except for Cabibbo angle �
� ' 0.225
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is nearly Cabibbo angle
The relation between quark masses and mixing angle
sin ✓13
sin ✓13 ' 0.148, sin ✓C = 0.225 ⌘ �
qmdms
' 0.225 ' sin ✓C
Neutrino masses and lepton mixing angles are also related each other
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q�m2
sol
�m2
atm
' 0.416 ' O(p�) ) sin2 ✓23
q�m2
sol
�m2
atm
' 0.173 ' �p2
) sin ✓13
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Texture with : 2 parameters
Extend to 3 generations: 3 parameters
sin ✓C =pmd/ms
S. Weinberg, HUTP-77-A057, Trans.New York Acad.Sci.38:185-201, 1977
Md =
✓0 AA B
◆=
✓0
pmdmsp
mdms ms
◆
H. Fritzsch, Phys. Lett. B73 (1978) 317; Nucl. Phys. B115 (1979) 189
Md =
0
@0 Ad 0Ad 0 Bd
0 Bd Cd
1
A , Mu =
0
@0 Au 0Au 0 Bu
0 Bu Cu
1
A ,
Vus 'r
md
ms�
rmu
mc' 0.185, Vcb '
rms
mb�
rmc
mt' 0.065
so good too large
Fritzsch texture does not work in quark sector...
2. Minimal texture and CP violation
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The charged lepton and Dirac neutrino mass matrices
M. Fukugita, M. Tanimoto, T. Yanagida, Prog. Theor. Phys. 89 (1993) 263
- Apply to the lepton sector
mE =
0
@0 A` 0A` 0 B`
0 B` C`
1
A , mD =
0
@0 A⌫ 0A⌫ 0 B⌫
0 B⌫ C⌫
1
A
We assume right-handed Majorana neutrino mass matrix is proportional to unit one: MR = M01
The left-handed Majorana neutrino mass eigenvalues
mi =�UT⌫ mT
DM�1R mDU⌫
�i
Pontecorvo-Maki-Nakagawa-Sakata(PMNS) mixing matrix
UPMNS = U †`QU⌫ , Q =
0
@1 0 00 ei� 00 0 ei⌧
1
A
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- The neutrino mixing matrix elementsU⌫(1, 1) =
sm2Dm3D(m3D �m2D)
(m2D +m1D)(m3D �m2D +m1D)(m3D �m1D),
U⌫(1, 2) = �
sm1Dm3D(m3D +m1D)
(m2D +m1D)(m3D �m2D +m1D)(m3D +m2D)'
rm1D
m2D= 4
rm1
m2,
U⌫(1, 3) =
sm1Dm2D(m2D �m1D)
(m3D �m1D)(m3D �m2D +m1D)(m3D +m2D)' m2D
m3D
rm1D
m3D=
rm2
m3
4
rm1
m3,
U⌫(2, 1) =
sm1D(m3D �m2D)
(m2D +m1D)(m3D �m1D),
~w
U⌫(2, 2) =
sm2D(m3D +m1D)
(m2D +m1D)(m3D +m2D),
U⌫(2, 3) =
sm3D(m2D �m1D)
(m3D +m2D)(m3D �m1D)'
rm2D
m3D= 4
rm2
m3,
U⌫(3, 1) = �
sm1D(m2D �m1D)(m3D +m1D)
(m3D �m1D)(m3D �m2D +m1D)(m2D +m1D),
U⌫(3, 2) = �
sm2D(m2D �m1D)(m3D �m2D)
(m3D +m2D)(m3D �m2D +m1D)(m2D +m1D),
U⌫(3, 3) =
sm3D(m3D +m1D)(m3D �m2D)
(m3D +m2D)(m3D �m2D +m1D)(m3D �m1D)
Because of seesaw mechanism
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- The lepton mixing matrix elementsM. Fukugita, Y. S., M. Tanimoto and T. T. Yanagida, Phys. Lett. B716 (2012) 294
Ue2 ' �✓m1
m2
◆1/4
+
✓me
mµ
◆1/2
ei�,
Uµ3 '✓m2
m3
◆1/4
ei� �✓mµ
m⌧
◆1/2
ei⌧ ,
Ue3 '✓me
mµ
◆1/2
Uµ3 +
✓m2
m3
◆1/2 ✓m1
m3
◆1/4
Free parameters: m1, �, ⌧
Charged lepton contributions✓me
mµ
◆1/2
' 0.0695,
✓mµ
m⌧
◆1/2
' 0.244
Relation between neutrino masses and lepton mixing angles
sin2 ✓23
' 4
s�m2
sol
�m2
atm
= 0.416 ' O(p�), sin ✓
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' (sin ✓23
)3 sin ✓12
' 0.158
0.40 0.45 0.50 0.55 0.600.000.050.100.150.200.250.30
sin2Θ23
sinΘ 13
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- Neutrino mass hierarchy and neutrino-less double beta decay
M. Fukugita, Y. Kaneta, Y. S., M. Tanimoto and T. T. Yanagida, work in progress
Neutrino mass hierarchy: Normal hierarchy
Neutrino-less double beta decay
is restricted bym1 ✓12
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.140.5
0.6
0.7
0.8
0.9
1.0
m1!m3
sin2 2Θ 12
0.0 0.5 1.0 1.5 2.0 2.5 3.00
2
4
6
8
10
m1 !meV"
#m ee#!meV
"
|mee| =
�����
3X
i=1
miU2ei
�����
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- CP violation in lepton sectorM. Fukugita, Y. Kaneta, Y. S., M. Tanimoto and T. T. Yanagida, work in progress
Leptonic CP violation via Jarlskog invariant
0 Π2
Π 3 Π2
2Π0.20.30.40.50.60.70.8
∆CP
sin2 Θ23
0 Π2
Π 3 Π2
2Π0
Π2
Π
3 Π2
2Π
Σ !rad"
Τ$Σ!rad"
JCP = Im
⇥Ue1Uµ2U
⇤e2U
⇤µ1
⇤
= sin ✓23 cos ✓23 sin ✓12 cos ✓12 sin ✓13 cos ✓213 sin �CP
0.77⇡ . �CP . ⇡, ⇡ . �CP . 1.24⇡
0.40 . sin2 ✓23 . 0.47
C. Jarlskog, Phys. Rev. Lett. 55 (1985) 1039
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3. Summary
0 Π2
Π 3 Π2
2Π0.20.30.40.50.60.70.8
∆CP
sin2 Θ23
The large is given impact for us
We propose minimal texture which makes the connection between masses and mixing angles
The effective mass of the neutrino-less double beta decay
✓13
|mee| = 4 ⇠ 5 meV
Normal hierarchy
Predictions:
0.40 . sin2 ✓23 . 0.47
0.77⇡ . �CP . ⇡,
⇡ . �CP . 1.24⇡