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

1

2nd Sep. 2016

Collaboration:

Morimitsu Tanimoto (Niigata U.), Tsutomu Yanagida (Kavli IPMU)

Masataka Fukugita (Kavli IPMU), Yuya Kaneta (Niigata U.),

2

- NOvA experiment @Neutrino 2016

1. Introduction

2. Minimal texture and CP violation

3. Summary

- Neutrino oscillation and lepton mixing

3

Plan of my talk

4

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

5

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

6

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

7

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

8

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 ✓

12

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

9

- 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

10

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

4

q�m2

sol

�m2

atm

' 0.416 ' O(p�) ) sin2 ✓23

q�m2

sol

�m2

atm

' 0.173 ' �p2

) sin ✓13

11

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

12

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

13

- 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

14

- 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 ✓

13

' (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

15

- 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

�����

16

- 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

17

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⇡