Predictions for the neutrino parameters in the minimal model - - PowerPoint PPT Presentation

浅井 健⼈ (東京⼤学)

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 1/48

Predictions for the neutrino parameters in the minimal model extended by general lepton flavor dependent U(1) gauge symmetries

素粒⼦物理学の進展 2019

2019年7⽉31⽇ @ 基礎物理学研究所

Based on KA (arXiv : 1907.04042 [hep-ph])

Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Introduction

Extension of Standard Model

• Neutrino mass

Seesaw mechanism

• Leptogenesis

Some motivations

Matter contents

SM fields + 3 right-handed neutrinos

• Introduction
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 2/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Introduction

Extension of Standard Model

• Introduction

Gauge sector

: combination of , and

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 3/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Introduction

Extension of Standard Model

• Introduction

Gauge sector

: combination of , and

Anomaly cancellation condition

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 4/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Introduction

Extension of Standard Model

• Muon g-2
• Dark Matter

Some motivations

• S. Baek, N. G. Deshpande, X. G. He, and P. Ko (2001);
• E. Ma, D. P. Roy, and S. Roy (2002); etc…
• Introduction

J.-C. Park, J. Kim, and S. C. Park (2016);

• S. Baek (2016); etc…

Gauge sector

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 5/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Introduction

Neutrino Mass Matrix Structure

Seesaw mechanism For Block diagonal Neutrino mixing

Matter contents

SM fields + 3 right-handed neutrinos

• Introduction
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 6/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Introduction

Neutrino Mixing Angles

Seesaw mechanism

Matter contents

SM fields + 3 right-handed neutrinos PMNS matrix

Neutrino experiments

(ex: Super-Kamiokande)

• Introduction

For

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 7/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Introduction

Neutrino Mixing Angles Matter contents

SM fields + 3 right-handed neutrinos

• Introduction

Minimal models can not explain the neutrino mixing as long as gauge symm. is conserved

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 8/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Introduction

Matter contents

SM fields + 3 right-handed neutrinos + U(1) breaking scalar Seesaw mechanism

(singlet) (doublet)

• r

Neutrino Mass Matrix Structure

• Introduction
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 9/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Introduction

Matter contents

SM fields + 3 right-handed neutrinos + U(1) breaking scalar Seesaw mechanism

(singlet)

two-zero minor structure Neutrino mixing &

Neutrino Mass Matrix Structure

Elements where zeros appear depend on

Minimal Gauged U(1)'()'* Models Driven into a Corner

• Introduction

For

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 10/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Introduction

Matter contents

SM fields + 3 right-handed neutrinos + U(1) breaking scalar Seesaw mechanism

(singlet)

Neutrino Mass Matrix Structure

two-zero minor structure

Dirac CP Majorana CP Mixing angle Squared mass difference

Point

KA, K. Hamaguchi and N. Nagata, Eur. Phys. J. C77 (2017) 763; KA, K. Hamaguchi, N. Nagata, S.-Y. Tseng and K. Tsumura,

• Phys. Rev. D99 (2019) 055029.

Minimal Gauged U(1)'()'* Models Driven into a Corner

• Introduction

For

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 11/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Introduction

Matter contents

SM fields + 3 right-handed neutrinos + U(1) breaking scalar Seesaw mechanism For

(doublet)

Neutrino Mass Matrix Structure

two-zero texture structure

Dirac CP Majorana CP Mixing angle Squared mass difference

Point

• Introduction

KA, K. Hamaguchi, N. Nagata, S.-Y. Tseng and K. Tsumura,

• Phys. Rev. D99 (2019) 055029.
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 12/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Introduction

Abstract of this talk

Extra U(1) gauge symmetry 2 zero minor structure

neutrino mass CP phase Effective Majorana neutrino mass

as functions of

Leptogenesis

Dirac Yukawa couplings sign of baryon asymmetry

• Introduction
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 13/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Outline

1, Introduction 2, Model 3, Mass Matrix 4, Leptogenesis 5, Conclusion

Two models (+singlet or +doublet scalar )

Analysis : two-zero minor (texture) condition Result : Dirac CP phase and sum of neutrino masses Analysis : seesaw formula Result : sign of the asymmetry parameter

• Introduction
• Leptogenesis
• Mass matrix
• Appendix
• Model
• Conclusion
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 14/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Model

Minimal Gauged U(1)%’ Models

Charge assignment Lagrangian

Charge assignment Lagrangian

Singlet Doublet

• Model
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 15/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Model

Mass matrix

Charge assignment Lagrangian

・Dirac mass ・Majorana mass ・ Charged lepton mass

Singlet Doublet

• Model

Minimal Gauged U(1)%’ Models

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 16/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Model

Charge assignment Lagrangian

Charge assignment Lagrangian

Singlet Doublet

• Model

Minimal Gauged U(1)%’ Models

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 17/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Model

Charge assignment Lagrangian

Mass matrix ・Dirac mass ・ Charged lepton mass ・Majorana mass

Singlet Doublet

Lepton flavor violation Enough small Assumption

• Model

Minimal Gauged U(1)%’ Models

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 18/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Mass matrix

Two-zero minor condition

Singlet Two complex equations in terms of Seesaw mechanism PMNS matirx

• Mass matrix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 19/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Two-zero texture condition

Two complex equations in terms of Doublet

Mass matrix

• Mass matrix

Seesaw mechanism PMNS matirx

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 20/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Flow of analysis

Two complex equations in terms of neutrino mass CP phase Effective Majorana neutrino mass as functions of Point Leptogenesis Asymmetry parameter

Neutrino oscillation parameter

Neutrino Dirac Yukawa coupling

Mass matrix

• Mass matrix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 21/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Two zero minor condition

Neutrino mass ratios can be obtained as functions

• f the Dirac CP phase

Mass matrix

• Mass matrix

Two complex equations

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 22/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Two zero minor condition

CP phase and neutrino masses can be obtained as functuions of the neutrino oscillation parameters

Mass matrix

• Mass matrix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 23/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Mass matrix

• Mass matrix

Notice !

The following discussion is applicable to 1, the other U(1) lepton flavor symmetries

The methods of analysis are same but the structures

• f the neutrino mass matrices are different

2, wide breaking scale

scale

Muon g-2 Leptogenesis

scale

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 24/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

5 Models

Mass matrix

• Mass matrix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 25/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

5 Models

Mass matrix

• Mass matrix

Two-zero minor Two-zero texture

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 26/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

5 Models

Mass matrix

• Mass matrix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 27/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

5 Models

Mass matrix

• Mass matrix

Two complex equations have no solution Normal Inverted

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 28/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

5 Models

Mass matrix

• Mass matrix

Two complex equations have no solution below EW scale ruled out by experiments Normal Inverted

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 29/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

5 Models

Mass matrix

• Mass matrix

Two complex equations have no solution below EW scale ruled out by experiments Prediction values for neutrino mass conflict with Planck limit

KA, K. Hamaguchi, N. Nagata, S.-Y. Tseng and K. Tsumura, Phys. Rev. D99 (2019) 055029.

Normal Inverted

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 30/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Sum of neutrino masses

Mass matrix

• Mass matrix

Normal Inverted Normal Inverted These cases are excluded by Planck limit

Planck limit

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 31/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Sum of neutrino masses

Mass matrix

• Mass matrix

Planck limit

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 32/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Sum of neutrino masses

Mass matrix

• Mass matrix

Planck limit dark (light) red band : uncertainty coming from the 1σ (2σ) errors in the parameters

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 33/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

• K. Asai (Univ. of Tokyo)

34/48

Sum of neutrino masses

TUHEP Seminar @ Tohoku Univ. (May 9) Minimal Gauged U(1)'()'* Models Driven into a Corner

Mass matrix

• Mass matrix

Planck limit

𝐃𝐒 case has a strong tension with Planck linit

Dirac CP phase

Mass matrix

• Mass matrix

dark (light) green band : 1σ (3σ) favored region of

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 35/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Effective Majorana neutrino mass

uncertainty of the nuclear matrix element for The strongest bound on

Mass matrix

• Mass matrix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 36/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Effective Majorana neutrino mass

Mass matrix

• Mass matrix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 37/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Neutrinoless double beta decay processes are observed 𝐄𝟐

𝐒, 𝐄𝟑 𝐒 cases are rejected

• In this work, minimal models are analyzed and
• nly the 3 cases with a scalar singlet survive experimental constraints.
• By analyzing two-zero minor condition，we found the prediction,

which is independent of the U(1) breaking scale, for the CP phases, the neutrino masses, and the effective Majorana neutrino mass.

Mass matrix

• Mass matrix

Summary

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 38/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Leptogenesis

• Leptogenesis

Parameters

Parameters in this model in Lagranginan from experiments Dirac Yukawa coupling Majorana mass : phase

Mixing angle Squared mass difference Lightest neutrino mass CP phase

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 39/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Parameters in this model in Lagranginan from experiments Dirac Yukawa coupling Majorana mass : phase

Mixing angle Squared mass difference Lightest neutrino mass CP phase Two zero minor condition

Leptogenesis

• Leptogenesis

Parameters

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 40/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Parameters in this model in Lagranginan from experiments Dirac Yukawa coupling

Mixing angle Squared mass difference

Majorana mass : phase

Leptogenesis

• Leptogenesis

Parameters

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 41/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Parameters in this model in Lagranginan from experiments Majorana mass : phase

Mixing angle Squared mass difference Lightest neutrino mass CP phase

Dirac Yukawa coupling Free parameters

Leptogenesis

• Leptogenesis

Parameters

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 42/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Baryon asymmetry

Sign of baryon asymmetry Asymmetry parameter Yukawa couplings

Sign of the asymmetry parameter depends on 𝜄, 𝜚

Leptogenesis

• Leptogenesis
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 43/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Sign of baryon asymmetry Observed baryon asymmetry of the universe Relation between baryon and lepton generated Sign of asymmetry parameter is negative

Minimal Gauged U(1)'()'* Models Driven into a Corner

Baryon asymmetry

Leptogenesis

• Leptogenesis
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 44/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Results

Sign of baryon asymmetry

Leptogenesis

• Leptogenesis
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 45/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Results

Sign of baryon asymmetry

Leptogenesis

• Leptogenesis
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 46/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Asymmetry parameter 𝜗5 can be negative 𝜗5 < 0 in the almost all parameter in the 𝐃𝐒 and 𝐄𝟐

𝐒 cases

Results

Size of baryon asymmetry

Leptogenesis

• Leptogenesis
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 47/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models π 4 π 2 2 4 6 8 10

ϕ

• ϵ1/λ2 × 105

tanθ=15 tanθ=1.5 tanθ=0.5 tanθ=1

π 4 π 2 2 4 6 8 10

ϕ

• ϵ1/λ2 × 104

tanθ=15 tanθ=1.5 tanθ=0.5 tanθ=1

π 4 π 2 2 4 6 8 10

ϕ

• ϵ1/λ2 × 105

tanθ=15 tanθ=1.5 tanθ=0.5 tanθ=1

Results

Leptogenesis

• Leptogenesis
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 47/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Non-thermal leptogenesis Shih-Yenʼs poster (Today 15:45~)

Conclusion

• Conclusion
• Only 𝐃𝐒, 𝐄𝟐

𝐒 and 𝐄𝟑 𝐒 cases with a singlet scalar satisfy two-zero minor

condition and are consistent with the neutrino oscillation data.

• By analyzing two-zero minor condition，we found the prediction,

which is independent of the U(1)89 breaking scale, for the CP phases, the neutrino masses, and the effective Majorana neutrino mass.

• We found that, in the 𝐃𝐒 and 𝐄𝟐

𝐒 cases, the correct sign of the baryon

asymmetry can be obtained, and it is possible that enough large baryon asymmetry can be realized.

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 48/48 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Muon g-2

Minimal Gauged U(1)'()'* Models Driven into a Corner

Appendix

： Landé g factor ： muon spin ： Bohr magneton Anomalous magnetic moment

Interaction between magnetic moment and magnetic field

• K. Hagiwara, R. Liao, A. D. Martin, D. Nomura, and T. Teubner (2011)
• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 49/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Muon g-2

Minimal Gauged U(1)'()'* Models Driven into a Corner

Appendix

Anomalous magnetic moment

Interaction between magnetic moment and magnetic field

• K. Hagiwara, R. Liao, A. D. Martin, D. Nomura, and T. Teubner (2011)

Classical level + Quantum corrections : Quantum corrections

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 50/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

• T. Araki, S. Hosino, T. Ota, J. Sato,

and T.Shimomura (2017)

• K. Hagiwara, R. Liao, A. D. Martin, D. Nomura, and T. Teubner (2011)

Muon g-2

Zʼboson contributes to muon g-2

Appendix

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 51/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Appendix

Neutrinoless Trident Production

• W. Altmannshofer, S. Gori, M. Pospelov,

and I. Yavin (2014)

0.01 0.1 1 10 102 103 10-3 0.01 0.1 1

m Z ' HGeVL g'

CCFR Hg-2Lm ±2s ZÆ4mûLHC

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 52/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Appendix

Neutrinoless Trident Production

• W. Altmannshofer, S. Gori, M. Pospelov,

and I. Yavin (2014)

0.01 0.03 0.1 0.3 1 3 3¥10-4 10-3 3¥10-3 0.01

m Z ' HGeVL g'

30% 1 % CCFR Hg-2L

m

±2s CHARM-II

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 53/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Appendix

Neutrinoless Trident Production

• W. Altmannshofer, S. Gori, M. Pospelov,

and I. Yavin (2014)

0.01 0.03 0.1 0.3 1 3 3¥10-4 10-3 3¥10-3 0.01

m Z ' HGeVL g'

30% 1 % CCFR Hg-2L

m

±2s CHARM-II

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 54/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Appendix

𝐶𝐵𝐶𝐵𝑆 experiment

BABAR, Phys. Rev. D94, 011102 (2016)

(GeV)

Z'

m

• 1

10 1 10 UL g'

• 3

10

• 2

10

• 1

10 Trident Borexino

g-2 favored

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 55/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Appendix

Neutrino-electron scattering

• S. Bilmis, I. Turan, T. M. Aliev, M.

Daniz, L. Singh, and H. T. Wong (2015) (MeV)

A'

M

• 3

10

• 2

10

• 1

10 1 10

2

10

3

10

4

10

B-L

g

• 7

10

• 6

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

10

CsI HPGe NPCGe

• e

µ

ν CHARM II

• e

µ

ν CHARM II LSND Borexino Gemma

Kinetic mixing contributes to process

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 56/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Scalar doublet VEVs in the doublet cases

Doublet Scalar doubelt VEVs

• symm. breaking scale
• symm. breaking scale in the doublet cases

should be below the EW scale

Appendix

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 57/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Neutrino Trident Production

Neutrino Trident Production

the production of a 𝜈>𝜈) pair from the scattering

• f a muon- neutrino with heavy nuclei

Sensitive to light 𝑎′ coupled with muon

Appendix

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 58/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Neutrino Trident Production

Neutrino Trident Production

the production of a 𝜈>𝜈) pair from the scattering

• f a muon- neutrino with heavy nuclei

Sensitive to light 𝑎′ coupled with muon

0.01 0.1 1 10 102 103 10-3 0.01 0.1 1

m Z ' HGeVL g'

CCFR Hg-2Lm ±2s ZÆ4mûLHC

𝑎′ is lighter than tauon :

Appendix

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 59/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

The minimal gauged model

Appendix

• Appendix
• M. Bauer, P. Foldenauer and J. Jaeckel, JHEP 1807 (2018) 094

◯ Constraints on

The VEV of Φ5 (𝑤5) breaks not only U(1)%9 but also SU(2)'

𝑤5 should be lower than the electroweak scale(𝑤5 ≲ 100 GeV)

• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 60/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Lepton Flavor Violation

Doublet 𝑎′ current Lepton Flavor Violation For simplisity

Appendix

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 61/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Lepton Flavor Violation

Doublet 𝑎′ current Lepton Flavor Violation For simplisity

diagonalizing

Appendix

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 62/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Lepton Flavor Violation

Decay width ARGUS limit

ARGUS collaboration (1995)

Limit on the mixing angle 𝜄'

• r

diagonal

Appendix

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 63/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Lepton Flavor Violation

Other experimental limits

○ Limits on 𝑧GH ○ Limits on 𝑧IG for

a) K. Hayasaka et al (1995) b) BaBar Collaboration (2010) c) A. Jodidio et al (1986) d) TWIST Collaboration (2015) e) MEG Collaboration (2016) a) b) c) d) e)

Charged lepton-flavor mixing is extremely small

(No charged lepton-flavor mixing)

Appendix

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 64/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Appendix

Minimal Gauged U(1)'()'* Models

Charge assignment charge of Only component in can be non-zero

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 65/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Appendix

Neutrino oscillation parameters

NuFIT v4.0 result with the Super-Kamiokande atmospheric data

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 66/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Appendix

PMNS matrix PMNS matrix : lepton version of the CKM matrix

PMNS CKM

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 67/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Appendix

Quantum correction to neutrino mass matrix The two-zero minor neutrino-mass structure in our model is robust against quantum corrections

𝑉(1)'K)'L symmetry breaking scale ≫ electroweak scale Large quantum corrections break two zero minor structure

• f ?

Result

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 68/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Appendix

Quantum correction to neutrino mass matrix The right-handed neutrinos are integrated out to give the following dimension-five effective operator:

@ right-handed neutrino mass scale

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 69/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Appendix

Quantum correction to neutrino mass matrix

gauge coupling up-type, down-type, and charged- lepton Yukawa matrices Higgs quartic coupling

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 70/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Appendix

Quantum correction to neutrino mass matrix

where : initial scale : diagonal : diagonal

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 71/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Appendix

Quantum correction to neutrino mass matrix

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 72/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models

Appendix

Neutrinoless double beta decay

Decay half time

Phase space factor Nuclear matrix element Effective Majorana mass

• Appendix
• K. Asai (Univ. of Tokyo)

PPP2019 @ YITP (July 31) 73/73 Predictions for the neutrino parameters in the minimal gauged U(1)%& models