CP violation and Leptogenesis in Minimal Seesaw Model Sin Kyu Kang - - PowerPoint PPT Presentation

CP violation and Leptogenesis in Minimal Seesaw Model

Sin Kyu Kang (Seoul-Tech) based on work in progress

Introduction

• Current situation of neutrino physics :
• We have determined three neutrino mixing angles, 𝜄12, 𝜄23, 𝜄13.
• Recent measurements of not-so-small 𝜄13 open up new window to

probe leptonic CPV.

• No compelling evidence for LCPV yet, but there is a fit to neutrino

data narrows down the allowed non-trivial values of Dirac-type CP phase 𝜀𝐷𝑄~1.5𝜌

Introduction

• Current situation of neutrino physics :
• Recent T2K results show -similar effects seen in NovA and

a hint for non-trivial CP phase SuperK

Averaged by Marrone (2016)



Dirac Phase : CP violation measurable in neutrino oscillations

13 13 12 12 23 23 12 12 23 23 13 13

1 cos sin cos sin cos sin 1 sin cos sin cos sin cos 1



                                  

i MNS i

e U P e

 

            Majorana Phase : Neutrinoless double beta decay 4 ( ) ( ) ( ) J P P

   

        

Neutrino Mixing Matrix

Neutrino Mixing parametrized by UPMNS

all measured

Leptonic CP violation

• Fundamental missing link that needs to be addressed in neutrino

experiments is to measure 𝜀𝐸, 𝜀𝑁𝑏𝑘 and to explore LCPV.

• If non-trivial 𝜀𝐸, 𝜀𝑁𝑏𝑘 are measured, what do they imply ?
• It is well known that the CPV in quark sector is not enough to explain

the measured matter-antimatter asymmetry in our Universe.

• Is the CPV in lepton sector responsible for the matter-antimatter asy. ?
• Are the CPV phases in ν mixing matrix directly responsible

for baryogenesis via leptogenesis ?

Leptonic CP violation

• Baryogenesis via leptogenesis can be realized in seesaw models.
• It is likely that the CPV phases in ν mixing matrix are not directly

responsible for leptogenesis in canonical seesaw with 3 heavy 𝜉𝑆

(Ellis, Hisano, Raidal, Shimiz,’01)

• The aim of this work is to show that the CPV phases in ν mixing

matrix can be directly responsible for leptogenesis in a minimal seesaw model.

Low energy ν experiments may give us opportunity to probe leptogenesis

7

Minimal Seesaw Model

(Frampton, Glashow, Yanagida,

• Phys. Lett. B 548, 119 (2002)
• Only 2 heavy RH neutrinos are added to the SM
• a 𝜀𝐸, 𝑏𝑜𝑒 𝑏 𝜀𝑁𝑏𝑘 exist in ν mixing matrix
• one light neutrino mass is zero

1 ( ) 1, 2 ( 1 3; ) 2

c Li Dij Rj Rj j Rj

L m N N M N j i      

Very predictive model !

• Impose additional simple theoretical assumptions to reduce free

parameters:

• From the seesaw mechanism, we get light neutrino mass matrix
• Diagonalizing by PMNS mixing matrix
• For normal hierarchy (NH), 𝑛1 = 0, whereas 𝑛3 = 0 for inverted hierarchy(IH)
• Parametrizing 3x2 matrix 𝑛𝐸

• The following relation holds in general
• 𝑃 is a 2x2 complex orthogonal matrix

𝑦2 + 𝑧2 = 1

• Introducing 1 zero texture in 𝑛𝐸

(reflecing lepton flavor symmetry)

𝑏𝑗 = 0 𝑐𝑗 = 0

𝑁1𝑏1 𝑁2𝑐1 𝑁2𝑐2 𝑁1𝑏3 𝑁2𝑐3 𝑁1𝑏1 𝑁2𝑐1 𝑁1𝑏2 𝑁2𝑐2 𝑁1𝑏3 𝑁1𝑏1 𝑁1𝑏2 𝑁2𝑐2 𝑁1𝑏3 𝑁2𝑐3 𝑁1𝑏1 𝑁2𝑐1 𝑁1𝑏2 𝑁2𝑐2 𝑁2𝑐3 𝑁2𝑐1 𝑁1𝑏2 𝑁2𝑐2 𝑁11𝑏3 𝑁2𝑐3 𝑁1𝑏1 𝑁2𝑐1 𝑁1𝑏2 𝑁1𝑏3 𝑁2𝑐3

Case(a) Case(b) Case(c) Case(d) Case(e) Case(f)

• Generate L from the direct CP violation in RH neutrino decay
• CP violation
• L gets converted to B via EW anomaly:

Leptogenesis

𝜃𝐶=

𝑜𝐶−𝑜

𝐶

𝑜𝛿

~κ

𝜁1 𝑕∗

Case(a) Case(b) Case(c) 𝜁1 ∝ sin 2(𝜀𝐸 + 𝜀𝑁𝑏𝑘) 𝜁1 ∝ 𝑑12

2 𝑑23 2 sin 2𝜀𝑁𝑏𝑘 − 2𝑑12𝑡12𝑑23𝑡23𝑡13 sin(𝜀𝐸 + 2𝜀𝑁𝑏𝑘)

𝜁1 ∝ 𝑑12

2 𝑡23 2 sin 2𝜀𝑁𝑏𝑘 + 2𝑑12𝑡12𝑑23𝑡23𝑡13 sin(𝜀𝐸 + 2𝜀𝑁𝑏𝑘)

For NH For IH

Case(a) Case(b) Case(c) 𝜁1 ∝ sin 2(𝜀𝑁𝑏𝑘) 𝜁1 ∝ 𝑡12

2 𝑑23 2 sin 2𝜀𝑁𝑏𝑘 − 2𝑑12𝑡12𝑑23𝑡23𝑡13 sin(𝜀𝐸 + 2𝜀𝑁𝑏𝑘)

𝜁1 ∝ 𝑑12

2 𝑑23 2 sin 2𝜀𝑁𝑏𝑘 + 2𝑑12𝑡12𝑑23𝑡23𝑡13 sin(𝜀𝐸 + 2𝜀𝑁𝑏𝑘)

• For 𝑁2 ≫ 𝑁1, 𝜁1 depends on 𝑁1

Numerical Results

(Gonsalez-Garcia, Maltoni, Schwetz, arXiv:1512.06856)

𝜽𝑪 vs. (𝜺𝑬 + 𝜺𝑵𝒃𝒌)

for NH case (a)

• 𝑁1 = 108 GeV
• 𝑁2

𝑁1 = 104

𝜃𝐶 = 6.5−0.3

+0.4 × 10−9

𝜽𝑪 𝜺 = (𝜺𝑬 + 𝜺𝑵𝒃𝒌)

𝜽𝑪 vs. 𝜺𝑬

• 𝑁1 = 108 GeV
• 𝑁2

𝑁1 = 104

• 𝜀𝑁𝑏𝑘=𝜌

𝜽𝑪 vs. 𝜺𝑬

• 𝑁1 = 108 GeV
• 𝑁2

𝑁1 = 104

• 𝜀𝑁𝑏𝑘=𝜌/2

𝜽𝑪 vs. 𝜺𝑵𝒃𝒌

• 𝑁1 = 108 GeV
• 𝑁2

𝑁1 = 104

• 𝜀𝐸=1.5𝜌

여기에 수식을 입력하십시오.

𝜀𝑁𝑏𝑘

Allowed region (𝑁1(× 105) vs. 𝜀𝐸 + 𝜀𝑁𝑏𝑘)

• 𝑁2

𝑁1 = 104

• For NH case (a)

𝜀𝐸 + 𝜀𝑁𝑏𝑘

𝜃𝐶 = 6.5−0.3

+0.4 × 10−9

Allowed region (𝑁1(× 105) vs. 𝜀𝐸)

• 𝑁2

𝑁1 = 104

• For NH case (b)

𝜀𝑁𝑏𝑘

• 𝑁2

𝑁1 = 104

• For NH case (c)

𝜀𝑁𝑏𝑘

Allowed region (𝑁1(× 105) vs. 𝜀𝐸)

𝜽𝑪 vs. 𝜺𝑵𝒃𝒌

for IH case (a)

• 𝑁1 = 108 GeV
• 𝑁2

𝑁1 = 104

𝜺𝑵𝒃𝒌

𝜽𝑪

Allowed region (𝑁1(× 105) vs. 𝜀𝑁𝑏𝑘)

• 𝑁2

𝑁1 = 104

• For IH case (a)

𝜺𝑵𝒃𝒌

Correlation to neutrinoless double beta decay

| 𝑛𝜉 | = |𝑛1𝑉𝑓1

2 + 𝑛2𝑉𝑓2 2 + 𝑛3𝑉𝑓3 2𝑓𝑗𝜀𝑁𝑏𝑘|

• For NH, 𝑛𝜉

depends on both 𝜀𝐷𝑄, 𝜀𝑁𝑏𝑘

• For IH, 𝑛𝜉

depends on 𝜀𝑁𝑏𝑘 but not so sensitive to it.

Conclusion

• Establishing LCPV is one of the most challenging tasks in future

neutrino experiments.

• Low energy LCPV may or may not play an essential role in existing
• ur universe.
• While leptogenesis in seesaw model with 3 RH vs is not related with

low E LCPV, we find that low energy LCP phases may be responsible for leptogenesis in a minimal seesaw model.