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, 𝜄 12 , 𝜄 23 , 𝜄 13 . - Recent measurements of not-so-small 𝜄 13 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 𝜀 𝐷𝑄 ~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)

Neutrino Mixing Matrix Neutrino Mixing parametrized by U PMNS              i 1 0 0 cos 0 sin e cos sin 0 13 13 12 12              U 0 cos sin  0 1 0  sin cos 0 P     MNS 23 23 12 12              i     0 sin cos sin e 0 cos 0 0 1   23 23 13 13 Dirac Phase : CP violation Majorana Phase : measurable in neutrino oscillations Neutrinoless double beta decay          4 ( ) J P ( ) P ( )     all measured

Leptonic CP violation Fundamental missing link that needs to be addressed in neutrino • experiments is to measure 𝜀 𝐸 , 𝜀 𝑁𝑏𝑘 and to explore LCPV. If non-trivial 𝜀 𝐸 , 𝜀 𝑁𝑏𝑘 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 𝜉 𝑆 (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

Minimal Seesaw Model (Frampton, Glashow, Yanagida, Phys. Lett. B 548, 119 (2002) - Only 2 heavy RH neutrinos are added to the SM 1 (    c L m N N ) M N Li Dij Rj Rj j Rj 2    ( 1 3; 1, 2 ) i j - a 𝜀 𝐸 , 𝑏𝑜𝑒 𝑏 𝜀 𝑁𝑏𝑘 exist in ν mixing matrix Very predictive model ! - one light neutrino mass is zero - Impose additional simple theoretical assumptions to reduce free parameters: 7

• From the seesaw mechanism, we get light neutrino mass matrix • Parametrizing 3x2 matrix 𝑛 𝐸 • Diagonalizing by PMNS mixing matrix • For normal hierarchy (NH), 𝑛 1 = 0, whereas 𝑛 3 = 0 for inverted hierarchy(IH)

• The following relation holds in general • 𝑃 is a 2x2 complex orthogonal matrix 𝑦 2 + 𝑧 2 = 1

• Introducing 1 zero texture in 𝑛 𝐸 (reflecing lepton flavor symmetry) 𝑐 𝑗 = 0 𝑏 𝑗 = 0 𝑁 1 𝑏 1 𝑁 2 𝑐 1 0 𝑁 2 𝑐 1 𝑁 1 𝑏 1 𝑁 2 𝑐 1 𝑁 1 𝑏 2 𝑁 2 𝑐 2 𝑁 1 𝑏 2 𝑁 2 𝑐 2 0 𝑁 2 𝑐 2 0 𝑁 2 𝑐 3 𝑁 11 𝑏 3 𝑁 2 𝑐 3 𝑁 1 𝑏 3 𝑁 2 𝑐 3 Case(c) Case(a) Case(b) 𝑁 1 𝑏 1 0 𝑁 1 𝑏 1 𝑁 2 𝑐 1 𝑁 1 𝑏 1 𝑁 2 𝑐 1 𝑁 1 𝑏 2 𝑁 2 𝑐 2 𝑁 1 𝑏 2 0 𝑁 1 𝑏 2 𝑁 2 𝑐 2 𝑁 1 𝑏 3 𝑁 2 𝑐 3 𝑁 1 𝑏 3 𝑁 2 𝑐 3 𝑁 1 𝑏 3 0 Case(f) Case(d) Case(e)

Leptogenesis  Generate L from the direct CP violation in RH neutrino decay • CP violation  L gets converted to B via EW anomaly: 𝑜 𝐶 −𝑜 𝜁 1 𝜃 𝐶 = 𝐶 ~κ 𝑜 𝛿 𝑕 ∗

For NH Case(a) 𝜁 1 ∝ sin 2(𝜀 𝐸 + 𝜀 𝑁𝑏𝑘 ) Case(b) 2 𝑑 23 2 sin 2𝜀 𝑁𝑏𝑘 − 2𝑑 12 𝑡 12 𝑑 23 𝑡 23 𝑡 13 sin(𝜀 𝐸 + 2𝜀 𝑁𝑏𝑘 ) 𝜁 1 ∝ 𝑑 12 2 𝑡 23 2 sin 2𝜀 𝑁𝑏𝑘 + 2𝑑 12 𝑡 12 𝑑 23 𝑡 23 𝑡 13 sin(𝜀 𝐸 + 2𝜀 𝑁𝑏𝑘 ) Case(c) 𝜁 1 ∝ 𝑑 12 For IH Case(a) 𝜁 1 ∝ sin 2(𝜀 𝑁𝑏𝑘 ) Case(b) 2 𝑑 23 2 sin 2𝜀 𝑁𝑏𝑘 − 2𝑑 12 𝑡 12 𝑑 23 𝑡 23 𝑡 13 sin(𝜀 𝐸 + 2𝜀 𝑁𝑏𝑘 ) 𝜁 1 ∝ 𝑡 12 2 𝑑 23 2 sin 2𝜀 𝑁𝑏𝑘 + 2𝑑 12 𝑡 12 𝑑 23 𝑡 23 𝑡 13 sin(𝜀 𝐸 + 2𝜀 𝑁𝑏𝑘 ) Case(c) 𝜁 1 ∝ 𝑑 12 • For 𝑁 2 ≫ 𝑁 1 , 𝜁 1 depends on 𝑁 1

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

𝜽 𝑪 vs. ( 𝜺 𝑬 + 𝜺 𝑵𝒃𝒌 ) for NH case (a) • 𝑁 1 = 10 8 GeV 𝑁 2 𝑁 1 = 10 4 • 𝜽 𝑪 +0.4 × 10 −9 𝜃 𝐶 = 6.5 −0.3 𝜺 = (𝜺 𝑬 + 𝜺 𝑵𝒃𝒌 )

• 𝑁 1 = 10 8 GeV 𝜽 𝑪 vs. 𝜺 𝑬 𝑁 2 • 𝑁 1 = 10 4 • 𝜀 𝑁𝑏𝑘 = 𝜌

• 𝑁 1 = 10 8 GeV 𝜽 𝑪 vs. 𝜺 𝑬 𝑁 2 • 𝑁 1 = 10 4 • 𝜀 𝑁𝑏𝑘 = 𝜌/2

• 𝑁 1 = 10 8 GeV 𝜽 𝑪 vs. 𝜺 𝑵𝒃𝒌 𝑁 2 • 𝑁 1 = 10 4 • 𝜀 𝐸 =1.5 𝜌 여기에 수식을 입력하십시오 . 𝜀 𝑁𝑏𝑘

Allowed region ( 𝑁 1 ( × 10 5 ) vs. 𝜀 𝐸 + 𝜀 𝑁𝑏𝑘 ) 𝑁 2 • 𝑁 1 = 10 4 • For NH case (a) +0.4 × 10 −9 𝜃 𝐶 = 6.5 −0.3 𝜀 𝐸 + 𝜀 𝑁𝑏𝑘

Allowed region ( 𝑁 1 (× 10 5 ) vs. 𝜀 𝐸 ) 𝑁 2 • 𝑁 1 = 10 4 • For NH case (b) 𝜀 𝑁𝑏𝑘

Allowed region ( 𝑁 1 (× 10 5 ) vs. 𝜀 𝐸 ) 𝑁 2 • 𝑁 1 = 10 4 • For NH case (c) 𝜀 𝑁𝑏𝑘

𝜽 𝑪 vs. 𝜺 𝑵𝒃𝒌 for IH case (a) • 𝑁 1 = 10 8 GeV 𝑁 2 𝑁 1 = 10 4 • 𝜽 𝑪 𝜺 𝑵𝒃𝒌

Allowed region ( 𝑁 1 (× 10 5 ) vs. 𝜀 𝑁𝑏𝑘 ) 𝑁 2 𝑁 1 = 10 4 • • For IH case (a) 𝜺 𝑵𝒃𝒌

Correlation to neutrinoless double beta decay 2 + 𝑛 2 𝑉 𝑓2 2 + 𝑛 3 𝑉 𝑓3 | 𝑛 𝜉 | = |𝑛 1 𝑉 𝑓1 2 𝑓 𝑗𝜀 𝑁𝑏𝑘 | • For NH, 𝑛 𝜉 depends on both 𝜀 𝐷𝑄 , 𝜀 𝑁𝑏𝑘 • For IH, 𝑛 𝜉 depends on 𝜀 𝑁𝑏𝑘 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 our 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.