Predictive leptogenesis from Minimal Lepton Flavour Violation

Predictive leptogenesis from Minimal Lepton Flavour Violation

Salvador Rosauro Alcaraz

Universidad Aut ´onoma de Madrid/ Instituto de F´ısica Te ´orica paper to appear in collab. with Luca Merlo

IX CPAN days, October 2017

Index

1 Introduction

2 MLFV

3 Leptogenesis

4 Numerical simulations

5 Conclusions

Introduction

Introduction

Flavour Problem and ν masses

Type-I Seesaw + Flavour symmetry→ Low-energy FCNC observables

Baryon asymmetry

η B = (6.11 ± 0.04) × 10 −10

Leptogenesis → High-energy process

Is leptogenesis possible within a flavour symmetry? Can we find a

relation with low-energy observables?

MLFV

Type-I Seesaw and flavour symmetries

L kinetic = ¯ ψ / Dψ − −−−−− Flavour →

symmetry

ψ = L L , e R , N R

G = U(3) L

× U(3) N

× U(3) e

G. D’Ambrosio et al., 0207036v2 S. Davidson & F. Palorini, 0607329v1 V. Cirigliano et al., 0507001 R. Alonso et al., 1103.5461v1

G can be decomposed as

G = U(1) Y × U(1) LN × U(1) R × G F , G F = SU(3) L

× SU(3) N

× SU(3) e

(1) Explicitly broken by

L Seesaw = − e ¯ L L Y e φe R − ν L ¯ L Y ν φN ˜ R − 1

2 2 ν µ LN N ¯ R c Y M N R + h.c. (2)

MLFV

Minimal Lepton Flavour Violation

MFV

The origin of flavour and CP violation in any BSM theory is the same than in the SM, Yukawa couplings → Λ F ∼ O(TeV )

MLFV → Y M , Y e & Y ν are taken to be sources of breaking

EFT approach, Y e,ν,M → spurion fields leaving L Seesaw formally

invariant under G F

MLFV

Minimal Lepton Flavour Violation

v Λ F µ LN

L eff (E < Λ F ) = L SM + L d=5 Seesaw + 1 Λ 2 F

X

i

c i O i d=6 (3)

Predictive MLFV context

Higher dimensional operators formally invariant under G F . Flavour structure of the spurions fully determined by low-energy observables, PMNS mixing matrix and active neutrino masses

Seesaw relation v 2

2µ LN Y ν Y ˆ M −1 Y ν T = U m ˆ ν U T

FCNC bilinears

Y ν Y ν †

MLFV

Minimal Lepton Flavour Violation

G F needs to be reduced → Two different scenarios EFCI

G F = SU(3) L

× O(3) N

× SU(3) e

× CP Y M = I

Y ν T = Y ν † → No CP violation in the lepton sector EFCII

G F = U(1) e

× SU(3) L

+N

× SU(3) e

Y ν = I unitary → Room for CP violation

EFCI and EFCII give different predictions on FCNC observables

D. Dinh et al., 1705.09284

Leptogenesis

Standard leptogenesis

M. Fukugita & T. Yanagida, Phys.Lett.B174 (1986)

N i −−−−−−→ L violating

decays L asymmetry −−−−−−→ Sphaleron

transitions B asymmetry

Final baryon asymmetry η B = 9.6 × 10 −3 X

i

i κ i (4)

Wash out factors K i ≡ Γ N

H(T = M i )

K i 1 → Strong wash out

(5)

Leptogenesis

Standard leptogenesis

L. Covi et al., 9605319v2

i ≡ Γ (N i → lφ ∗ ) − Γ N i → ¯ lφ

Γ (N i → lφ ∗ ) + Γ N i → ¯ lφ (6)

Tree level Self-energy Vertex

Leptogenesis will be possible

Im h

(λ † ν λ ν ) ij i

6= 0 for i 6= j

M i − M j 6= 0 for i 6= j

Leptogenesis

Leptogenesis in EFCI

V. Cirigliano et al., 0607068

Breaking of the RHN mass degeneracy M R = M R (0) + X

n

c n M R (n) , M R (0) ≡ µ LN I (7) Introduction of 3 high-energy CP violating phases

Y ν =

√ 2

v U m ˆ ν 1/2 RM R 1/2 −−−−→ O(3)

EFCI Y ν =

p 2µ LN

v U m ˆ ν 1/2 H (8)

Loss of the predictability on low-energy FCNC observables

Leptogenesis

Leptogenesis in EFCII

L. Merlo & S.R., to appear

e ≈ √

2m τ /v , ν ≈ 1, µ LN ∼ v 2 2 √

∆m 2 ∼ O(10 15 GeV ) (9) Breaking of the unitarity of Y ν

Y ν = I + c 1 Y M † Y M + c 2 Y e Y e † (10) In the RHN mass basis

λ ν = ˆ Y ν

I + c 1 Y ˆ M † Y ˆ M + c 2 Y ˆ ν † Y e Y e † Y ˆ ν

(11)

Leptogenesis

Leptogenesis in EFCII

From the seesaw relation v 2

2µ LN λ ν Y ˆ M −1 λ T ν = U m ˆ ν U T (12) and c i 1:

Y ˆ ν = U, Y ˆ M = v 2

2µ LN m ˆ −1 ν (13)

λ ν = U I + c 1 v 4

4µ 2 LN m ˆ ν −2 + c 2 U † Y e 2 U

!

(14)

Predictions on low-energy FCNC processes kept

Leptogenesis

0ν2β decay in EFCII

|m ee | =

c 2 13 c 12 2 m ˆ ν1 + c 13 2 s 12 2 m ˆ ν2 e iα

+ + s 13 2 m ˆ ν3 e i(α

−2δ)

(15) The CP violating phases δ, α 21 and α 31 appearing in |m ee | are those responsible for

leptogenesis

Leptogenesis ↔ 0ν2β decay

Numerical simulations

Numerical simulations

EFCII

G = U(1) e

× SU(3) L

+N

× SU(3) e

Simplification→ c 1 = c 2

Best-fit values from PDG 2016 for

∆m 2 21 , |∆m 2 |, δ, sin 2 θ 12 , sin 2 θ 23 , and sin 2 θ 13

λ ν = U I + c v 4

4µ 2 LN m ˆ ν −2 + cU † Y e 2 U

!

For different values of c < 1:

Constraints on parameter space by leptogenesis

Impact on 0ν2β decay

Numerical simulations

Leptogenesis preliminary results

c = 0.01

Leptogenesis not possible

Figure: NO

m lightest allowed ≈ [0.0051, 0.024] eV

Figure: IO

Numerical simulations

Leptogenesis preliminary results

c = 0.01

Dependence of η B on the Majorana phases

Figure: IO Figure: α

vs. α

for IO

Numerical simulations

Leptogenesis preliminary results

c = 0.015

m allowed lightest ≈ [0.15, 0.2] eV

Figure: NO

m lightest allowed ≈ [0.0051, 0.063] eV

Figure: IO

Numerical simulations

Leptogenesis preliminary results

c = 0.015

Numerical simulations

Leptogenesis preliminary results

c = 0.025

m allowed lightest ≈ [0.016, 0.2] eV

Figure: NO

m lightest allowed = [0.0051, 0.2] eV

Figure: IO

Numerical simulations

Leptogenesis preliminary results

c = 0.025 c = 0.1: Fine tuning

Numerical simulations

0ν2β decay

GERDA II bounds

|m ee | < [160, 290] meV (16)

c = 0.01 for IO

Numerical simulations

0ν2β decay

c = 0.015 for NO

Numerical simulations

0ν2β decay

c = 0.025 for IO

Conclusions

Conclusions

EFCI and EFCII give different predictions on FCNC observables Present indications on CP violation in the lepton sector favour the EFCII over EFCI

Leptogenesis in the EFCII model depends on 4 free parameters,

3 of which are low-energy parameters → m lightest , α 21 , α 31

The study of 0ν2β decay can test the predictions form the EFCII

model using the leptogenesis constraint

Conclusions

Thank you!