juraj klari´c (tu m...

Introduction Testing the seesaw Testing Leptogenesis Conclusions

Testing the low scale seesaw and leptogenesis

Juraj Klaric (TU Munchen)based on 1606.6690 and 1609.09069 with Marco Drewes, Bjorn Garbrecht and Dario Gueter

Neutrinos in Cosmology, in Astro- Particle- and Nuclear physics

EMFCSC, Erice, Sicily, 17. September 2017

Juraj Klaric (TUM) EMFCSCErice 2017 1/23


Some of the missing pieces of the standard model:

BAU baryon asymmetry of the universe

WMAP, Planck and Big bangnucleosynthesis:

nB/nγ = 6.05(7)× 10−10

Neutrino massesNobel prize 2015Kajita, McDonald

Is there a way to explain both?



Standard Model

left

rightu

up

2.3 MeV

left

rightd

down

4.8 MeV

left

righte

electron

511 keV

left νe

e neutrino

< 2 eV

left

rightc

charm

1.28 GeV

left

rights

strange

95 MeV

left

right

µmuon

105.7 MeV

left νµ

µ neutrino

< 190 keVleft

rightttop

173.2 GeV

left

rightb

bottom

4.7 GeV

left

rightτ

tau

1.777 GeV

left ντ

τ neutrino

< 18.2 MeV

W±80.4 GeV

Z91.2 GeV

γphoton

ggluon

HHiggs

125.1 GeV

N1 right N2 right N3 right

quarksleptons

I II III



BAU baryon asymmetry of the universe

WMAP, Planck and Big bangnucleosynthesis:

nB/nγ = 6.05(7)× 10−10

LEPTOGENESIS

Neutrino massesNobel prize 2015Kajita, McDonald

SEE-SAW MECHANISM

mν = −v2Y †M−1M Y ∗



Seesaw Mechanism

Dirac Mass mD = vY †

Right handed neutrino (RHN) Majorana mass MM

L ⊃ 12

(νLN

)(0 mD

mTD MM

)(νL N

)

Active neutrino masses

mν = −mDM−1M mT

D

Mixing with RHN

|Uai|2 =∣∣∣(mDM

−1M

)ai

∣∣∣2



Constraints on RHN parameters

Direct constraints - past experimentsSeesaw constraints - neutrino oscillation dataradiatively corrected Casas-Ibarra parametrization[Lopez-Pavon/Molinaro/Petcov 1506.05296]

Cosmological constraints - BBN τN < 0.1sIndirect constraints

neutrinoless double β decaylepton universalityCKM universalityelectroweak precision dataLFV in rare lepton decays:

µ → eγτ → eγτ → µγ



Direct constraints

[Plot from arXiv:1502.00477]



Seesaw and BBN constraints

0.5 1 5 10 5010

-14

10-12

10-10

10-8

10-6

10-4

M [GeV]

U2

seesaw

BBN



Constraints on flavour patterns: Inverted hierarchy

0. 0.2 0.4 0.6 0.8 1.

0.

0.2

0.4

0.6

0.8

1.0.

0.2

0.4

0.6

0.8

1.

Ue2/U

2

Uμ 2/U

2

Uτ

2 /U2

sin2θ23 = 0.576

sin2θ23 = 0.45

δ = 277°

[Drewes/Garbrecht/Gueter/JK 1609.09069]



Global constraints: Inverted hierarchy

0.5 1 5 10 5010-14

10-12

10-10

10-8

10-6

10-4

M [GeV]

U2

global constraints



Global constraints: Inverted hierarchy

0.5 1 5 10 5010-14

10-12

10-10

10-8

10-6

10-4

M [GeV]

U2

global constraints

LEPTOGENESIS?



Leptogenesis via Neutrino Oscillations

SM Thermal Bath

CP - even

RHN states

Vanishing initial

abundance

CP - odd

RHN states

Oscillations

((((((hhhhhhSM Lepton Number

��ZZLe ��ZZLµ ��ZZLτ

��XXXConserved Generalized Lepton Number

Baryon Number

Asymmetry

0.

2.× 10-3

nu

mb

er

de

nsi

tyo

fR

HN

-1.× 10-4

0.

1.× 10-4

sou

rce

-3.× 10-9

2.× 10-9

lep

ton

fla

vo

ur

asy

mm

etr

y

10-12

10-11

10-10

|YB|

10-2 10-1 100

z=TEW /T



Goals of this work:

derivation of the density matrix equations from firstprinciples [Drewes/Garbrecht/Gueter/JK 1606.06690]

use the more recent calculations of rates[Anisimov/Besak/Bodeker 1012.3784] [Garbrecht/Glowna/Schwaller 1303.5498]

inclusion of spectator effects [Barbieri/Creminelli/Strumia/Tetradis

hep-ph/9911315] [Garbrecht/Schwaller 1404.2915]

analyitical approximations for different regimes[Drewes/Garbrecht/Gueter/JK 1606.06690]

explore parameter space/ phenomenologicalimplications [Hernandez/Kekic/Lopez-Pavon/Racker/Salvado 1606.06719]


violation of generalized lepton number [Hambye/Teresi

1606.00017] [Eijima/Shaposhnikov 1703.06085] [Laine/Ghiglieri 1703.06087]

Schwinger-

Dyson

Equations

Quantum

Boltzmann-like

kinetic

equations

Rate equations

for number

densities



Evolution Equations

RHN density matrix

dndz = − i

2 [H,n]− 12 {Γ, n− n

eq} − Γq`

Active lepton equations

dq`dz = S`(n)

T−Wq` + W qN

Density matrix of theRHNn =

(n11 n12n21 n22

)Effective HamiltonianH of the RHN ∼M2

Production rateΓ ∼ Y 2T

Source term S` of theactive neutrinosWashout term W



Evolution Equations

RHN density matrix

dndz = − i

2 [H,n]− 12 {Γ, n− n

eq} − Γq`

Active lepton equations

dq`dz = S`(n)

T−Wq` + W qN

Temperature (time) scales

Tosc = 3√Tcom

(M2

11 −M222)

Teq = TcomγavTr(Y Y †

)

Possible to solvenumericallyApproximationsneeded for parameterscans



Temperature scales and observables

ΔM 2/M 2

=10 -4, Tosc=T

eq

Tosc<<Teq

Tosc>>Teq

10-11

10-10

10-9

10-8

10-7

10-6

|U 2

10-1 100 101 102

M [GeV ]




Oscillatory regime: Tosc � Teq (small mixing angles)

oscillations begin longbefore relaxation toequillibriumalmost all lepton flavourasymmetry produced duringfirst few oscillationslepton number asymmetryproduced only throughflavour asymmetricwashout


0.

2.× 10-3

nu

mb

er

de

nsi

tyo

fR

HN

-1.× 10-4

0.

1.× 10-4

sou

rce

-3.× 10-9

2.× 10-9

lep

ton

fla

vo

ur

asy

mm

etr

y

10-12

10-11

10-10

|YB|

10-2 10-1 100

z=TEW /T



Temperature scales and observables

ΔM 2/M 2

=10 -4, Tosc=T

eq

ΔM 2/M 2

=10 -8, Tosc=T

eq

Tosc<<Teq

Tosc>>Teq

10-11

10-10

10-9

10-8

10-7

10-6

|U 2

10-1 100 101 102

M [GeV ]




Overdamped regime: Tosc � Teq (large mixing angles)

naively for Tosc < Teq,already in equilibriumrequirement of reproducingthe neutrino masses onlyallows one interactioneigenstate to equilibratemixing between interactioneigenstates → equilibrationapproximate B − L canpostpone the production ofBAU, preventing too muchwashout


0.

2.× 10-3

nu

mb

er

de

nsi

tyo

fR

HN

-1.× 10-5

0.

1.× 10-5

sou

rce

-3.× 10-9

0.

3.× 10-9

lep

ton

fla

vo

ur

asy

mm

etr

y

10-11

10-10

|YB|

10-3 10-2 10-1 100

z=TEW /T



Results: Inverted hierarchy

0.5 1 5 10 50

10-13

10-11

10-9

10-7

10-5

M [GeV]

U2

SHiPLBNE

FCC-ee(Z)

CEPC

ILC

BAU (upper bound)

BAU (lower bound)

disfavoured by global constraints

[Drewes/Garbrecht/Gueter/JK 1609.09069]Juraj Klaric (TUM) EMFCSCErice 2017 18/23


Flavour patterns from leptogenesis: Inverted hierarchy

large mixing angles require aflavour asymmetricwashout, which correspondsto a flavour asymmetricmixingtogether with seesawconstraints this imposesconstraints on the mixingpatterns for large mixingangles

0. 0.2 0.4 0.6 0.8 1.0.

0.2

0.4

0.6

0.8

1.0.

0.2

0.4

0.6

0.8

1.

Ue2/U2

Uμ 2/U

2

Uτ

2 /U2

Log10(U2)

-9.0

-8.8

-8.6

-8.4

-8.2

-8.0

-7.8

-7.6

M = 30 GeV




Leptogenesis and neutrinoless double β decay

mmin → 0

[Bilenky 1203.5250]



Leptogenesis and neutrinoless double β decay

[Eijima/Drewes 1606.06221,

Hernandez/Kekic/Lopez-Pavon/Salvado 1606.06719]

RHN can contribute to mββ

large mass splitting isrequired to have anobservable effect (not alwayscompatible withleptogenesis)some leptogenesis scenarioscan already be excluded bycurrent results



Full Testability?

full testability requires a complete determination of the RHNparametersin principle possible from a measurement of all mixing anglesand massesleptogenesis requires degenerate masses - hard to resolve inexperimentsremaining parameters could be probed by:

neutrinoless double β decay requires large ∆M and U2

[Eijima/Drewes 1606.06221,Hernandez/Kekic/Lopez-Pavon/Salvado 1606.06719]

CP violation requires ∆M comparable to the decay width

lepton number violation requires ∆M comparable to the decay width



Conclusions

adding GeV-scale RHNs to the standard model can explainboth the observed neutrino masses and the BAUthe seesaw mechanism gives constraints on RHN mixingpatterns (stronger if δ is measured!)testable leptogenesis within reach offuture experiments (SHiP,LBNE , FCC, ILC, CEPC)large mixing angles + leptogenesis → even strongerpredictions on the flavour patternswhile complete determination of the RHN parameters ispossible in principle, it requires extreme experimentalsensitivity


Backup slides

0. 0.2 0.4 0.6 0.8 1.

0.

0.2

0.4

0.6

0.8

1.0.

0.2

0.4

0.6

0.8

1.

Ue2/U

2

Uμ 2/U

2

Uτ

2 /U2

sin2θ23 = 0.451

sin2θ23 = 0.574

δ = 261°


Backup slides

0. 0.2 0.4 0.6 0.8 1.0.

0.2

0.4

0.6

0.8

1.0.

0.2

0.4

0.6

0.8

1.

Ue2/U2

Uμ 2/U

2

Uτ

2 /U2

Log10(U2)

-8.9

-8.8

-8.7

-8.6

-8.5

-8.4


Backup slides

[Eijima/Drewes 1606.06221]


juraj klari´c (tu m...

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