Neutrino Physics and 0νββ

Werner Rodejohann

(MPI Heidelberg)

Aarhus, 05/09/07

• Neutrino Mixing and 0νββ

• |mee| and NH vs. IH

• What’s more to 0νββ (Majorana phases, mass scale, |Ue3|)

• If we don’t observe 0νββ: vanishing effective mass

• If we observe

• MiniBooNE and 0νββ

Status and goal of neutrino physicsunderstand form and origin of

fundamental object in low energy Lagrangian:

L = 12

νcα (mν)αβ νβ + h.c. with mν = UT diag(m1, m2, m3) U

P (νe → νµ) = sin2 2θ sin2 ∆m2

4E L mν = −mTD M−1R mD

Oscillations! See-saw!

Masses? Lepton Number Violation?

What we know and don’t know9 physical parameters in mν

• θ12 and m22 − m21 (or θ⊙ and ∆m2⊙)

• θ23 and |m23 − m22| (or θA and ∆m2A)

• θ13 (or |Ue3|)

• m1, m2, m3• sgn(m23 − m22)

• Dirac phase δ

• Majorana phases α and β (or α1 and α2, or φ1 and φ2, or. . .)

Neutrino masses

• neutrino masses ↔ scale of their origin• neutrino mass ordering ↔ form of mν

• m23 ≃ ∆m2A ≫ m22 ≃ ∆m2⊙ ≫ m21: normal hierarchy (NH)• m22 ≃ |∆m2A| ≃ m21 ≫ m23: inverted hierarchy (IH)• m3 ≃ m2 ≃ m1 ≡ m0 ≫

√

∆m2A: quasi-degeneracy (QD)

∆L 6= 0: Neutrinoless Double Beta DecaySM vertex

Nuclear Process Nucl

Σi

νiUei

e

W

νi

e

W

Uei

Nucl

• only works when ν = νc and mν 6= 0 ⇔ See-saw mechanism• spin flip ⇒ Amplitude ∝ mi/(q2 − m2i ) → mi• Nuclear Matrix Elements: Uncertainty ζ = O(1) !?

Amplitude proportional to coherent sum

(“Effective mass”):

|mee| ≡∣

∣

∣

∑

U2ei mi

∣

∣

∣

∆L 6= 0: Neutrinoless Double Beta DecayIm

Rem

mm

ee

ee

ee

(1)

(3)

(2)

| |

| || | e

e.

.

eem

2iβ2iα

Effective mass |mee| ≡∣

∣

∑

U2ei mi∣

∣:

=∣

∣c212 c213 m1 + s

212 c

213 m2 e

2iα + s213 m3 e2iβ∣

∣

=∣

∣cos2 θ⊙ m1 + sin2 θ⊙ m2 e

2iα + sin2 θCHOOZ m3 e2iβ∣

∣

=∣

∣

∣|m(1)ee | + |m(2)ee | e2iα + |m(3)ee | e2iβ∣

∣

∣

= f(

θ12, mi, |Ue3|, sgn(∆m2A), α, β)

7 out of 9 parameters of mν . . .

Kim, 1996; Minakata & Yasuda, 1996; Hirsch & Klapdor-Kleingrothaus, 1997;

Bilenky, Giunti & Monteno, 1997; Fukuyama, Matsuda & Nishiura, 1997; Bilenky,

Giunti, Kim & Monteno, 1998; Fukuyama, Matsuda & Nishiura, 1998; Vissani, 1999;

Giunti, 1999; Bilenky, Giunti, Grimus, Kayser & Petcov, 1999; Ma, 1999; Wodecki &

Kaminsky, 2000; Kalliomaki & Maalampi, 2000; Rodejohann, 2000; Matsuda,

Takeda, Fukuyama & Nishiura, 2000; Klapdor-Kleingrothaus, Päs & Smirnov, 2001;

Falcone & Tramontano, 2001; Bilenky, Pascoli & Petcov, 2001; Xing, 2001; Osland

& Vigdel, 2001; Pascoli & Petcov, 2001; Barger, Glashow, Marfatia & Whisnant,

2002; Hambye, 2002; Minakata & Sugiyama, 2002; Klapdor-Kleingrothaus &

Sarkar, 2002; Xing, 2002; Haba & Suzuki, 2002; Pakvasa & Roy, 2002; Rodejohann,

2002; Haba, Nakamura & Suzuki, 2002; Päs & Weiler, 2002; Barger, Glashow ,

Langacker, Marfatia, 2002; Civitarese & Suhonen, 2002; Pascoli, Petcov &

Rodejohann, 2002; Sugiyama, 2002; Avignone & King, 2002; Minakata &

Sugiyama, 2002; Cheung, 2003; Abada & Bhattacharyya, 2003; Giunti, 2003;

Pascoli & Petcov, 2003; Elliott, 2003; Stoica, 2004; Brahmachari, 2004; Bilenky,

Fäßler & Simkovic, 2004; Pascoli & Petcov; 2004; Deppisch, Päs & Suhonen, 2004;

Joniec & Zralek, 2004; Pascoli & Petcov, 2005; Pascoli, Petcov & Schwetz, 2005;

Goswami & Rodejohann, 2005; Choubey & Rodejohann, 2005; Bilenky, Fäßler,

Gutsche, & Simkovic, 2005; Lindner, Merle & Rodejohann, 2005;

,Neutrino 2006, Santa Fe, 14/06/2006 – p.21/34

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sin2 2Θ13 = 0.03

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sin2 2Θ13 = 0.10

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Our plots are blue and yellow!

Experiment Isotope

Enriched

isotope mass

(kg)

T1/2

(yr) (eV) Start Status

CUORE 130Te 203 2.1 1026 0.03 - 0.07* 2011 Funded

GERDA phase I

phase II76Ge

17.9

40

3. 1025

2. 1026

0.2 – 0.5*

0.07 – 0.2*

2009

2011

Funded

Funded

Majorana 76Ge 30 - 60 1.1026 0.1 – 0.3* 2011 Funded

EXO-200 136Xe 200 6.4 1025 0.2 - 0.7* 2008 Funded

SuperNEMO82Se

150Nd

100

100

2. 1026

1026

0.05- 0.09*

0.072011 R&D

CANDLES 48Ca 0.5 ~0.5 2008 Funded

MOON II 100Mo 120 0.09 – 0.13 ? R&D

DCBA 150Nd 20 ? R&D

SNO++ 150Nd 500 R&D

COBRA116Cd,

130Te

420R&D

SummarySummary

* Calcu

lation w

ith N

ME

from R

odim

et al., Su

hon

enet al., C

aurier et al. P

MN

07

Piquemal, talk at Lepton/Photon

Lindner, Merle, W.R., Phys. Rev. D 73, 053005 (2006)

Distinguish NH from IH?!

Normal vs. Inverted Hierarchy vs. NuclearPhysics

∆|mee| ≡ |mee|IHMIN − ζ |mee|NHMAX

!> 0

upper limit on experimental uncertainty

0.01 0.02 0.03 0.04 0.05sin2Θ13

0.005

0.01

0.015

0.02

0.025

HDÈm

eeÈHΖLL@e

VD

sin2 Θ12=0.28

0.01 0.02 0.03 0.04 0.05sin2Θ13

0.005

0.01

0.015

0.02

0.025

HDÈm

eeÈHΖLL@e

VD

sin2Θ12=0.40

Ζ=3

Ζ=2

Ζ=1.5

Ζ=1

Lindner, Merle, W.R., PRD 73, 053005 (2006);

S. Choubey, W.R.; Pascoli, Petcov, Schwetz; de Gouvea, Jenkins

• likes ζ

Other (non-oscillation) probes of NH vs. IH1) Cosmology: Σ =

∑

mi

ΣNH ≃√

∆m2A < ΣIH ≃ 2

√

∆m2A

• independent on mixing angles

• systematics?

Cosmology and 0νββ

σΣ mee

= 0.01 eVm

ee

eV

0.05 0.1 0.2 0.410

−2

10−1

InvertedBothNormal

σΣ mee

= 0.05 eV

Σ eV0.05 0.1 0.2 0.4

σΣ mee

= 0.1 eV

0.05 0.1 0.2 0.4

Jenkins, de Gouvea, hep-ph/0507021

2) β-decay: mνe =√∑ |Uei|2 m2i

mNHνe ≃√

s212 c213 ∆m

2⊙ + s

213 ∆m

2A ≪ mIHνe ≃

√

c213 ∆m2A

• almost independent on mixing angles• difference of normal and inverted shows up well below KATRIN limit• different for sterile (LSND/MiniBooNE!!) neutrinos

KATRIN and 0νββ

0νββ ∆m2A KATRIN Conclusion

yes > 0 yes QD, Majorana

yes > 0 no QD, Majorana or

NH, Majorana + heavy particles

yes < 0 no IH, Majorana

yes < 0 yes QD, Majorana

no > 0 no NH, Dirac or Majorana

no < 0 no Dirac

no < 0 yes Dirac

no > 0 yes Dirac

APS study, Mohapatra et al., hep-ph/0510213

Σ mβ |mee|

NHp

∆m2A

q

sin2 θ⊙∆m2⊙ + |Ue3|2∆m

2

A

˛

˛

˛

˛

sin2 θ⊙

q

∆m2⊙ + |Ue3|2p

∆m2Aeiφ

˛

˛

˛

˛

IH 2p

∆m2Ap

∆m2Ap

∆m2Ap

1 − sin2 2θ⊙ sin2α

QD 3m0 m0 m0p

1 − sin2 2θ⊙ sin2α

Other (non-oscillation) probes of NH vs. IH3) Other elements of mν : “the lobster”

Recall: (A, Z) → (A, Z + 2) +2 e− is proportional to

mee =∑

i

U2ei mi

is ee element of mass matrix (unique!!)

Therefore, K+ → π− e+ µ+ is proportional to∑

i

Uei Uµi mi

eµ element of mass matrix

Other (non-oscillation) probes of NH vs. IH3) Other elements of mν : “the lobster”

BR(K+ → π− e+ µ+) ∝ |meµ|2 =∣

∣

∣

∑

Uei Uµi mi

∣

∣

∣

2

∼ 10−30( |meµ|

eV

)2

Merle, W.R., Phys. Rev. D 74, 017701 (2006)

(mν)αβ =

Merle, W.R., Phys. Rev. D 74, 017701 (2006)

3) Other elements of mν : “the lobster”

1e-9

1e-7

1e-5

1e-3

0.1

1

1e3

1e5

1e7

1e9

1e-6 1e-4 0.01 1 100 1e4 1e6

σ [

10

-33 b

]

mi [GeV]

µµµτττ

Eµ = 50 GeV

νµ N → µ− α+β+XW.R., K. Zuber, Phys. Rev. D 63, 054031 (2001)

(νN scattering, ν-fac, HERA,. . .)

BR, Γ, σ ∝ m2

(q2 − m2)2 ≃

m2i q2 ≫ m2i

1m2i

q2 ≪ m2i

What’s more to 0νββ?∗ Mass scale: consider QD spectrum

m0 ≤1 + tan2 θ12

1 − tan2 θ12 − 2 |Ue3|2|mee|exp

Majorana phasesPascoli, Petcov, Schwetz, Nucl. Phys. B 734, 24 (2006)

10-2

10-1

100

1 2 3 410

-2

10-1ob

serv

ed Σ

[eV

]

1 2 3 4uncertainty in || from NME

1 2 3 4

σββ = 0.004 eV, σΣ = 0.04 eV

||obs

= 0.018 eV

|| and Σ inconsistent at 2σ

sin2θ

12 = 0.31 +− 3%sin

2θ12 = 0.38 +− 3%

sin2θ

13 = 0 +− 0.002, ∆m

2

21 = 8x10

-5 +− 2%, ∆m2

31 = −2.2x10-3 +− 3%,

||obs

= 0.032 eV

data consistent with α21

= π data consistent with α21

= 0

CP violation established at 2σ

||obs

= 0.047 eV

|Ue3| and 0νββ

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⇒ Value of Ue3 influences |mee|, in particular NH vs. IH

Cosmology and |Ue3|2

Merle, W.R., hep-ph/0703135

Measuring |Ue3|2 with Neutrino-less Double BetaDecay?

Example inverted hierarchy:

|Ue3|2 = 1 −|mee|

√

∆m2A√

1 − sin2 2θ12 sin2 α

Merle, W.R., hep-ph/0703135

if we don’t observe 0νββ: vanishing |mee|

The “chimney”

if we don’t observe 0νββ: vanishing |mee|• a triangle can be formed!

∣

∣

∣|m(1)ee | + |m(2)ee | e2iα + |m(3)ee | e2iβ

∣

∣

∣= 0

Im

Rem

mm

ee

ee

ee

(1)

(3)

(2)

| |

| || | e

e.

.

eem

2iβ2iα

• texture zero in charged lepton basis! (only meµ or meτ can inaddition be zero)

cos 2α =|m(1)ee |2 + |m(2)ee |2 − |m(3)ee |2

2|m(1)ee | |m(2)ee |=

m21(

c413(

s412 + c412

)

− s413)

+ ∆m2⊙ s412 c

413 − ∆m2A s413

2m1

√

m21 + ∆m2⊙ s

212 c

212 c

413

• only possible for normal ordering

• if θ13 = 0: m1 = sin2 θ12√

∆m2⊙cos 2θ12

≃ 4.5 (2.8 ÷ 8.4) meV

• if m1 = 0: sin2 2θ13 ≃ 4 sin2 θ12

√

∆m2⊙∆m2A

≃ 0.24 (0.14 ÷ 0.40)

60 70 80 90 100 110 120alpha

0

0.002

0.004

0.006

0.008

0.01

m 1

0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2sin22Θ13

0.02

0.04

0.06

0.08

0.1

0.12

m1+

m2+

m3

ineV

mee=0.0001 eV

0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2sin22Θ13

0.02

0.04

0.06

0.08

0.1

0.12

m1+

m2+

m3

ineV

3 Σ

1 Σ

best-fit

Dev, Kumar, hep-ph/0607048 Lindner, Merle, W.R., PRD 73, 053005 (2006)

d

d

e

u

u

e

u

u~

~

R L

R

L

L

L

L

L

χ, g~

dR

L

e

u

~L

u

e

L

~dR

Lχ

R

, g

L

d

~

u

2n → 2p + 2e− ⇒ 2d → 2u + 2e− ⇒ 0 → ud̄ + ud̄ + 2e−

• SUSY• Higgs triplets• Right-handed interactions• Majorons

⇒ limits on masses and couplingscomplementary to collider or DM

Leptogenesis and Majorana NeutrinosDecay asymmetry of heavy Majorana neutrinos (see-saw!)

εα1 =Γ(N1 → φ l̄α) − Γ(N1 → φ† lα)Γ(N1 → φ l̄α) + Γ(N1 → φ† lα)

∝ ∑j 6=i

Im

{

(mD)iα (m†D)αj

(

mD m†D

)

ij

}

Parameterize mD a la Casas-Ibarra:

mD = i√

MR R√

mdiagν U with complex R RT = 1

leads to

εα1 = f(mD, m†D) = f(R, U)

ε1 =∑

α εα1 = f(mD m

†D) = f(R)

⇒ if flavor effects are important (M1

Caveat:Leptogenesis works with |mee| = 0 and with no phases in U

If we observe 0νββ. . .

• Neutrinos are Majorana (Schechter-Valle)

BLACK

BOX

W

W

ν

ν

−e

e

u

d

u

d−e

e

−

• we still need to identify the mechanism of 0νββ: SUSY, RHcurrents, heavy Majorana neutrinos,. . .

solution: EC/EC, EC/β, excited states, angular distribution,

measure 0νββ in many different nuclei,. . .

• reduce/check NME uncertainty: same solution

• |mee| can rule out models

• we tested a prediction of the see-saw mechanism!

• we will believe much more firmly in leptogenesis!

• if non-zero, Majorana phases DO CONTRIBUTE to leptogenesis

Sterile Neutrinos?!

• Solar (∆m221 ≃ 8 · 10−5 eV2) and atmospheric (∆m232 ≃ 2.5 · 10−3eV2) neutrinos oscillate

∆m221 + ∆m232 = ∆m

213

• LSND ν̄µ ↔ ν̄e flavor transition:∆m2s1 ≃ (0.1 ÷ 1) eV2 ⇒ add sterile neutrino!! (3 + 1)

• confronted with KARMEN, Bugey, CDHS, Chooz, Palo VerdeMaltoni, Schwetz, Tortola, Valle, Phys. Rev. D 67, 013011 (2003):

10-3

10-2

10-1

100

sin22θ

LSND

10-1

100

101

∆m2 LS

ND

[eV

2 ]

(3+1) NEV+atm

LSND DAR

LSND global

95% C

L

99% C

L

MiniBooNE Results

)θ(22sin

-310 -210 -110 1

)4

/c2|

(eV

2m

∆|

-210

-110

1

10

210

LSND 90% C.L.

LSND 99% C.L.

) upper limitθ(22sin

yMiniBooNE 90% C.L.MiniBooNE 90% C.L. sensitivityBDT analysis 90% C.L.

★

10-4

10-3

10-2

10-1

100

sin22θ

SBL

10-1

100

101

∆m

2 41 [

eV2 ]

NEV(incl. MB475)

LSND

90%, 99% CL

LSND (2-flavor oscillation!) ruled out at 98 % C.L.

Aguilar-Arevalo et al., arXiv:0704.1500 [hep-ex]

Maltoni, Schwetz, arXiv:0705.0107 [hep-ph]

Add two sterile Neutrinos!

• LSND more compatible with other experimentsSorel, Conrad, Shaevitz, Phys. Rev. D 70, 073004 (2004)

• CP violation studies with LSND and MiniBooNEKaragiorgi, Aguilar-Arevalo, Conrad, Shaevitz, Whisnant, Sorel,

Barger, Phys. Rev. D 75, 013011 (2007)

• LSND compatible with MiniBooNEMaltoni, Schwetz, arXiv:0705.0107 [hep-ph]

– good fit to LSND and MiniBooNE

– can explain low energy excess

– requires non-trivial CP phase

– tension with disappearance experiments CDHS and Bugey

– 3 sterile neutrinos don’t provide much better fit

Add two sterile Neutrinos!

★

0.1 1 10

∆m241

[eV2]

0.1

1

10

∆m2 51

[eV

2 ]

0.1 1 10

0.1

1

10

90 100 110 120 130

χ290 100 110 120 130

(3+2) (3+1)

(3+2) fit to global data (MB475)

Maltoni, Schwetz, arXiv:0705.0107 [hep-ph]

∆m2s1 = 6.49+1.0−1.0 eV

2 or 1.90+0.60−0.90 eV2 with |Ue5| = 0.12+0.06−0.06

∆m2s2 = 0.89+0.1−0.1 eV

2 or 0.90+0.05−0.20 eV2 with |Ue4| = 0.11+0.05−0.05

Mass scales of 1 ÷ 3 eV ⇒ will have effect on mass-related observables

∆L 6= 0: Neutrinoless Double Beta DecaySM vertex

Nuclear Process Nucl

Σi

νiUei

e

W

νi

e

W

Uei

Nucl

Effective mass:

|mee| ≡∣

∣

∣

∣

5∑

i=1

U2ei mi

∣

∣

∣

∣

=∣

∣m3ee + mstee

∣

∣

where m3ee ≡ cos2 θ⊙ m1 + sin2 θ⊙ m2 eiα2 + sin2 θCHOOZ m3 eiα3

and mstee ≡ |Ue4|2 m4 eiα4 + |Ue5|2 m5 eiα5

Sterile term can dominate, active term can dominate, cancellation

possible

0.0001 0.001 0.01 0.1 1m @eVD

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0.001

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0.1

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VD Dm31

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sin2 2Θ13 = 0.03

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VD

3 active neutrinos: 2 mass orderings

How many massorderings?

8 possible Orderings

• two 2 + 3 scenarios

• active neutrinos normally (SSN) or inversely (SSI) ordered

• active neutrinos as in NH or in IH, m4 ≃√

∆m2s2, m5 ≃√

∆m2s1

8 possible Orderings

• Σ ≃√

∆m2s1 +√

∆m2s2 >∼ 1.5 eV best-fit: 3.5 eV

• mβ ≃√

|Ue4|2 ∆m2s2 + |Ue5|2 ∆m2s1 >∼ 0.1 eV best-fit: 0.32 eV

• 〈m〉st ≃∣

∣

∣|Ue4|2

√

∆m2s2 + |Ue5|2√

∆m2s1ei(α5−α4)

∣

∣

∣≃ (0.02 ÷ 0.05) eV

• SSN: 〈m〉3 ≃ sin2 θ⊙√

∆m2⊙

8 possible Orderings

• two 3 + 2 scenarios• active neutrinos QD with m0 =

√

∆m2s1, m4 ≃√

∆m2s1 − ∆m2s2• normal or inverted ordering not distinguishable with mass-related

observables

8 possible Orderings

• Σ ≃ 3√

∆m2s1 +√

∆m2s1 − ∆m2s2 >∼ 3 eV best-fit: 10 eV• mβ ≃

√

∆m2s1 best-fit: 2.55 eV > 2.3 eV (!)

– constrains allowed region of ∆m2s1

– KATRIN will find something!

8 possible Orderings

• |mee| ≃√

∆m2s1

√

1 − sin2 2θ⊙ sin2 α2/2 ≃ (1.02 ÷ 2.55) eV• larger than SSN, SSI• |mee| 6= 0 due to θ⊙ 6= π/4• future 0νββ will find something!• constraints on ∆m2s1, θ⊙ and α2

0.2 0.25 0.3 0.35 0.4 0.2 0.25 0.3 0.35 0.4

sin2θο. sin

2θο

α 2 α2

.

π/2

3π/4

π

5π/4

3π/2

π/2

3π/4

π

5π/4

3π/2

|mee| ≤ 1 eV |mee| ≤ 0.5 eV

• four 1 + 3 + 1 scenarios• heaviest ν separated either by ∆m̃2s1 (“a”) or ∆m̃2s2 (“b”)• SNSb and SISb: active neutrinos QD with m0 =

√

∆m̃2s1 < m5⇒ indistinguishable from NSS and ISS

• SNSa and SISa: active neutrinos QD with m0 =√

∆m̃2s2 < m5

• normal/inverted ordering not distinguishable with mass-relatedobservables

On 1 + 3 + 1 ScenariosAnalyzes of Maltoni, Schwetz and Sorel et al. use

P (νµ → νe) = 4 |Ue4|2 |Uµ4|2 sin2∆m2s2 L

4E+ 4 |Ue5|2 |Uµ5|2 sin2

∆m2s1 L

4E

+8 |U∗e4 Uµ4 Ue5 U∗µ5| sin∆m2s2 L

4Esin

∆m2s1 L

4Ecos

(

∆m2ss L

4E− δ)

with ∆m2ss = ∆m2s1 − ∆m2s2

But: 1 + 3 + 1 scenarios have ∆m2ss = ∆m2s1 + ∆m

2s2

No fit available ⇒ ∆m̃2s1 ≃ ∆m2s1 and ∆m̃2s2 ≃ ∆m2s2

• Σ ≃ 3√

∆m̃2s2 +√

∆m̃2s1 + ∆m̃2s2

>∼ 2 eV best-fit: 5.55 eV

• mβ ≃√

∆m̃2s2 ≃ 1 eV

• KATRIN will find something!

• |mee| ≃√

∆m̃2s2

√

1 − sin2 2θ⊙ sin2 α2/2 ≃ (0.38 ÷ 0.9) eV• active neutrinos dominate• |mee| 6= 0 due to θ⊙ 6= π/4• future 0νββ will find something!

NSS, ISS, (SNSb, SISb) SNSa, SISa

√

∆m2s1

√

1 − sin2 2θ⊙ sin2 α2/2√

∆m̃2s2

√

1 − sin2 2θ⊙ sin2 α2/2

distinguish from each other if√

∆m2s1 cos 2θ⊙ ≥ ζ√

∆m̃2s2

Scenarios with 3 Sterile Neutrinos∆m2s1, ∆m

2s2, ∆m

2s3: 16 possible orderings, 5 phenomenologies

∆m2s1 = 1.84 eV , ∆m2s2 = 0.83 eV , ∆m

2s3 = 0.46 eV

|Uei| = 0.1 (assumption)

• SSSN: NH plus 3 heavy sterile, KATRIN and 0νββ maybe

• SSSI: IH plus 3 heavy sterile, KATRIN and 0νββ maybemβ ≃ 0.2 eV , |mee|

Distinguish QD scenarios via 0νββ for

√

∆m2s1 cos 2θ⊙ ≥ ζ√

∆m2s2√

∆m2s1 cos 2θ⊙ ≥ ζ√

∆m2s3√

∆m2s2 cos 2θ⊙ ≥ ζ√

∆m2s3

Summary• – Oscillations ⇒ mν 6= 0

– almost all models/scenarios explain mν 6= 0 in connection withLepton Number Violation ⇒ 0νββ

• 0νββ can– distinguish NH from IH

– Mass scale (consistency with KATRIN and cosmology)

– consistency with Ue3

– Majorana phases (Leptogenesis?)

• identify structure of mass matrix

Summary Sterile Neutrinos

8 Orderings → 4 phenomenologiesscheme feature KATRIN 0νββ

SSN NH plus νs1 , νs2 maybe maybe

SSI IH plus νs1 , νs2 maybe maybe

NSS, ISS QD with√

∆m2s1 yes yes

SNSb, SISb QD with√

∆m̃2s1 yes yes

SNSa, SISa QD with√

∆m̃2s2 yes yes