neutrino mass: overview of ββ0 , cosmology and direct...

Neutrino Mass: Overview of ββ0ν, Cosmology

and Direct Measurements

Carlo Giunti

INFN, Sezione di Torino, and Dipartimento di Fisica Teorica, Universita di Torino

mailto://[email protected]

Neutrino Unbound: http://www.nu.to.infn.it

Neutrino Town Meeting

European Strategy for Neutrino Oscillation Physics - II

14-16 May 2012, CERN

C. Giunti − Neutrino Mass: Overview of ββ0ν , Cosmology and Direct Measurements − 14 May 2012 − 1/17

mailto://[email protected]

http://www.nu.to.infn.it

Three-Neutrino Mixing Paradigm

νe νµ ντ

∆m2A

∆m2S

ν2

ν1

ν3

m2

Normal Spectrum

m2

∆m2S

ν2

ν1

∆m2A

ν3

Inverted Spectrum

absolute scale is not determined by neutrino oscillation data


Absolute Values of Neutrino Masses

Lightest mass: m1 [eV]

m1,

m2,

m3

[e

V]

10−4 10−3 10−2 10−1 110−4

10−3

10−2

10−1

1

m1

m2

m3 Cosm

ological Limit

Normal Hierarchy

Quasi−DegenerateNormal Spectrum

1σ2σ3σ

m22 = m2

1 +∆m221 = m2

1 +∆m2S

m23 = m2

1 +∆m231 = m2

1 +∆m2A

Lightest mass: m3 [eV]m

3, m

1, m

2

[eV

]10−4 10−3 10−2 10−1 1

10−4

10−3

10−2

10−1

1

m3

m1

m2

Cosm

ological Limit

Inverted Hierarchy

Quasi−DegenerateInverted Spectrum

1σ2σ3σ

m21 = m2

3 −∆m231 = m2

3 +∆m2A

m22 = m2

1 +∆m221 ≃ m2

3 +∆m2A

Quasi-Degenerate for m1 ≃ m2 ≃ m3 ≃ mν ≫√

∆m2A ≃ 5× 10−2 eV


Tritium Beta-Decay

3H → 3He + e− + νe

dΓ

dT=

(cosϑCGF)2

2π3|M|2 F (E) pE (Q − T )

√

(Q − T )2 −m2νe

Q = M3H −M3He −me = 18.58 keV

Kurie plot

K(T ) =

√

√

√

√

√

dΓ/dT

(cosϑCGF)2

2π3|M|2 F (E) pE

=

[

(Q − T )

√

(Q − T )2 −m2νe

]1/2

mνe > 0

Q−mνe Q

mνe = 0

T

K(T

)

mνe < 2.2 eV (95% C.L.)

Mainz & Troitsk[Weinheimer, hep-ex/0210050]

future: KATRIN[www.katrin.kit.edu]

start data taking 2014

sensitivity: mνe ≃ 0.2 eVC. Giunti − Neutrino Mass: Overview of ββ0ν , Cosmology and Direct Measurements − 14 May 2012 − 4/17

www.katrin.kit.edu

Neutrino Mixing =⇒ K (T ) =

[

(Q − T )∑

k

|Uek |2√

(Q − T )2 −m2k

]1/2

Q−m2 T Q−m1

K(T

)

Q

analysis of data isdifferent from theno-mixing case:2N − 1 parameters(

∑

k

|Uek |2 = 1

)

if experiment is not sensitive to masses (mk ≪ Q − T )

effective mass: m2β =

∑

k

|Uek |2m2

k

K2 = (Q − T )2

∑

k

|Uek |2

√

1−m2

k

(Q − T )2≃ (Q − T )2

∑

k

|Uek |2

[

1−1

2

m2k

(Q − T )2

]

= (Q − T )2[

1−1

2

m2β

(Q − T )2

]

≃ (Q − T )√

(Q − T )2 −m2β


Predictions of 3ν-Mixing Paradigm

m2β = |Ue1|

2 m21 + |Ue2|

2 m22 + |Ue3|

2m23

mmin [eV]

mβ

[e

V]

NS

IS

Current Bound

KATRIN Sensitivity

Cosm

ological Limit

10−3 10−2 10−1 1 1010−3

10−2

10−1

1

10

1σ2σ3σ

◮ Quasi-Degenerate:

m2β ≃ m2

ν

∑

k|Uek |

2 = m2ν

◮ Inverted Hierarchy:

m2β ≃ (1− s213)∆m2

A ≃ ∆m2A

◮ Normal Hierarchy:

m2β ≃ s212c

213∆m2

S + s213∆m2A

≃ 2× 10−5 + 6× 10−5 eV2

◮ If mβ . 4× 10−2 eV⇓

Normal Spectrum


Neutrinoless Double-Beta Decay

7632Ge

7633As

7634Se

0+

2+

0+

β−

β−β−

β+

Effective Majorana Neutrino Mass: mββ =∑

k

U2ekmk


Two-Neutrino Double-β Decay: ∆L = 0

N (A,Z ) → N (A,Z + 2) + e− + e

− + νe + νe

(T 2ν1/2)

−1 = G2ν |M2ν |2

second order weak interaction processin the Standard Model

d u

W

W

d u

��

e

��

e

e

�

e

�

Neutrinoless Double-β Decay: ∆L = 2

N (A,Z ) → N (A,Z + 2) + e− + e−

(T 0ν1/2)

−1 = G0ν |M0ν |2 |mββ |

2

effectiveMajoranamass

mββ =∑

k

U2ek mk

d u

W

�

k

m

k

U

ek

U

ek

W

d u

e

�

e

�


Effective Majorana Neutrino Mass

mββ =∑

k

U2ek mk complex Uek ⇒ possible cancellations

mββ = |Ue1|2 m1 + |Ue2|

2 e iα2 m2 + |Ue3|2 e iα3 m3

α2 = 2λ2 α3 = 2 (λ3 − δ13)

α3

α2

Im[mββ]

|Ue2|2e

iα2m2

|Ue1|2m1

mββ

Re[mββ]

|Ue3|2e

iα3m3

α2

α3

Im[mββ]

|Ue2|2e

iα2m2

|Ue1|2m1 Re[mββ]

mββ

|Ue3|2e

iα3m3


Experimental Bounds

CUORICINO (130Te) [AP 34 (2011) 822]

T 0ν1/2 > 2.8× 1024 y (90% C.L.) =⇒ |mββ | . 0.3− 0.7 eV

Heidelberg-Moscow (76Ge) [EPJA 12 (2001) 147]

T 0ν1/2 > 1.9× 1025 y (90% C.L.) =⇒ |mββ| . 0.32 − 1.0 eV

IGEX (76Ge) [PRD 65 (2002) 092007]

T 0ν1/2 > 1.57 × 1025 y (90% C.L.) =⇒ |mββ| . 0.33 − 1.35 eV

NEMO 3 (100Mo) [PRL 95 (2005) 182302]

T 0ν1/2 > 4.6× 1023 y (90% C.L.) =⇒ |mββ | . 0.7− 2.8 eV


Experimental Positive Indication[Klapdor et al., MPLA 16 (2001) 2409]

T 0ν1/2 = (2.23+0.44

−0.31)× 1025 y 6.5σ evidence [MPLA 21 (2006) 1547]

0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

Energy ,keV

Cou

nts

/ keV

SSE2n2b Rosen − Primakov Approximation

Q=2039 keV

[PLB 586 (2004) 198]

2000 2010 2020 2030 2040 2050 2060

0

1

2

3

4

5

6

7

8

[MPLA 21 (2006) 1547]

the indication must be checked by other experiments

|mββ | = 0.32 ± 0.03 eV [MPLA 21 (2006) 1547]

if confirmed, very exciting: Majorana ν and large mass scale


Predictions of 3ν-Mixing Paradigm

mββ = |Ue1|2 m1 + |Ue2|

2 e iα2 m2 + |Ue3|2 e iα3 m3

mmin [eV]

|mββ

| [

eV]

NS

IS

Cosm

ological Limit

Current Bound or Positive Indication

10−4 10−3 10−2 10−1 110−4

10−3

10−2

10−1

1

1σ2σ3σ

◮ Positive indication:tension with cosmology

◮ Quasi-Degenerate:

|mββ | ≃ mν

√

1− s22ϑ12s2α2

◮ Inverted Hierarchy:

|mββ | ≃√

∆m2A(1− s22ϑ12

s2α2)

◮ Normal Hierarchy:

|mββ| ≃ |s212√

∆m2S + e iαs213

√

∆m2A|

≃ |2.7 + 1.2e iα| × 10−3 eV

◮ If |mββ | . 10−2 eV⇓

Normal Spectrum


New Experiments

EXO200 GERDA1 CUORE-0 KamLAND-Zen SNO+ GERDA2 CUORE NEXT SuperNemo D. Majorana D.10

20

50

100

200

500

Experiments

mββ(meV)

[Gomez-Cadenas, Martin-Albo, Mezzetto, Monrabal, Sorel, Riv. NC 35 (2012) 29]


Beyond Three-Neutrino Mixing

ν1

m21

∆m2SOL

logm2m22

ν2 ν3

m23

∆m2ATM

νe

νµ

ντνs1 · · ·

3ν-mixing

ν4 ν5 · · ·

m24 m2

5

νs2

∆m2SBL


3+1

sin22ϑeµ

∆m412

[e

V2 ]

10−4 10−3 10−2 10−1

10−1

1

10

+

DIS

APP

3+1 − GLO+SUN

68.27% C.L. (1σ)90.00% C.L.95.45% C.L. (2σ)99.00% C.L.99.73% C.L. (3σ)

sin22ϑee

10−2 10−1

+

DIS

sin22ϑµµ

10−2 10−1

+

DIS

[Giunti, Laveder, Y.F. Li, in preparation]


3+1 Predictions

β Decay0

24

68

10

mβ(4)

[eV]

∆χ2

10−2 10−1 1

68.27%

90%

95.45%

99%

99.73%

3+1 − GLO3+1 − GLO+SUN

m(4)β = |Ue4|

√

∆m241

m(4)β ≫ m

(3ν)β (IH)

ββ0ν Decay

02

46

810

mββ(4)

[eV]

∆χ2

10−3 10−2 10−1 1

68.27%

90%

95.45%

99%

99.73%

3+1 − GLO3+1 − GLO+SUN

m(4)ββ = |Ue4|2

√

∆m241

m(4)ββ & m

(3ν)ββ (IH)


Conclusions

D.3 – What is the likelihood of there being✟✟no interesting physics beyondmeasuring CP violation and mass hierarchy?

◮ Majorana Neutrinos: Very Likely

ββ0ν Decay; Majorana Phases; Lepton Number Violation; See-SawMechanism; Physics Beyond the Standard Model; Leptogenesis; . . .

◮ Sterile Neutrinos: Possible

More Mixing Parameters: Masses, Mixing Angles, Phases; RichPhenomenology at “Easily” Measurable eV Scale; Physics Beyond theStandard Model; . . .

◮ . . . ?


neutrino mass: overview of ββ0 , cosmology and direct...

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