Neutrino Masses in Cosmology, Neutrinoless Double-Beta...

Neutrino Masses in Cosmology, Neutrinoless

Double-Beta Decay and Direct Neutrino Masses

Carlo Giunti

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

mailto://[email protected]

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

LIONeutrino2012

Neutrinos at the forefront of elementary particle physics

and astrophysics

22-24 October 2012, Lyon, France

C. Giunti − Neutrino Masses − LIONeutrino2012 − 24 Oct 2012 − 1/33

mailto://[email protected]://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

∆m2S ≃ 7.5× 10−5 eV2 ∆m2A ≃ 2.5× 10

−3 eV2


Open Problems

◮ CP violation ?◮ Nova, LAGUNA, CERN-GS, HyperK, . . .

◮ Mass Hierarchy ?◮ Nova, Atmospheric Neutrinos, Day Bay II, Supernova Neutrinos, . . .

◮ Absolute Mass Scale ?◮ β Decay, Neutrinoless Double-β Decay, Cosmology, . . .

◮ Dirac or Majorana ?◮ Neutrinoless Double-β Decay, . . .

Cosmology: see Verde and Saviano talks


Absolute Scale 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 Spectrum1σ2σ3σ

m22 = m21 +∆m

221 = m

21 +∆m

2S

m23 = m21 +∆m

231 = m

21 +∆m

2A

Lightest mass: m3 [eV]m

3, m

1, m

2

[eV

]

10−4 10−3 10−2 10−1 110−4

10−3

10−2

10−1

1

m3

m1

m2

Cosm

ological Limit

Inverted Hierarchy

Quasi−DegenerateInverted Spectrum1σ2σ3σ

m21 = m23 −∆m

231 = m

23 +∆m

2A

m22 = m21 +∆m

221 ≃ m

23 +∆m

2A

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

∆m2A ≃ 5× 10−2 eV


Tritium Beta-Decay

3H → 3He + e− + ν̄edΓ

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 in 2015

sensitivity: mνe ≃ 0.2 eV


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 |2m2k

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 ≃ m2ν

∑

k|Uek |

2 = m2ν

◮ Inverted Hierarchy:

m2β ≃ (1− s213)∆m

2A ≃ ∆m

2A

◮ Normal Hierarchy:

m2β ≃ s212c

213∆m

2S + s

213∆m

2A

≃ 2× 10−5 + 6× 10−5 eV2

◮ 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

U2ek mk


Two-Neutrino Double-β Decay: ∆L = 0

N (A,Z ) → N (A,Z + 2) + e− + e− + ν̄e + ν̄e

(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

EXO (136Xe) [PRL 109 (2012) 032505]

T 0ν1/2 > 1.6× 1025 y (90% C.L.) =⇒ |mββ | . 0.14 − 0.38 eV

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)× 10

25 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]

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

very exciting: Majorana ν and large mass scale

partially excluded by EXO and CUORICINO


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 + eiαs213

√

∆m2A|

≃ |2.7 + 1.2e iα| × 10−3 eV

m1 & 10−3 eV⇒cancellation?

|mββ | . 10−2 eV =⇒ Normal Spectrum


ββ0ν Decay ⇔ Majorana Neutrino Mass

|mββ | can vanish because of unfortunate cancellations among m1, m2, m3contributions or because neutrinos are Dirac

ββ0ν decay can be generated by another mechanism beyond SM

d

d u

u

e−

e−

ββ0ν =⇒

d

d u

u

e−

W+

W+

e−ββ0ν

ν̄e ≡ νe(h = +1)

νe ≡ νe(h = −1)

[Schechter, Valle, PRD 25 (1982) 2951] [Takasugi, PLB 149 (1984) 372]

Majorana Mass Term: LMeL

= −12 mee(

νceLνeL + νeL ν

c

eL

)

four-loop diagram calculation: mee ∼ 10−24 eV [Duerr, Lindner, Merle, JHEP 06 (2011) 091]


◮ In any case finding ββ0ν decay is important information to solve theDirac-Majorana question in favor of Majorana

◮ On the other hand, it is not possible to prove experimentally thatneutrinos are Dirac.A Dirac neutrino is equivalent to 2 Majorana neutrinos with the samemass.Impossible to prove experimentally that mass splitting is exactly zero.


Beyond Three-Neutrino Mixing

ν1

m21 logm2m22

ν2 ν3

m23

νe

νµ

ντνs1 · · ·

ν4 ν5 · · ·

m24 m25

νs2

3ν-mixing

∆m2ATM ∆m2SBL∆m

2SOL

[see Schwetz and Cribier talks]


Sterile Neutrinos

◮ Sterile means no standard model interactions (e.g. νcR= νsL)

◮ Oscillation observables:

◮ Disappearance of active neutrinos (neutral current deficit)

◮ Indirect evidence through combined fit of data (current indication)

◮ Short-baseline anomalies + 3ν-mixing:

∆m221 ≪ |∆m231| ≪ |∆m

241| ≤ . . .

ν1 ν2 ν3 ν4 . . .

νe νµ ντ νs1 . . .

◮ Neutrino number and mass observable:

◮ Number of thermalized relativistic particles in early Universe (BBN, CMB,BAO)

◮ m4 effects in cosmology (CMB, LLS), direct β-decay neutrino massmeasurements and neutrinoless double-β decay (if Majorana)


Reactor Electron Antineutrino Anomaly

[Mention et al, PRD 83 (2011) 073006]

[update in White Paper, arXiv:1204.5379

new reactor ν̄e fluxes[Mueller et al, PRC 83 (2011) 054615]

[Huber, PRC 84 (2011) 024617]

2.8σ anomaly

0 20 40 60 80 100

0.7

0.8

0.9

1.0

1.1

1.2

L [m]

R

R = 0.93 ± 0.024

Reactor Rates

Bugey3−15Bugey3−40Bugey3−95Bugey4ROVNOGosgen−38

Gosgen−45Gosgen−65ILLKrasno−33Krasno−92Krasno−57

Average Rate


Gallium Anomaly

Gallium Radioactive Source Experiments: GALLEX and SAGE

Detection Process: νe +71Ga → 71Ge + e−

νe Sources: e− + 51Cr → 51V + νe e

− + 37Ar → 37Cl + νe

Anomaly supported by new 71Ga(3He, 3H)71Ge cross section measurement[Frekers et al., PLB 706 (2011) 134]

0.7

0.8

0.9

1.0

1.1

R

Cr1GALLEX

CrSAGE

Cr2GALLEX

ArSAGE

R = 0.84 ± 0.05

E ∼ 0.7MeV

〈L〉GALLEX = 1.9m

〈L〉SAGE = 0.6m

2.9σ anomaly


3+1 SBL νe and ν̄e Survival Probability

P(−)νe→

(−)νe

= 1− sin2 2ϑee sin2

(

∆m241L

4E

)

sin2 2ϑee = 4|Ue4|2(

1− |Ue4|2)

standard parameterization

Ue1 = c12c13c14 Ue2 = s12c13c14 Ue3 = s13c14e−iδ13 Ue4 = s14e

−iδ14

sin2 2ϑee = sin2 2ϑ14


Global νe and ν̄e Disappearance[Giunti, Laveder, Y.F. Li, Q.Y. Liu, H.W. Long, arXiv:1210.5715]

sin22ϑee

∆m412

[e

V2 ]

+

10−2 10−1 110−2

10−1

1

10

102

++

+

95% CL

GalliumReactorsνeCSunCombined

95% CL

GalliumReactorsνeCSunCombined

νe +12C → 12Ng.s. + e−

KARMEN + LSND[Conrad, Shaevitz, PRD 85 (2012) 013017]

[Giunti, Laveder, PLB 706 (2011) 200]

sin22ϑee

∆m412

[e

V2 ]

10−2 10−1 110−1

1

10

+

GAL+REA+νeC+SUN68.27% CL (1σ)90.00% CL95.45% CL (2σ)99.00% CL99.73% CL (3σ)


solar νe + KamLAND ν̄e + ϑ13[Giunti, Li, PRD 80 (2009) 113007]

[Palazzo, PRD 83 (2011) 113013]

[Palazzo, PRD 85 (2012) 077301]


The existence of ν4 with m4 & 1 eV can have dramatic effects not only onneutrino oscillations but also on all phenomena sensitive to the absolutevalue of neutrino masses:

◮ direct β-decay neutrino mass measurements

◮ neutrinoless double-β decay (if Majorana)

◮ cosmology

Information on νe and ν̄e disappearance is crucial for β decay andneutrinoless double-β decay

◮ νe and ν̄e disappearance depends on sin2 2ϑee = 4|Ue4|

2(1− |Ue4|2)

◮ In β decay and neutrinoless double-β decay ν4 contribution depends on|Ue4|

2


Direct β-Decay Neutrino Mass Measurements

−5 −4 −3 −2 −1 0

T − Q [eV]

1−

K(T

)/(Q

−T

)

10−4

10−3

10−2

(sin22ϑee,∆m412 [eV2])

( 0.12 , 7.6 )( 0.1 , 2 )( 0.07 , 0.9 )( 0.052 , 0.46 )

sin22ϑee∆m

412

[eV

2 ]10−2 10−1 1

10−1

1

10

+

++

+ GAL+REA+νeC+SUN68.27% CL (1σ)90.00% CL95.45% CL (2σ)99.00% CL99.73% CL (3σ)


(

K (T )

Q − T

)2

= 1− |Ue4|2 + |Ue4|

2

√

1−m24

(Q − T )2θ(Q − T −m4)


Mainz Neutrino Mass Experiment[Kraus, Singer, Valerius, Weinheimer, arXiv:1210.4194]


∆m241 Upper Bound

sin22ϑee

∆m412

[e

V2 ]

10−2 10−1 110−2

10−1

1

10

102

103

104

+

Osc. vs Mainz

68.27% CL (1σ)90.00% CL95.45% CL (2σ)99.00% CL99.73% CL (3σ)

Osc. vs Mainz

68.27% CL (1σ)90.00% CL95.45% CL (2σ)99.00% CL99.73% CL (3σ)

sin22ϑee

∆m412

[e

V2 ]

10−2 10−1 110−2

10−1

1

10

102

103

104

+

Osc. + Mainz

68.27% CL (1σ)90.00% CL95.45% CL (2σ)99.00% CL99.73% CL (3σ)

Osc. + Mainz

68.27% CL (1σ)90.00% CL95.45% CL (2σ)99.00% CL99.73% CL (3σ)


KATRIN Sensitivity

[Formaggio, Barrett, PLB 706 (2011) 68]

10-2 10-1 110-2

10-1

1

10

20

Sin22ΘsD

m41

2He

V2 L

Bugey4+Rovno , 99% C.L.Bugey3 , 99% C.L.

global fit , 90% C.L.m1 = 2 eV , 90% C.L.m1 = 1 eV , 90% C.L.

m1 = 0 , 90% C.L.

[Esmaili, Peres, PRD 85 (2012) 117301]

[see also Sejersen Riis, Hannestad, JCAP (2011) 1475; Sejersen Riis, Hannestad, Weinheimer, PRC 84 (2011) 045503]


Neutrinoless Double-β Decay0

24

68

10

mββ(4)

[eV]

∆χ2

EXO90% CL

KK10−3 10−2 10−1 1

68.27%

90%

95.45%

99%

99.73%

GAL+REA+νeC+SUN

|mββ| =∣

∣

∣

∑4k=1 U

2ek

mk

∣

∣

∣

m(4)ββ = |Ue4|

2√

∆m241


Cancellation with m(light)ββ ?

[Barry, Rodejohann, Zhang, JHEP 07 (2011) 091]; Li, Liu, PLB 706 (2012) 406; Rodejohann, arXiv:1206.2560]

m(light)ββ =

∣

∣

∣

∣

∣

3∑

k=1

U2ek mk

∣

∣

∣

∣

∣

m(4)ββ = |Ue4|

2√

∆m241

mββ = m(light)ββ + e

iα4m(4)ββ m

(4)ββ & 10

−2 eV

◮ Normal Hierarchy: m(light)ββ . 4.5× 10

−3 eV (95%CL)no cancellation is possible

◮ Inverted Hierarchy: 1.4× 10−2 . m(light)ββ . 5.0× 10

−2 eV (95%CL)cancellation is possible

◮ Quasi-Degenerate: m(light)ββ & 5.0 × 10

−2 eV cancellation is possible



mββ

[e

V]

EXO90% CL

10−4 10−3 10−2 10−1 110−4

10−3

10−2

10−1

Normal Spectrum

1σ2σ3σ


mββ

[e

V]

EXO90% CL

10−4 10−3 10−2 10−1 110−4

10−3

10−2

10−1

Inverted Spectrum

1σ2σ3σ


Assumption: no cancellation

mββ ≥ m(4)ββ

= |Ue4|2√

∆m241

∆m241 =

m(4)ββ

|Ue4|2

2

≤

(

mββ

|Ue4|2

)2

sin22ϑee

∆m412

[e

V2 ]

EXO90% CL

KK

10−2 10−1 110−2

10−1

1

10

102

103

104

+

GAL+REA+νeC+SUN

68.27% CL (1σ)90.00% CL95.45% CL (2σ)99.00% CL99.73% CL (3σ)

GAL+REA+νeC+SUN

68.27% CL (1σ)90.00% CL95.45% CL (2σ)99.00% CL99.73% CL (3σ)


Cosmology

◮ Ns = number of thermalized sterile neutrinos (not necessarily integer)[see Saviano talk]

◮ CMB and LSS in ΛCDM: Ns = 1.3 ± 0.9 ms < 0.66 eV (95% C.L.)[Hamann, Hannestad, Raffelt, Tamborra, Wong, PRL 105 (2010) 181301]

Ns = 1.61± 0.92 ms < 0.70 eV (95% C.L.)[Giusarma, Corsi, Archidiacono, de Putter, Melchiorri, Mena, Pandolfi, PRD 83 (2011) 115023]

◮ BBN:

{

Ns ≤ 1 at 95% C.L. [Mangano, Serpico, PLB 701 (2011) 296]Ns = 0.0 ± 0.5 [Pettini, Cooke, arXiv:1205.3785]

◮ CMB+LSS+BBN: Ns = 0.85+0.39−0.56 (95% C.L.)

[Hamann, Hannestad, Raffelt, Wong, JCAP 1109 (2011) 034]

◮ Standard ΛCDM: 3+1 allowed, 3+2 disfavored


2 3 4 5 6 7Neff

0.0

0.5

1.0

1.5

2.0

∑ mν [

eV

]

CMBWMAP+CMBSPT+H(z)+SNLS+BAO+WiggleZ

CMBWMAP+H0CMBWMAP+H0+CMBSPTCMBWMAP+H0+H(z)

CMBWMAP+BAO

CMBWMAP+H0+WiggleZ

68% and 95% CL[Riemer-Sørensen, Parkinson, Davis, Blake, arXiv:1210.2131]

Σ mν

Ne

ff

0 0.5 1 1.5 2

2

4

6

8

CMB (blue), CMB+WL (red)CMB+BAO+OHD (magenta)CMB+BAO+SNIa (green)

CMB+WL+BAO+OHD+SNIa (cyan)

[Wang et al., arXiv:1210.2136]


Conclusions

◮ Cosmology◮ Very powerful probe of neutrino number and masses

◮ Model dependent. Thermalization loophole

◮ Bright future (Plank, . . . )

◮ Direct β-Decay Neutrino Mass Measurements◮ Model independent and robust

◮ Sensitive to large neutrino masses beyond three-neutrino mixing

◮ KATRIN will start in 2015

◮ Unclear future (bolometers, project 8: radio-frequency)

◮ Neutrinoless Double-β Decay◮ Crucial for Majorana discovery

◮ Sensitive to large neutrino masses beyond three-neutrino mixing

◮ Many running and future experiments


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