Neutrinos: Recent Results, New Standard Model Paradigm and...

Neutrinos: Recent Results,

New Standard Model Paradigmand Beyond

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

22eme Congres General de la Societe Francaise de Physique

Marseille

1-5 July 2013

C. Giunti − Neutrinos: Recent Results,,New Standard Model Paradigm,and Beyond − IN2P3 − 2 July 2013 − 1/26

mailto://[email protected]

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

Fermion Mass Spectrum

m [e

V]

10−1

1

10

102

103

104

105

106

107

108

109

1010

1011

1012

νe

e

u

d

νµ

µs

c

ντ

τ

b

t

ν1, ν2, ν3


Parity Violation

◮ Parity is the symmetry of space inversion (mirror transformation)

x

z

y

mirror

x

y

z

right-handed frame left-handed frame

◮ Parity was considered to be an exact symmetry of nature

◮ 1956: Lee and Yang understand that Parity can be violated in WeakInteractions

◮ 1957: Wu et al. discover Parity violation in β-decay of polarized 60CoWeak Interaction process: 60Co→ 60Ni + e− + νe


Left-Handed Neutrinos

◮ 1957: Landau, Lee & Yang, Salam propose that neutrinos are masslessand are only left-handed or right-handed

right-handed particle left-handed particle

~v ~v

mirror

◮ 1958: Goldhaber, Grodzins and Sunyar measure neutrino helicity:

LEFT-HANDED


Standard Model of ElectroWeak Interactions

◮ Glashow (1961), Weinberg (1967) and Salam (1968)

◮ Left-Handed Neutrinos νL and Right-Handed Antineutrinos νR

◮ Parity is violated: νLP−→✟✟❍❍νR νR

P−→��❅❅νL

◮ Particle-Antiparticle symmetry (Charge Conjugation) is violated:

νLC−→��❅❅νL νR

C−→✟✟❍❍νR

◮ CP is conserved (one or two generations): νLCP←−→νR

◮ 1964: Christenson, Cronin, Fitch and Turlay discover unexpectedviolation of CP in weak interactions of hadrons

◮ 1973: Kobayashi and Maskawa understand that CP violation requiresexistence of third generation: complex phase in mixing matrix


Standard Model: Three Generations

1st Generation 2nd Generation 3rd Generation

Quarks:

(

uLdL

)

uRdR

(

uRdR

)

uLdL

(

cLsL

)

cRsR

(

cRsR

)

cLsL

(

tLbL

)

tRbR

(

tRbR

)

tLbL

Leptons:

(

νeLeL

)

✟✟❍❍νeReR

(

νeReR

)

✟✟❍❍νeLeL

(

νµLµL

)

✟✟❍❍νµRµR

(

νµRµR

)

✚✚❩❩νµLµL

(

ντLτL

)

✘✘❳❳ντRτR

(

ντRτR

)

✟✟❍❍ντLτL

◮ No νR =⇒ No Dirac mass term LDνe ∼ mDνeRνeL

◮ Majorana Neutrino: ν = ν =⇒ νR = νR

Majorana mass term: LMνe ∼ mMνeRνeL = mMνeRνeL

forbidden by Standard Model SU(2)L × U(1)Y symmetry!

◮ In Standard Model neutrinos are massless!

◮ Experimentally allowed until 1998, when the Super-Kamiokandeatmospheric neutrino experiment obtained a model-independent proof of

Neutrino OscillationsC. Giunti − Neutrinos: Recent Results,,New Standard Model Paradigm,and Beyond − IN2P3 − 2 July 2013 − 6/26

Neutrino Oscillations

◮ 1957: Bruno Pontecorvo proposed Neutrino Oscillations in analogy withK 0 ⇆ K 0 oscillations (Gell-Mann and Pais, 1955)

◮ Flavor Neutrinos: νe , νµ, ντ produced in Weak Interactions

◮ Massive Neutrinos: ν1, ν2, ν3 propagate from Source to Detector

◮ A Flavor Neutrino is a superposition of Massive Neutrinos

|νe〉 = Ue1 |ν1〉+ Ue2 |ν2〉+ Ue3 |ν3〉|νµ〉 = Uµ1 |ν1〉+ Uµ2 |ν2〉+ Uµ3 |ν3〉|ντ 〉 = Uτ1 |ν1〉+ Uτ2 |ν2〉+ Uτ3 |ν3〉

◮ U is the 3× 3 unitary Neutrino Mixing Matrix


|ν(t = 0)〉=|νe〉 = Ue1 |ν1〉+ Ue2 |ν2〉+ Ue3 |ν3〉

νe

ν3

ν2

ν1

source propagation

νµ

detector

|ν(t > 0)〉 = Ue1 e−iE1t |ν1〉+ Ue2 e

−iE2t |ν2〉+ Ue3 e−iE3t |ν3〉6=|νe〉

E 2k = p2 +m2

k

at the detector there is a probability > 0 to see the neutrino as a νµ

Neutrino Oscillations are Flavor Transitions

νe → νµ νe → ντ νµ → νe νµ → ντνe → νµ νe → ντ νµ → νe νµ → ντ

transition probabilities depend on U and ∆m2kj ≡ m2

k −m2j


◮ Neutrino Oscillations are due to interference of different phases ofmassive neutrinos

◮ Phases of massive neutrinos depend on distance =⇒ Oscillations dependon distance L

◮ Relativistic neutrinos: ∆E ≃ ∆m2/E

◮ Pνe→νµ = sin2 2ϑeµ sin2

(

∆m2L

4E

)

distance

Pνe→νµ

1

0.8

0.6

0.4

0.2

0

◮ Oscillations measured without doubt for the first time by theSuper-Kamiokande atmospheric neutrino experiment in 1998C. Giunti − Neutrinos: Recent Results,,New Standard Model Paradigm,and Beyond − IN2P3 − 2 July 2013 − 9/26

Observations of Neutrino Oscillations

Solarνe → νµ, ντ

SNO, BOREXino

Super-Kamiokande

GALLEX/GNO, SAGE

Homestake, Kamiokande

VLBL Reactorνe disappearance

(KamLAND)

→

∆m2S ≃ 7.6× 10−5 eV2

sin2 ϑS ≃ 0.30

Atmosphericνµ → ντ

Super-Kamiokande

Kamiokande, IMB

MACRO, Soudan-2

LBL Acceleratorνµ disappearance

(K2K, MINOS, T2K)

LBL Acceleratorνµ → ντ

(Opera)

→

∆m2A ≃ 2.4× 10−3 eV2

sin2 ϑA ≃ 0.50

LBL Acceleratorνµ → νe

(T2K, MINOS)

LBL Reactorνe disappearance

(

Daya Bay, RENO

Double Chooz

)

→

∆m2A

sin2 ϑ13 ≃ 0.023


New SM Paradigm: Three-Neutrino Mixing

νe νµ ντ

∆m2A

∆m2S

ν2

ν1

ν3

m2

Normal Spectrum

m2

∆m2S

ν2

ν1

∆m2A

ν3

Inverted Spectrum

∆m2S = ∆m2

21 = 7.50 ± 0.20 × 10−5 eV2 uncertainty ≃ 2.6%

∆m2A = |∆m2

31| ≃ |∆m232| = 2.32+0.12

−0.08 × 10−3 eV2 uncertainty ≃ 5%


New Standard Model with Massive Neutrinos

Standard Model can be extended with νR

Dirac neutrino mass term LD ∼ mDνRνL ⇒ mD . 100GeV

surprise: Majorana neutrino mass for νR is allowed! LMR ∼ −1

2mM

R νRνR

Four degrees of freedom: νL , νR , νR , νL

Total neutrino mass term: LD+M ∼(

νL νR)

(

0 mD

mD mMR

)(

νLνR

)

mMR can be arbitrarily large (not protected by SM symmetries)

mMR ∼ scale of new physics beyond Standard Model ⇒ mM

R ≫ mD

diagonalization of

(

0 mD

mD mMR

)

⇒ mℓ ≃(mD)2

mMR

, mh ≃ mMR

νh

νℓ

see-saw mechanism

natural explanation of smallnessof light neutrino masses

massive neutrinos are Majorana!

3-GEN ⇒ effective low-energy 3-ν mixing

[Minkowski, PLB 67 (1977) 42]

[Yanagida (1979); Gell-Mann, Ramond, Slansky (1979); Mohapatra, Senjanovic, PRL 44 (1980) 912]


να =3∑

k=1

Uαkνk (α = e, µ, τ)

U =

c12c13 s12c13 s13e−iδ13

−s12c23−c12s23s13eiδ13 c12c23−s12s23s13e

iδ13 s23c13

s12s23−c12c23s13eiδ13 −c12s23−s12c23s13e

iδ13 c23c13

1 0 0

0 e iλ2 0

0 0 e iλ3

=

1 0 0

0 c23 s23

0 −s23 c23

ϑ23 = ϑA

sin2 ϑ23 ≃ 0.4− 0.6

c13 0 s13e−iδ13

0 1 0

−s13eiδ13 0 c13

Chooz, Palo Verde

T2K, MINOS

Daya Bay, RENO

sin2 ϑ13 = 0.023 ± 0.002

c12 s12 0

−s12 c12 0

0 0 1

ϑ12 = ϑS

sin2 ϑ12 = 0.30± 0.01

1 0 0

0 e iλ2 0

0 0 e iλ3

ββ0ν

δ sin2 ϑ23

sin2 ϑ23≃ 40%

δ sin2 ϑ13

sin2 ϑ13≃ 10%

δ sin2 ϑ12

sin2 ϑ12≃ 5%

δ13 6= 0, π =⇒ CP violation in ν osc.

Pνα→νβ 6= Pνα→νβ (α 6= β)


0

1

2

3

4

σN

23θ 2sin0.3 0.4 0.5 0.6 0.7

π/δ0.0 0.5 1.0 1.5 2.0

oscillation analysis

NHIH

[Fogli, Lisi, Marrone, Montanino, Palazzo, Rotunno,

PRD 86 (2012) 013012]

60

5

10

∆χ2

0.4 0.6

sin2θ23

13

3 -1 0 1

δ/π[Forero, Tortola, Valle, PRD 86 (2012) 073012]

0

5

10

15

∆χ2

00

5

10

15

∆χ2

0.3 0.4 0.5 0.6 0.7

sin2 θ23

0 90 180 270 360δCP

NO (Huber)NO (Free + RSBL)IO (Huber)IO (Free + RSBL)

[Gonzalez-Garcia, Maltoni, Salvado, Schwetz,

JHEP 12 (2012) 123; http://www.nu-fit.org]


Open Problems

◮ ϑ23 < 45◦ ?◮ Atmospheric ν, T2K, NOνA, . . . . . .

◮ Mass Hierarchy ?◮ NOνA, Atmospheric ν, Day Bay II, RENO-50, Supernova ν, . . .

◮ CP violation ?◮ NOνA, LAGUNA-LBNO, LBNE (USA), HyperK, . . .

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

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

◮ Beyond Three-Neutrino Mixing ? Sterile Neutrinos ?


Absolute Scale of Neutrino Masses

Lightest mass: m1 [eV]

m1,

m2,

m3

[e

V]

10−3 10−2 10−1 110−3

10−2

10−1

1

m1m2

m3

95% K

inematical Lim

it

95% K

ATR

IN S

ensitivity

95% C

osmological Lim

itNormal 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

]

10−3 10−2 10−1 110−3

10−2

10−1

1

m3

m1

m2

95% K

inematical Lim

it

95% K

ATR

IN S

ensitivity

95% C

osmological Lim

itInverted 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

95% Cosmological Limit: Planck + WMAP9 + highL + BAO [arXiv:1303.5076]


Majorana ν: Neutrinoless Double-Beta Decay

7632Ge

7633As

7634Se

Germanium

Arsenic

Selenium

β−

β+

β−β−

(T 0ν1/2)

−1 = G0ν |M0ν |2 m2

ββ

Effective Majorana Mass

mββ =

∣

∣

∣

∣

∣

3∑

k=1

U2ekmk

∣

∣

∣

∣

∣

32 protons + 42 neutrons

n p

n p

e−

e−

7632Ge

7634Se

44n32 p 34 p

42n

νe

νe

KamLAND-Zen + EXO13654Xe→

13656Ba + e− + e−

[PRL 109 (2012) 032505; arXiv:1211.3863]

T 0ν1/2 > 1.9×1025 y (90%C.L.)

|mββ| . 0.12 − 0.25 eV


Three Active Neutrinos ⇔ Three Generations

10

10 2

10 3

10 4

10 5

0 20 40 60 80 100 120 140 160 180 200 220

Centre-of-mass energy (GeV)

Cro

ss-s

ecti

on (

pb)

CESRDORIS

PEP

PETRATRISTAN

KEKBPEP-II

SLC

LEP I LEP II

Z

W+W-

e+e−→hadrons

0

10

20

30

86 88 90 92 94Ecm [GeV]

σ had

[nb]

3ν

2ν

4ν

average measurements,error bars increased by factor 10

ALEPHDELPHIL3OPAL

[LEP, Phys. Rept. 427 (2006) 257, arXiv:hep-ex/0509008]

ΓZ =∑

ℓ=e,µ,τ

ΓZ→ℓℓ +∑

q 6=t

ΓZ→qq + Γinv Γinv = Nνa ΓZ→νν

Nνa = 2.9840 ± 0.0082


Beyond 3ν Mixing =⇒ Sterile Neutrinos

ν1

m21 logm2m2

2

ν2 ν3

m23

νe

νµ

ντνs1 · · ·

ν4 ν5 · · ·

m24 m2

5

νs2

3ν-mixing

∆m2ATM ∆m2

SBL∆m2SOL


Light Sterile Neutrinos

◮ Sterile means no standard model interactions

◮ Active neutrinos (νe , νµ, ντ ) can oscillate into light sterile neutrinos (νs)

◮ Observables:

◮ Disappearance of active neutrinos (neutral current deficit)

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

◮ Short-baseline anomalies + 3ν-mixing:

∆m221 ≪ |∆m2

31| ≪ |∆m241| ≤ . . .

ν1 ν2 ν3 ν4 . . .νe νµ ντ νs1 . . .


LSND[PRL 75 (1995) 2650; PRC 54 (1996) 2685; PRL 77 (1996) 3082; PRD 64 (2001) 112007]

νµ → νe L ≃ 30m 20MeV ≤ E ≤ 200MeV

other

p(ν_

e,e+)n

p(ν_

µ→ν_

e,e+)n

L/Eν (meters/MeV)

Bea

m E

xces

s

Beam Excess

0

2.5

5

7.5

10

12.5

15

17.5

0.4 0.6 0.8 1 1.2 1.4 10-2

10-1

1

10

10 2

10-3

10-2

10-1

1sin2 2θ

∆m2 (

eV2 /c

4 )

BugeyKarmen

NOMAD

CCFR

90% (Lmax-L < 2.3)99% (Lmax-L < 4.6)

3.8σ excess ∆m2LSND & 0.2 eV2 (≫ ∆m2

A ≫ ∆m2S)


MiniBooNE

L ≃ 541m 200MeV ≤ E . 3GeV

νµ → νe [PRL 102 (2009) 101802]

LSND signal

νµ → νe [PRL 110 (2013) 161801]

LSND signal

◮ Agreement with LSND signal?

◮ CP violation?

◮ Low-energy anomaly!Neutrino energy reconstruction problem? [Martini, Ericson, Chanfray, PRD 85 (2012) 093012]


Reactor Electron Antineutrino Anomaly

[Mention, Fechner, Lasserre, Mueller,

Lhuillier, Cribier, Letourneau,

PRD 83 (2011) 073006]

[update in White Paper, arXiv:1204.5379]

new reactor νe fluxes[Mueller, Lhuillier, Fallot, Letourneau,

Cormon, Fechner, Giot, Lasserre, Martino,

Mention, Porta, Yermia,

PRC 83 (2011) 054615]

[Huber, PRC 84 (2011) 024617]

2.8σ anomaly0 20 40 60 80 100

0.7

0.8

0.9

1.0

1.1

1.2

L [m]

R

R = 0.930 ± 0.024

Reactor Rates

Bugey3−15Bugey3−40Bugey3−95Bugey4−15ROVNO−18Gosgen−38

Gosgen−45Gosgen−65ILL−9Krasno−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 Global Fit[Giunti, Laveder, Y.F. Li, H.W. Long, in preparation (2013)]

sin22ϑeµ

∆m412

[e

V2 ]

10−4 10−3 10−2 10−1 110−1

1

10

+

10−4 10−3 10−2 10−1 110−1

1

10

+

3+1 − GLO

68.27% CL90.00% CL95.45% CL99.00% CL99.73% CL

3+1 − 3σνe DISνµ DISDISAPP

No Osc. GoF = 1%3+1 GoF = 33%PGoF = 10%

◮ APP νµ → νe & νµ → νe :LSND (Y), MiniBooNE (?),OPERA (N), ICARUS (N),KARMEN (N), NOMAD (N),BNL-E776 (N)

◮ DIS νe & νe : Reactors (Y),Gallium (Y), νeC (N),Solar (N)

◮ DIS νµ & νµ: CDHSW (N),MINOS (N),Atmospheric (N),MiniBooNE/SciBooNE (N)

[see also Kopp, Machado,

Maltoni, Schwetz, JHEP 1305 (2013) 050]


Conclusions◮ Robust New Standard Model Paradigm: Three-Neutrino Mixing

Experimental problems: ϑ23 < 45◦?, CP Violation, Mass Hierarchy,Absolute Mass Scale, Dirac or Majorana?Theoretical problems: Why lepton mixing is so different from quarkmixing? Is it due to Majorana nature of ν’s?Why 0 < sin2 ϑ13 ≪ sin2 ϑ12 < sin2 ϑ23 ≃ 0.5?

◮ Short-Baseline νe and νe Disappearance:◮ Reactor νe and Gallium νe anomalies

◮ Many promising projects to test short-baseline νe and νe disappearance in afew years with reactors and radioactive sources

◮ Independent tests through effect of m4 in β-decay and (ββ)0ν -decay

◮ Short-Baseline νµ → νe LSND Signal:◮ MiniBooNE experiment has been inconclusive

◮ If |Ue4| > 0 why not |Uµ4| > 0? =⇒ Maybe LSND luckily observed afluctuation of a small νµ → νe transition probability with amplitudesin2 2ϑeµ = 4|Ue4|2|Uµ4|2, not seen by other appearance experiments

◮ Better experiments are needed to check LSND signalC. Giunti − Neutrinos: Recent Results,,New Standard Model Paradigm,and Beyond − IN2P3 − 2 July 2013 − 26/26

Backup Slides


Mass Hierarchy

1. Matter Effect (Atmospheric, Long-Baseline, Supernova Experiments):

◮ νe ⇆ νµ MSW resonance: V =∆m2

13 cos 2ϑ13

2E⇔ ∆m2

13 > 0 NH

◮ νe ⇆ νµ MSW resonance: V = −∆m2

13 cos 2ϑ13

2E⇔ ∆m2

13 < 0 IH

2. Phase Difference (Reactor νe → νe):

Normal Hierarchy

|∆m231|

q

|∆m232|+|∆m2

21|

|∆m231| > |∆m2

32|ν2

ν1

ν3

m2 m2

ν2

ν1

ν3

Inverted Hierarchy

|∆m231|

q

|∆m232|−|∆m2

21|

|∆m231| < |∆m2

32|


CP Violation

Pνα→νβ − Pνα→νβ = −16Jαβ sin

(

∆m221L

4E

)

sin

(

∆m231L

4E

)

sin

(

∆m232L

4E

)

Jαβ = Im(Uα1U∗α2U

∗β1Uβ2) = ±J

J = s12c12s23c23s13c213 sin δ13

Necessary conditions for observation of CP violation:

◮ Sensitivity to all mixing angles, including small ϑ13

◮ Sensitivity to oscillations due to ∆m221 and ∆m2

31


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 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 |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 95% Bound

KATRIN 95% Sensitivity

95% C

osmological Lim

it10−3 10−2 10−1 1 10

10−3

10−2

10−1

1

10

1σ2σ3σ

◮ Quasi-Degenerate:

m2β ≃ m2

ν

∑

k |Uek |2 = m2

ν

◮ Inverted Hierarchy:

m2β ≃ (1− s213)∆m2

A ≃ ∆m2A

◮ Normal Hierarchy:

m2β ≃ s212c

213∆m2

S + s213∆m2A

≃ 2× 10−5 + 6× 10−5 eV2

◮ mβ . 4× 10−2 eV⇓

Normal Spectrum


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)

α2

α3

U 2

e1m1

mββ

Re[mββ]

U 2

e3m3

Im[mββ]

U 2

e2m2

α3

α2

U 2

e1m1 Re[mββ]

Im[mββ]

U 2

e3m3 U 2

e2m2

|mββ| = 0


Experimental Bounds

KamLAND-Zen (136Xe) [arXiv:1211.3863]

T 0ν1/2 > 1.9× 1025 y (90% C.L.) =⇒ |mββ | . 0.12− 0.25 eV (KLZ+EXO)

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 of ββ0ν-Decay[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]

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

very exciting: Majorana ν and large mass scale

partially excluded by KamLAND-Zen, EXO and CUORICINO


Xe (yr)136 1/2T

Ge

(yr)

76 1/

2T

0.2

0.3

0.4

0.5

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.2

0.3

0.4

0.5

0.6

0.7

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

2410 2510 26102410

2510

2610

EX

O-2

0090

% C

.L.

Kam

LAN

D-Z

enK

amLA

ND

90%

C.L

.

Com

bine

d90

% C

.L.

GCM

NSM

IBM

-2

(R)Q

RPA

KK 68% C.L.

[KamLAND-Z

en,arX

iv:1211.3863]


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 95% C

osmological Lim

it

Current 90% 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

m1 & 10−3 eV⇒cancellation?

|mββ | . 10−2 eV =⇒ Normal Spectrum


Effective SBL Oscillation Probabilities in 3+1 Schemes

Pνα→νβ = sin2 2ϑαβ sin2

(

∆m241L

4E

)

sin2 2ϑαβ = 4|Uα4|2|Uβ4|

2

No CP Violation!

Pνα→να = 1− sin2 2ϑαα sin2(

∆m241L

4E

)

sin2 2ϑαα = 4|Uα4|2(

1− |Uα4|2)

Perturbation of 3ν Mixing

|Ue4|2 ≪ 1 , |Uµ4|

2 ≪ 1 , |Uτ4|2 ≪ 1 , |Us4|

2 ≃ 1

Ue4

Uµ4

Uτ4

Us4

Uτ3

Ue3

Uµ3

Us3

Uµ2

Uτ2

Ue2

Us2

Uτ1

Ue1

Uµ1

Us1

U =

SBL

sin2 2ϑαα ≪ 1

⇓

|Uα4|2 ≃

sin2 2ϑαα

4


Cosmology

◮ Relativistic energy density before photon decoupling:

ρR =

[

1 +7

8

(

4

11

)4/3

Neff

]

ργ

◮ Neff = effective neutrino number

◮ Neff = 3.046 + Ns

◮ Ns = effective number of sterile neutrinos (not necessarily integer)


Planck[arXiv:1303.5076]

Neff < 3.80 meffν,sterile < 0.42 (95%;CMB + BAO)

◮ meffν,sterile ≡ 94.1ων4 eV

◮ Thermally distributed:

fs(E ) =1

eE/Ts + 1

meffν,sterile =

(

Ts

Tν

)3

m4

= (∆Neff)3/4m4

◮ Dodelson-Widrow:

fs(E ) =χ

eE/Tν + 1

meffν,sterile = χsm4


Standard Cosmological Scenario Mixing Bounds[Mirizzi, Mangano, Saviano, Borriello, Giunti, Miele, Pisanti, arXiv:1303.5368]

10-110-210-310-410-5

10-1

10-2

10-3

10-4

10-5

1

101

102

sin2Θ14

Dm

412He

V2 L

L 41 34

KATRIN

10-2

10-1.5

10-3

sin 2Θ

24 =0

SBL

sol. upturn

10-110-210-310-410-5

10-1

10-2

10-3

10-4

10-5

1

101

102

sin2Θ24

Dm

412He

V2 L

L 41 34

ΝΜ disap.

SBL

10-2

10-1.5

10-3

sin 2Θ14 =

0

Non-standard mechanism for partial thermalization of νs is neededLarge primordial neutrino asymmetry?

[Hannestad, Tamborra, Tram, JCAP 1207 (2012) 025; Mirizzi, Saviano, Miele, Serpico, PRD 86 (2012) 053009;

Saviano, Mirizzi, Pisanti, Serpico, Mangano, Miele, PRD 87 (2013) 073006]


CMB + H0[Gariazzo, Giunti, Laveder, in preparation (2013)]

H0 =

67.4 ± 1.4 Planck70.0 ± 2.2 WMAP-973.8 ± 2.4 Cepheids+SNIa74.3 ± 2.6 Carnegie HP78.7 ± 4.5 COSMOGRAIL

[kms−1Mpc−1]

Gaussian Prior: H0 = 74.7 ± 1.6 kms−1Mpc−1

weighted average of Cepheids+SNIa, Carnegie HP, COSMOGRAIL


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