Eligio  Lisi    

INFN,  Bari,  Italy  

 

 3ν  masses,  mixings  and  CPV  phases:  status  and  prospects    Tensions  in  flavor  measurements:  A  path  towards  BSM  physics  -­‐  Naples,  24  May  2017    

 

Oscar  Ricciardi  (1864-­‐1935),  Marina  di  Napoli  

 Main  results  based  on:  

 F.  Capozzi,  E.  Di  ValenCno,  E.  Lisi,  A.  Marrone,  A.  Melchiorri,  A.  Palazzo,    

“Global  constraints  on  absolute  neutrino  masses  and  their  ordering”  arXiv:1703/04471  [PRD  in  press]  

 

 See  also:  

 F.  Capozzi,  E.  Lisi,  A.  Marrone,  D.  Montanino,  A.  Palazzo,  arXiv:1601/07777  [Special  Issue  of  NPB  celebraCng  the  2015  Nobel  Prize  for  neutrino  oscillaCons]  

 

2  

OUTLINE:  

•  IntroducNon  •  Knowns  and  unknowns  from  3ν  oscillaNons  •  NonoscillaNon  constraints  from  0νββ  &  Cosmology  •  Combining  oscillaNon  +  nonoscillaNon  data    •  Summary  and  prospects  

3  

4  

IntroducCon  

Established facts: α à β oscillations in vacuum and matter...

a

b

c

d

e

f

g

eàe ( δm2 , θ12 )

eàe ( δm2 , θ12 )

µàµ ( Δm2 , θ23 )

µàµ ( Δm2 , θ23 )

eàe ( Δm2 , θ13 )

µàe ( Δm2 , θ13 , θ23 )

µàτ ( Δm2 , θ23 ) Data from various types of neutrino experiments: (a) solar, (b) long-baseline reactor, (c) atmospheric, (d) long-baseline accelerator, (e) short-baseline reactor, (f,g) long baseline accelerator (and, in part, atmospheric). (a) KamLAND [plot]; (b) Borexino [plot], Homestake, Super-K, SAGE, GALLEX/GNO, SNO; (c) Super-K atmosph. [plot], DeepCore, MACRO, MINOS etc.; (d) T2K (plot), MINOS, K2K; (e) Daya Bay [plot], RENO, Double Chooz; (f) T2K [plot], MINOS, NOvA; (g) OPERA [plot], Super-K atmospheric.

5  

...can be interpreted in a simple 3ν theoretical framework

a

b

c

d

e

f

g

eàe ( δm2 , θ12 )

eàe ( δm2 , θ12 )

µàµ ( Δm2 , θ23 )

µàµ ( Δm2 , θ23 )

eàe ( Δm2 , θ13 )

µàe ( Δm2 , θ13 , θ23 )

µàτ ( Δm2 , θ23 )

δm2 |Δm2| θ12 θ23 θ13  Five parameters measured so far:

6  

Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix

[ only if Majorana ]

Mass (squared) spectrum

Mixing angles θ23, θ13, θ12 CP-violat. phase(s) δ (α, β)

1 2

1 2

δm2

δm2 Δm2

Δm2 “Normal” Hierarchy

or Ordering

“Inverted” Hierarchy

or Ordering

Squared mass splittings δm2, |Δm2| Ordering = sign(Δm2) [+ abs. mass scale]

7  

U↵i =

2

41 0 00 c23 s230 �s23 c23

3

5

2

4c13 0 s13e�i�

0 1 0�s13ei� 0 c13

3

5

2

4c12 s12 0�s12 c12 00 0 1

3

5

2

41 0 00 ei↵/2 00 0 ei�/2

3

5

+ matter effects ~ GF . E . density

Parameters of the 3ν theoretical framework  

“Broad-brush” 3ν picture (with 1-digit accuracy)

+Δm2

δm2 m2ν

ν2 ν1

ν3

ν3 -Δm2

8  

e µ τ  

δm2 ~ 7 x 10-5 eV2

Δm2 ~ 2 x 10-3 eV2

sin2θ12 ~ 0.3 sin2θ23 ~ 0.5 sin2θ13 ~ 0.02

δ (CP)

sign(Δm2) = ordering

octant(θ23) absolute mass scale Dirac/Majorana nature

Knowns:   Unknowns:  

9  

CPV:  In  ν  oscillaCons,  driven  only  by  δ (Majorana  phases  -­‐if  any-­‐  decouple)    

P (⌫↵ ! ⌫�)� P (⌫↵ ! ⌫�) / JPMNS

JPMNS =

1

8

sin 2✓12 sin 2✓23 sin 2✓13 cos ✓13 sin �

[Valid  in  vacuum.  In  ma_er,  oscillaNon  pick  up  further  (background)  CPV  effects]  

' 3⇥ 10�2 sin �

[JCKM ' 3⇥ 10�5]

=      known    x    unknown  

If  |sinδ|  ~  1  (maximal  CPV)  à  JPMNS  ~  103  JCKM  

Remark  

more  on...  

Knowns  and  unknowns    from  3ν  oscillaCons  

10  

From a “broad-brush” to a more detailed picture, circa 2017

Global analysis includes increasingly rich oscillation data sets:

LBL Acc + Solar + KL LBL Acc + Solar + KL + SBL Reactor LBL Acc + Solar + KL + SBL Reactor + Atmosph.

(Δm2 , θ13 , θ23) + (δm2 , θ12) + sublead.

...+(Δm2 , θ13)

Parameters not shown are marginalized away

C.L.’s refer to Nσ = √ Δχ2 = 1, 2, 3, ...

NO / IO = Normal / Inverted Ordering

11  

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

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��θ�VLQ��� ��� ��� ��� ���

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12,2

Current 1σ errors (1/6 of ±3σ range):

Note: Δm2 = (Δm2

31 + Δm232)/2

Five known oscillation parameters:

δm2 2.3 % Δm2 1.6 % sin2θ12 5.8 % sin2θ13 4.0 % sin2θ23 ~ 9 %

all  <  10%...    

Precision Era!

[but PMNS still very far from

CKM accuracy]

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

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��θ�VLQ��� ��� ��� ��� ���

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12,2

12  

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

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��θ�VLQ��� ��� ��� ��� ���

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12,2

θ23 octant

δCP  

Three unknown oscillation parameters

NO or IO 12e2sin0.25 0.30 0.35

0

1

2

3

4

23e2sin0.3 0.4 0.5 0.6 0.7

13e2sin0.01 0.02 0.03 0.04

2 eV -5/102mb6.5 7.0 7.5 8.0 8.50

1

2

3

4

2 eV -3/102m62.0 2.2 2.4 2.6 2.8

//b0.0 0.5 1.0 1.5 2.0

LBL Acc + Solar + KL + SBL Reactors

mNmN

NHIH

12e2sin0.25 0.30 0.35

0

1

2

3

4

23e2sin0.3 0.4 0.5 0.6 0.7

13e2sin0.01 0.02 0.03 0.04

2 eV -5/102mb6.5 7.0 7.5 8.0 8.50

1

2

3

4

2 eV -3/102m62.0 2.2 2.4 2.6 2.8

//b0.0 0.5 1.0 1.5 2.0

LBL Acc + Solar + KL + SBL Reactors

mNmN

NHIH

P (⌫↵ ! ⌫�)� P (⌫↵ ! ⌫�) / JPMNS

13  

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

2 eV-5/102mδ6.5 7 7.5 8 8.5

2 eV-3/102mΔ2 2.2 2.4 2.6 2.8

π/δ0 0.5 1 1.5 2

12θ2sin0.25 0.3 0.35

23θ2sin0.3 0.4 0.5 0.6 0.7

13θ2sin0.01 0.015 0.02 0.025 0.03

σN

0

1

2

3

4

σN

0

1

2

3

4

LBL Acc + Solar + KamLAND

NHIH

LBL+Sol+KL

θ23

Δχ2 (IO-NO)  

octant

+1.1

12e2sin0.25 0.30 0.35

0

1

2

3

4

23e2sin0.3 0.4 0.5 0.6 0.7

13e2sin0.01 0.02 0.03 0.04

2 eV -5/102mb6.5 7.0 7.5 8.0 8.50

1

2

3

4

2 eV -3/102m62.0 2.2 2.4 2.6 2.8

//b0.0 0.5 1.0 1.5 2.0

LBL Acc + Solar + KL + SBL Reactors

mNmN

NHIH

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

2 eV-5/102mδ6.5 7 7.5 8 8.5

2 eV-3/102mΔ2 2.2 2.4 2.6 2.8

π/δ0 0.5 1 1.5 2

12θ2sin0.25 0.3 0.35

23θ2sin0.3 0.4 0.5 0.6 0.7

13θ2sin0.01 0.015 0.02 0.025 0.03

σN

0

1

2

3

4

σN

0

1

2

3

4

LBL Acc + Solar + KamLAND

NHIH

12e2sin0.25 0.30 0.35

0

1

2

3

4

23e2sin0.3 0.4 0.5 0.6 0.7

13e2sin0.01 0.02 0.03 0.04

2 eV -5/102mb6.5 7.0 7.5 8.0 8.50

1

2

3

4

2 eV -3/102m62.0 2.2 2.4 2.6 2.8

//b0.0 0.5 1.0 1.5 2.0

LBL Acc + Solar + KL + SBL Reactors

mNmN

NHIH

δCP  

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

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12,2

More on unknown oscillation parameters: 14  

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

2 eV-5/102mδ6.5 7 7.5 8 8.5

2 eV-3/102mΔ2 2.2 2.4 2.6 2.8

π/δ0 0.5 1 1.5 2

12θ2sin0.25 0.3 0.35

23θ2sin0.3 0.4 0.5 0.6 0.7

13θ2sin0.01 0.02 0.03

σN

0

1

2

3

4

σN

0

1

2

3

4

LBL Acc + Solar + KamLAND + SBL Reactors

NHIH

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

2 eV-5/102mδ6.5 7 7.5 8 8.5

2 eV-3/102mΔ2 2.2 2.4 2.6 2.8

π/δ0 0.5 1 1.5 2

12θ2sin0.25 0.3 0.35

23θ2sin0.3 0.4 0.5 0.6 0.7

13θ2sin0.01 0.015 0.02 0.025 0.03

σN

0

1

2

3

4

σN

0

1

2

3

4

LBL Acc + Solar + KamLAND

NHIH

LBL+Sol+KL +SBL Reac

θ23

Δχ2 (IO-NO)  

octant

+1.1 +1.1

12e2sin0.25 0.30 0.35

0

1

2

3

4

23e2sin0.3 0.4 0.5 0.6 0.7

13e2sin0.01 0.02 0.03 0.04

2 eV -5/102mb6.5 7.0 7.5 8.0 8.50

1

2

3

4

2 eV -3/102m62.0 2.2 2.4 2.6 2.8

//b0.0 0.5 1.0 1.5 2.0

LBL Acc + Solar + KL + SBL Reactors

mNmN

NHIH

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

2 eV-5/102mδ6.5 7 7.5 8 8.5

2 eV-3/102mΔ2 2.2 2.4 2.6 2.8

π/δ0 0.5 1 1.5 2

12θ2sin0.25 0.3 0.35

23θ2sin0.3 0.4 0.5 0.6 0.7

13θ2sin0.01 0.015 0.02 0.025 0.03

σN

0

1

2

3

4

σN

0

1

2

3

4

LBL Acc + Solar + KamLAND

NHIH

12e2sin0.25 0.30 0.35

0

1

2

3

4

23e2sin0.3 0.4 0.5 0.6 0.7

13e2sin0.01 0.02 0.03 0.04

2 eV -5/102mb6.5 7.0 7.5 8.0 8.50

1

2

3

4

2 eV -3/102m62.0 2.2 2.4 2.6 2.8

//b0.0 0.5 1.0 1.5 2.0

LBL Acc + Solar + KL + SBL Reactors

mNmN

NHIH

δCP  

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

2 eV-5/102mδ6.5 7 7.5 8 8.5

2 eV-3/102mΔ2 2.2 2.4 2.6 2.8

π/δ0 0.5 1 1.5 2

12θ2sin0.25 0.3 0.35

23θ2sin0.3 0.4 0.5 0.6 0.7

13θ2sin0.01 0.02 0.03

σN

0

1

2

3

4

σN

0

1

2

3

4

LBL Acc + Solar + KamLAND + SBL Reactors

NHIH

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

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12,2

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

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��θ�VLQ��� ��� ��� ��� ���

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12,2

More on unknown oscillation parameters: 15  

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

2 eV-5/102mδ6.5 7 7.5 8 8.5

2 eV-3/102mΔ2 2.2 2.4 2.6 2.8

π/δ0 0.5 1 1.5 2

12θ2sin0.25 0.3 0.35

23θ2sin0.3 0.4 0.5 0.6 0.7

13θ2sin0.01 0.02 0.03

σN

0

1

2

3

4

σN

0

1

2

3

4

LBL Acc + Solar + KamLAND + SBL Reactors

NHIH

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

2 eV-5/102mδ6.5 7 7.5 8 8.5

2 eV-3/102mΔ2 2.2 2.4 2.6 2.8

π/δ0 0.5 1 1.5 2

12θ2sin0.25 0.3 0.35

23θ2sin0.3 0.4 0.5 0.6 0.7

13θ2sin0.01 0.015 0.02 0.025 0.03

σN

0

1

2

3

4

σN

0

1

2

3

4

LBL Acc + Solar + KamLAND

NHIH

LBL+Sol+KL +SBL Reac +Atmos

θ23

Δχ2 (IO-NO)  

octant

+1.1 +1.1 +3.6

Max-mixing disfavored; octant flips with NO/IO

[difficult to solve the ambiguity]

Intriguing! NO favored

12e2sin0.25 0.30 0.35

0

1

2

3

4

23e2sin0.3 0.4 0.5 0.6 0.7

13e2sin0.01 0.02 0.03 0.04

2 eV -5/102mb6.5 7.0 7.5 8.0 8.50

1

2

3

4

2 eV -3/102m62.0 2.2 2.4 2.6 2.8

//b0.0 0.5 1.0 1.5 2.0

LBL Acc + Solar + KL + SBL Reactors

mNmN

NHIH

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

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��θ�VLQ��� ��� ��� ��� ���

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12,2

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

2 eV-5/102mδ6.5 7 7.5 8 8.5

2 eV-3/102mΔ2 2.2 2.4 2.6 2.8

π/δ0 0.5 1 1.5 2

12θ2sin0.25 0.3 0.35

23θ2sin0.3 0.4 0.5 0.6 0.7

13θ2sin0.01 0.015 0.02 0.025 0.03

σN

0

1

2

3

4

σN

0

1

2

3

4

LBL Acc + Solar + KamLAND

NHIH

12e2sin0.25 0.30 0.35

0

1

2

3

4

23e2sin0.3 0.4 0.5 0.6 0.7

13e2sin0.01 0.02 0.03 0.04

2 eV -5/102mb6.5 7.0 7.5 8.0 8.50

1

2

3

4

2 eV -3/102m62.0 2.2 2.4 2.6 2.8

//b0.0 0.5 1.0 1.5 2.0

LBL Acc + Solar + KL + SBL Reactors

mNmN

NHIH

δCP  

sin δ ~ -1 (or sin δ < 0)

favored; sin δ ~ +1 excluded

[next talk; stay tuned!] 6.5 7 7.5 8 8.5

0

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

2 eV-5/102mδ6.5 7 7.5 8 8.5

2 eV-3/102mΔ2 2.2 2.4 2.6 2.8

π/δ0 0.5 1 1.5 2

12θ2sin0.25 0.3 0.35

23θ2sin0.3 0.4 0.5 0.6 0.7

13θ2sin0.01 0.02 0.03

σN

0

1

2

3

4

σN

0

1

2

3

4

LBL Acc + Solar + KamLAND + SBL Reactors

NHIH

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

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12,2

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

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12,2

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

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12,2

More on unknown oscillation parameters: 16  

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

2 eV-5/102mδ6.5 7 7.5 8 8.5

2 eV-3/102mΔ2 2.2 2.4 2.6 2.8

π/δ0 0.5 1 1.5 2

12θ2sin0.25 0.3 0.35

23θ2sin0.3 0.4 0.5 0.6 0.7

13θ2sin0.01 0.015 0.02 0.025 0.03

σN

0

1

2

3

4

σN

0

1

2

3

4

LBL Acc + Solar + KamLAND

NHIH

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

2 eV-5/102mδ6.5 7 7.5 8 8.5

2 eV-3/102mΔ2 2.2 2.4 2.6 2.8

π/δ0 0.5 1 1.5 2

12θ2sin0.25 0.3 0.35

23θ2sin0.3 0.4 0.5 0.6 0.7

13θ2sin0.01 0.02 0.03

σN

0

1

2

3

4

σN

0

1

2

3

4

LBL Acc + Solar + KamLAND + SBL Reactors

NHIH

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

2 eV-5/102mδ6.5 7 7.5 8 8.5

2 eV-3/102mΔ2 2.2 2.4 2.6 2.8

π/δ0 0.5 1 1.5 2

12θ2sin0.25 0.3 0.35

23θ2sin0.3 0.4 0.5 0.6 0.7

13θ2sin0.01 0.015 0.02 0.025 0.03

σN

0

1

2

3

4

σN

0

1

2

3

4

LBL Acc + Solar + KamLAND

NHIH

LBL+Sol+KL +SBL Reac +Atmos

θ23

Δχ2 (IO-NO)  

octant

+1.1 +1.1 +3.6

12e2sin0.25 0.30 0.35

0

1

2

3

4

23e2sin0.3 0.4 0.5 0.6 0.7

13e2sin0.01 0.02 0.03 0.04

2 eV -5/102mb6.5 7.0 7.5 8.0 8.50

1

2

3

4

2 eV -3/102m62.0 2.2 2.4 2.6 2.8

//b0.0 0.5 1.0 1.5 2.0

LBL Acc + Solar + KL + SBL Reactors

mNmN

NHIH

Compare the current results (circa 2017) with...

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

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12,2

12e2sin0.25 0.30 0.35

0

1

2

3

4

23e2sin0.3 0.4 0.5 0.6 0.7

13e2sin0.01 0.02 0.03 0.04

2 eV -5/102mb6.5 7.0 7.5 8.0 8.50

1

2

3

4

2 eV -3/102m62.0 2.2 2.4 2.6 2.8

//b0.0 0.5 1.0 1.5 2.0

LBL Acc + Solar + KL + SBL Reactors

mNmN

NHIH

δCP  

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

2 eV-5/102mδ6.5 7 7.5 8 8.5

2 eV-3/102mΔ2 2.2 2.4 2.6 2.8

π/δ0 0.5 1 1.5 2

12θ2sin0.25 0.3 0.35

23θ2sin0.3 0.4 0.5 0.6 0.7

13θ2sin0.01 0.02 0.03

σN

0

1

2

3

4

σN

0

1

2

3

4

LBL Acc + Solar + KamLAND + SBL Reactors

NHIH

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

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12,2

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

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12,2

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

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12,2

17  

2 eV-5/102mb6.5 7 7.5 8 8.5

2 eV-3/102m62 2.2 2.4 2.6 2.8

//b0 0.5 1 1.5 2

12e2sin0.25 0.3 0.35

23e2sin0.3 0.4 0.5 0.6 0.7

13e2sin0.01 0.02 0.03 0.04

mN

0

1

2

3

4

mN

0

1

2

3

4

LBL Acc + Solar + KamLAND

NHIH

2 eV-5/102mb6.5 7 7.5 8 8.5

2 eV-3/102m62 2.2 2.4 2.6 2.8

//b0 0.5 1 1.5 2

12e2sin0.25 0.3 0.35

23e2sin0.3 0.4 0.5 0.6 0.7

13e2sin0.01 0.02 0.03

mN

0

1

2

3

4

mN

0

1

2

3

4

LBL Acc + Solar + KamLAND + SBL Reactors + Atmos

NHIH

2 eV-5/102mb6.5 7 7.5 8 8.5

2 eV-3/102m62 2.2 2.4 2.6 2.8

//b0 0.5 1 1.5 2

12e2sin0.25 0.3 0.35

23e2sin0.3 0.4 0.5 0.6 0.7

13e2sin0.01 0.02 0.03

mN

0

1

2

3

4

mN

0

1

2

3

4

LBL Acc + Solar + KamLAND + SBL Reactors

NHIH

2 eV-5/102mb6.5 7 7.5 8 8.5

2 eV-3/102m62 2.2 2.4 2.6 2.8

//b0 0.5 1 1.5 2

12e2sin0.25 0.3 0.35

23e2sin0.3 0.4 0.5 0.6 0.7

13e2sin0.01 0.02 0.03 0.04

mN

0

1

2

3

4

mN

0

1

2

3

4

LBL Acc + Solar + KamLAND

NHIH

LBL+Sol+KL +SBL Reac +Atmos

θ23

Δχ2 (IO-NO)  

octant

-1.2 -0.9 +1.0

12e2sin0.25 0.30 0.35

0

1

2

3

4

23e2sin0.3 0.4 0.5 0.6 0.7

13e2sin0.01 0.02 0.03 0.04

2 eV -5/102mb6.5 7.0 7.5 8.0 8.50

1

2

3

4

2 eV -3/102m62.0 2.2 2.4 2.6 2.8

//b0.0 0.5 1.0 1.5 2.0

LBL Acc + Solar + KL + SBL Reactors

mNmN

NHIH

12e2sin0.25 0.30 0.35

0

1

2

3

4

23e2sin0.3 0.4 0.5 0.6 0.7

13e2sin0.01 0.02 0.03 0.04

2 eV -5/102mb6.5 7.0 7.5 8.0 8.50

1

2

3

4

2 eV -3/102m62.0 2.2 2.4 2.6 2.8

//b0.0 0.5 1.0 1.5 2.0

LBL Acc + Solar + KL + SBL Reactors

mNmN

NHIH

δCP  

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

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12,2

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

��H9������P�� � ��� � ���

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��θ�VLQ��� ��� ��� ��� ���

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12,2

2 eV-5/102mb6.5 7 7.5 8 8.5

2 eV-3/102m62 2.2 2.4 2.6 2.8

//b0 0.5 1 1.5 2

12e2sin0.25 0.3 0.35

23e2sin0.3 0.4 0.5 0.6 0.7

13e2sin0.01 0.02 0.03

mN

0

1

2

3

4

mN

0

1

2

3

4

LBL Acc + Solar + KamLAND + SBL Reactors

NHIH

2 eV-5/102mb6.5 7 7.5 8 8.5

2 eV-3/102m62 2.2 2.4 2.6 2.8

//b0 0.5 1 1.5 2

12e2sin0.25 0.3 0.35

23e2sin0.3 0.4 0.5 0.6 0.7

13e2sin0.01 0.02 0.03

mN

0

1

2

3

4

mN

0

1

2

3

4

LBL Acc + Solar + KamLAND + SBL Reactors + Atmos

NHIH

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

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12,2

... 1yr ago, 2016: trends were somewhat weaker 18  

Current  indicaCon  Δχ2ΙΟ-ΝΟ  = 3.6 from  oscill.  data  starts  to  be  interesCng.

Useful  to  see  the  effect  of  excluding/including  this  offset  in  the  analysis:

6.5 7 7.5 8 8.50

1

2

3

4

2 2.2 2.4 2.6 2.80

1

2

3

4

0 0.5 1 1.5 20

1

2

3

4

0.25 0.3 0.350

1

2

3

4

0.01 0.015 0.02 0.025 0.030

1

2

3

4

0.3 0.4 0.5 0.6 0.70

1

2

3

4

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12,2

6.5 7 7.5 8 8.50

5

10

15

2.4 2.5 2.6 2.70

5

10

15

0 0.5 1 1.5 20

5

10

15

0.25 0.3 0.350

5

10

15

1.8 2 2.2 2.4 2.60

5

10

15

0.3 0.4 0.5 0.6 0.70

5

10

15

2 eV-5/102mδ6.5 7 7.5 8 8.5

2 eV-3/102mΔ2.4 2.5 2.6 2.7

π/δ0 0.5 1 1.5 2

12θ2sin0.25 0.3 0.35

23θ2sin0.3 0.4 0.5 0.6 0.7

-2/1013θ2sin1.8 2 2.2 2.4 2.6

0

5

10

15

0

5

10

15

2χ

2χ

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NOI O

Two  different  ways  of  marginalizing  over  mass  ordering(s)  à  

19  

parameter  P  

Apply  a  “Δχ2  cut”  to  SEPARATE  minima  in  NO,  IO....  

χ2  

(does  not  include  IO-­‐NO  offset  informaNon)  

20  

parameter  P  

...or  minimize  and  expand  over  ANY  ORDERING  

χ2  

(includes  IO-­‐NO  offset  informaNon)  

21  

6.5 7 7.5 8 8.50

5

10

15

2.4 2.5 2.6 2.70

5

10

15

0 0.5 1 1.5 20

5

10

15

0.25 0.3 0.350

5

10

15

1.8 2 2.2 2.4 2.60

5

10

15

0.3 0.4 0.5 0.6 0.70

5

10

15

2 eV-5/102mδ6.5 7 7.5 8 8.5

2 eV-3/102mΔ2.4 2.5 2.6 2.7

π/δ0 0.5 1 1.5 2

12θ2sin0.25 0.3 0.35

23θ2sin0.3 0.4 0.5 0.6 0.7

-2/1013θ2sin1.8 2 2.2 2.4 2.6

0

5

10

15

0

5

10

15

2χ

2χ

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NOI O

OscillaCon    parameter    ranges  

22  

Non-­‐oscillaCon  constraints    from  0νββ  &  Cosmology  

23  

(  mβ  ,  mββ  ,  Σ  )  

   β  decay,  sensiNve  to  the  “effecNve  electron  neutrino  mass”:  

         0νββ  decay:  only  if  Majorana.  “EffecNve  Majorana  mass”:  

       Cosmology:  Dominantly  sensiNve  to  sum  of  neutrino  masses:  

Note 1: They may provide handles to distinguish NO/IO. Note 2: Majorana case may provide a new source of CPV Note 3: Available phase space constrained by oscillations à

Three observables sensitive to absolute ν masses:

Limits:  

sub-­‐eV  

sub-­‐eV  

~  2  eV  

24  

6.5 7 7.5 8 8.50

5

10

15

2.4 2.5 2.6 2.70

5

10

15

0 0.5 1 1.5 20

5

10

15

0.25 0.3 0.350

5

10

15

1.8 2 2.2 2.4 2.60

5

10

15

0.3 0.4 0.5 0.6 0.70

5

10

15

2 eV-5/102mδ6.5 7 7.5 8 8.5

2 eV-3/102mΔ2.4 2.5 2.6 2.7

π/δ0 0.5 1 1.5 2

12θ2sin0.25 0.3 0.35

23θ2sin0.3 0.4 0.5 0.6 0.7

-2/1013θ2sin1.8 2 2.2 2.4 2.6

0

5

10

15

0

5

10

15

2χ

2χ

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NOI O

1.4− 1.2− 1.0− 0.8− 0.6− 0.4− 0.2− 0.0−3.0−

2.5−

2.0−

1.5−

1.0−

0.5−

0.0

10

20

30

40

50

60

70

80

90

100

23θ 2sin

1−10 1

13θ 2si

n

3−10

2−10

1−10

1

23θ 2sin

1−10 1

13θ 2si

n

3−10

2−10

1−10

1Oscillations

SeparateNO IO,

)σ and 3σ(2

AnyOrdering

(eV)Σ (eV)Σ

(eV)

ββm

Sum  of  neutrino  masses  (Cosmology)  

EffecCv

e  Majoran

a  Mass  (DB

D)  

(mββ  ,  Σ)  plane  

spread  from  Majorana  CPV  phases  

25  

=  construcNve        interference  

=  destrucNve        interference  

yr)25 (101/2T

0 5 10 15 20 25 30 35 40

2 r6

0

1

2

3

4

5

6

7

8

9

10KamLAND-Zen Phase-I

KamLAND-Zen Phase-II

KamLAND-Zen Combined

EXO-200 (2014)

KamLAND-­‐Zen  half-­‐life  limits    

+  theoreNcal  esNmates  of      nuclear  matrix  element      for  136-­‐Xe  

RepresentaCve  (leading)  0νββ  limits  

2−10 1−100

1

2

3

4

5

6

7

8

9

10

(eV)ββm

2χ

(KamLAND-Zen)ββν0

sub-­‐eV  

26  

Analysis  of  various  datasets  within  standard  (6-­‐param.)  ΛCDM  model  augmented  with  Σ    (plus  one  possible  1  extra  parameter  Alens,  to  account  for  syst’s  or  nonstandard  effects)    Code:  CosmoMC  with  NO  /  IO  opCons  explicitly  included  in  Σ, via  the  two  mass2  differences  à  unphysical  spectra  of  neutrino  masses  (e.g.,  Σ =  0)  excluded  by  construcNon.  à  expect  small  NO-­‐IO  differences  at  low  Σ,  but  vanishing  at  high  Σ  (degenerate  spectrum)    

Cosmological  constraints  (circa  2017)    27  

Cosmological  constraints  (circa  2017)    Analysis  of  various  datasets  within  standard  (6-­‐param.)  ΛCDM  model  augmented  with  Σ    (plus  one  possible  1  extra  parameter  Alens,  to  account  for  syst’s  or  nonstandard  effects)    Code:  CosmoMC  with  NO  /  IO  opCons  explicitly  included  in  Σ, via  the  two  mass2  differences  à  unphysical  spectra  of  neutrino  masses  (e.g.,  Σ =  0)  excluded  by  construcNon.  à  expect  small  NO-­‐IO  differences  at  low  Σ,  but  vanishing  at  high  Σ  (degenerate  spectrum)    

Results  on  Σ (upper  bounds)  and  on  Δχ2ΙΟ-ΝΟ  :  

sub-­‐eV  

28  

χ2  profile  for  NO,  IO  in  representaCve  cases  

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6

7

8

9

10

#10

#1

#9#6

Cosmology

(eV)Σ

2χ

IO

NO

convergence  of  NO,  IO    curves  at  high  Σ

bifurcaCon  of  NO,  IO    curves  at  low  Σ

Note:      Σ  >  0.06  eV  (NO)   Σ  >  0.10  eV  (IO)  

29  

   Combining  oscillaCon        +  nonoscillaCon  data    

30  

1.4− 1.2− 1.0− 0.8− 0.6− 0.4− 0.2− 0.0−3.0−

2.5−

2.0−

1.5−

1.0−

0.5−

0.0

10

20

30

40

50

60

70

80

90

100

23θ 2sin

1−10 1

13θ 2si

n

3−10

2−10

1−10

1

23θ 2sin

1−10 1

13θ 2si

n

3−10

2−10

1−10

1Oscillations

SeparateNO IO,

)σ and 3σ(2

AnyOrdering

(eV)Σ (eV)Σ

(eV)

ββm

31  

1.4− 1.2− 1.0− 0.8− 0.6− 0.4− 0.2− 0.0−3.0−

2.5−

2.0−

1.5−

1.0−

0.5−

0.0

20

40

60

80

100

120

140

160

180

23θ 2sin

1−10 1

13θ 2si

n

3−10

2−10

1−10

1

23θ 2sin

1−10 1

13θ 2si

n

3−10

2−10

1−10

1ββνOscill. + 0

SeparateNO IO,

AnyOrdering

(eV)Σ (eV)Σ

(eV)

ββm

32  

1.4− 1.2− 1.0− 0.8− 0.6− 0.4− 0.2− 0.0−3.0−

2.5−

2.0−

1.5−

1.0−

0.5−

0.0

20

40

60

80

100

120

140

160

180

23θ 2sin

1−10 1

13θ 2si

n

3−10

2−10

1−10

1

23θ 2sin

1−10 1

13θ 2si

n

3−10

2−10

1−10

1 + CosmoββνOscill. + 0 #10

SeparateNO IO,

AnyOrdering

(eV)Σ (eV)Σ

(eV)

ββm

33  

[Case  with  “conservaNve”  bounds  from  cosmology]  

1.4− 1.2− 1.0− 0.8− 0.6− 0.4− 0.2− 0.0−3.0−

2.5−

2.0−

1.5−

1.0−

0.5−

0.0

20

40

60

80

100

120

140

160

180

23θ 2sin

1−10 1

13θ 2si

n

3−10

2−10

1−10

1

23θ 2sin

1−10 1

13θ 2si

n

3−10

2−10

1−10

1 + CosmoββνOscill. + 0 #1

SeparateNO IO,

AnyOrdering

(eV)Σ (eV)Σ

(eV)

ββm

34  

1.4− 1.2− 1.0− 0.8− 0.6− 0.4− 0.2− 0.0−3.0−

2.5−

2.0−

1.5−

1.0−

0.5−

0.0

20

40

60

80

100

120

140

160

180

200

23θ 2sin

1−10 1

13θ 2si

n

3−10

2−10

1−10

1

23θ 2sin

1−10 1

13θ 2si

n

3−10

2−10

1−10

1 + CosmoββνOscill. + 0 #9

SeparateNO IO,

AnyOrdering

(eV)Σ (eV)Σ

(eV)

ββm

35  

[RHS  plot  (inner  red  curve)  shows  how  a  cosmological  “claim”  of  Σ>0 could  look  like]  

1.4− 1.2− 1.0− 0.8− 0.6− 0.4− 0.2− 0.0−3.0−

2.5−

2.0−

1.5−

1.0−

0.5−

0.0

20

40

60

80

100

120

140

160

180

200

23θ 2sin

1−10 1

13θ 2si

n

3−10

2−10

1−10

1

23θ 2sin

1−10 1

13θ 2si

n

3−10

2−10

1−10

1 + CosmoββνOscill. + 0 #6

SeparateNO IO,

AnyOrdering

(eV)Σ (eV)Σ

(eV)

ββm

[Case  with  “aggressive”  bounds  from  cosmology]  

36  

Δχ2 (IO-NO)  

+1.1 +1.1 +3.6

LBL+Sol+KL +SBL Reac +Atmos +DBD, Cosmo

+3.6 ... +4.4

Small  steps  in  one  direcNon:  N.O.  favored...  Overall  preference  at  1.9σ - 2.1σ

Recap  of  IO-­‐NO  differences:  

If  these  are  not  fluctuaCons,  expect  (fracConal)  improvements  in  upcoming  years  

37  

Summary  and  prospects  

38  

SUMMARY  

•  Status  of  known  3ν  oscillaCon  parameters:          Precision  era  (but  PMNS  accuracy  far  from  CKM)          

•  Trends  of  unknown  oscillaCon  parameters:            Favoring  CPV  with  sinδ<0,  nonmax  θ23,  and  NO    

•  Status  of  constraints  from  0νββ  &  Cosmology:          Sub-­‐eV  sensiCvity;  Cosmo  analysis  with  NO  vs  IO      

•  OscillaCon  +  nonoscillaCon  global  analysis:          Corroborates  NO  with  respect  to  IO  at  ∼2σ level  

39  

PROSPECTS  -­‐  oscillaCons  •  Known  3ν  oscillaCon  parameters:        Higher  accuracy  with  LBL  acceler.,  JUNO  react.  +  others    

•  CPV:            If  sinδ ∼ -­‐1,  then  T2K+NOvA  may  probe  CPV  at  ∼3σ          Higher  C.L.  requires  future  LBL  acc.  (DUNE,  Hyper-­‐K)    

•  Hierarchy:          Expect  progress  from  T2K+NOvA  and  future  expts:          JUNO  reactor,  LBL  acceler.,  Large-­‐volume  atmospheric        

•  Octant  of  θ23:          Liring  degeneracy  possible,  but  not  easy  at  high  CL    

40  

-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

-110 1-310

-210

-110

1

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

10

20

30

40

50

60

70

80

90

100

-310 -210 -110 1-310

-210

-110

1-1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4

-2.0

-1.5

-1.0

-0.5

0.0

-110 1-310

-210

-110

1

(NH)m2 (IH)m2

(eV)Y (eV)`m

(eV)

``m

(eV)

`m

β    :  KATRIN

Σ : Precision Cosmology 0νββ  :  Upgraded/New expt. (+ NME)

oscillation constraints

Non-­‐oscillaCons:  Upper limits on mβ,  mββ,  Σ   in ~10 years ?

Large phase space for discoveries... and surprises (beyond 3ν?)

[Debated “tensions” for a 4th eV-mass sterile neutrino would require a separate talk]

41  

ν  physics  ...   is  ready  to  sail  towards  new  horizons!