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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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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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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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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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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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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: 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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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
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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
���������������������������2VFLOODWLRQ�SDUDPHWHUV
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
���������������������������2VFLOODWLRQ�SDUDPHWHUV
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
���������������������������2VFLOODWLRQ�SDUDPHWHUV
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!
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