PDF Neutrino Masses, Mixings and CP Violation from Oscillation Experiments

Neutrino

Masses, Mixings and CP Violation from Oscillation Experiments

Michel Sorel

(IFIC - CSIC & U. Valencia)

4th Workshop on Flavor Physics in the LHC era

Valencia, November 2015

2015: neutrino oscillations year

Breakthrough Prize Special Breakthrough Prize New Horizons Prize Physics Frontiers Prize 2016 2015 2014 2013 2012

Kam-Biu Luk and the Daya Bay Collaboration

Yifang Wang and the Daya Bay Collaboration

Koichiro Nishikawa and the K2K and T2K

Collaboration

Atsuto Suzuki and the KamLAND Collaboration

Arthur B. McDonald and the SNO Collaboration

Takaaki Kajita and the Super K Collaboration

Yoichiro Suzuki and the Super K Collaboration

LAUREATESLAUREATES

BOARD TROPHY EVENTS NOMINATIONS NEWS CONTACTS COMMITTEE PRIZES LAUREATES RULES

Search

BOARD TROPHY EVENTS NOMINATIONS NEWS CONTACTS SUBSCRIBESUBSCRIBE

2016 Breakthrough Prize in Fundamental Physics:

awarded to six experimental collaborations

“for the fundamental discovery and exploration of neutrino oscillations, revealing a new frontier beyond, and possibly far beyond, the standard model of particle physics”

2

Nobel Prize in Physics 2015:

awarded to Takaaki Kajita (Super-Kamiokande) and Arthur B. McDonald (SNO)

“for the discovery of neutrino oscillations, which shows that neutrinos have mass”

Neutrino oscillations

↔ Flavour physics in neutrino sector

• Neutrinos change flavour as they propagate

• Flavour change follows oscillatory pattern depending on baseline L and energy E

• Neutrino oscillation implies massive neutrinos and neutrino mixing

2-neutrino mixing example, for νμ beam with energy E

ν1

ν2

νe

νμ

ϑ

Δm²=m22-m12

ν1

ν2

mass

Source Detector

P(νμ→νe) = |Amp(νμ➝νe)|² = sin²2ϑ⋅sin²[∆m²L/(4E)]

∑i U*μi exp[-imi2L/(2E)] Uei

νi

μ⁺ e^-

Neutrino oscillations

↔ Flavour physics in neutrino sector

• Neutrinos change flavour as they propagate

• Flavour change follows oscillatory pattern depending on baseline L and energy E

• Neutrino oscillation implies massive neutrinos and neutrino mixing

2-neutrino mixing example, for νμ beam with energy E

ν1

ν2

νe

νμ

ϑ

Δm²=m22-m12

ν1

ν2

mass

3

Probability

0 1

Distance L / Energy E

sin²2ϑ L/E

∝

^1/Δm2

P(νμ)

P(νe)

Neutrino oscillation experiments

By neutrino sources

Reactor neutrinos

• Flavors: ν̅e

• Eν ~ 1-10 MeV Solar neutrinos

• Flavors: νe

• Eν ~ 0.1-10 MeV

Atmospheric neutrinos

• Flavors: νμ, ν̅μ, νe, ν̅e

• Eν ~ 0.1-100 GeV

Accelerator neutrinos

• Flavors: νμ, ν̅μ (νe, ν̅e)

• Eν ~ 0.1-100 GeV

3-Neutrino mixing parametrisation

{

Atmospheric Oscillations

Solar Oscillations

Interference

{

c

₂₃

= cos

₂₃

etc...

⇤

_µ^e

⇤

⇥

⌅ = ⇤ 1 0 0 0 c

₂₃

s

₂₃

0 s

₂₃

c

₂₃

⇥

⌅ ⇤ c

₁₃

0 s

₁₃

e

ⁱ

0 1 0

s

₁₃

e

ⁱ

0 c

₁₃

⇥

⌅ ⇤ c

₁₂

s

₁₂

0 s

₁₂

c

₁₂

0

0 0 1

⇥

⌅ ⇤

¹₂

3

⇥

⌅

5

ν1

ν2

ν3

Δm²21

Δm²31

• 2 mass splittings, 3 mixing angles, 1 CPV phase

• Describe all convincing evidence for neutrino oscillations

Global 3-neutrino fits

Mass splittings and mixing angles measured with 10% precision or better

• θ12 and Δm221 measured by solar and reactor experiments

• θ23 and |Δm231| measured by atmospheric and accelerator experiments

• θ13 measured by reactor and accelerator experiments

• δCP phase compatible with any value at 3σ, sgn(Δm231) unknown

ν

1

ν

2

ν

3

mass

μ τ

e sin²ϑ13 = 0.022±0.001

sin²ϑ23 = 0.452±0.052

sin²ϑ12 = 0.304±0.013

Δm221 =

(7.50±0.19)⋅10^-5 eV²

|

^Δm231

|

⁼

(2.46±0.05)⋅10^-3 eV²

NuFIT 2.0 (2014)

θ 13 and Δm 221 From solar neutrinos

0 1 2 3 4 5 6

0 1 2 3 4 5 6 7 8

-1)

-2 s

6 cm

e (10 φ

)-1 s-2 cm6 (10 τµφ SNO

φNC

φSSM SNO

φCC SNO

φES

7

•

Disappearance of solar νe’s, appearance into other “active” flavours (μ, τ)

•

Experiments: Super-Kamiokande, SNO, Borexino, etc.

•

Energy dependence of νe suppression also measured

[MeV]

Eν

10-1 1 10

survival probabilityeν: eeP

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

pp - All solar Be - Borexino

7

pep - Borexino

B - SNO + SK + Borexino

8

MSW-LMA Prediction

Vacuum- dominated

Matter- dominated

SNO

θ 13 and Δm 221 From solar neutrinos

0 1 2 3 4 5 6

0 1 2 3 4 5 6 7 8

-1)

-2 s

6 cm

e (10 φ

)-1 s-2 cm6 (10 τµφ SNO

φNC

φSSM SNO

φCC SNO

φES

•

Disappearance of solar νe’s, appearance into other “active” flavours (μ, τ)

•

Experiments: Super-Kamiokande, SNO, Borexino, etc.

•

Energy dependence of νe suppression also measured

[MeV]

Eν

10-1 1 10

survival probabilityeν: eeP

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

pp - All solar Be - Borexino

7

pep - Borexino

B - SNO + SK + Borexino

8

MSW-LMA Prediction

Vacuum- dominated

Matter- dominated

SNO ^{= 1/2}

θ 13 and Δm 221

From long-baseline reactor neutrinos

(km/MeV)

νe

0/E L

20 30 40 50 60 70 80 90 100

Survival Probability

0 0.2 0.4 0.6 0.8 1

νe

Data - BG - Geo

Expectation based on osci. parameters determined by KamLAND

8

★

★

0.2 0.25 0.3 0.35 0.4

sin²θ₁₂ 0

2 4 6 8 10 12 14

∆m2 21 [10−5 eV2 ]

θ₁₃ = 8.5°

2 4 6 8 10

∆m²₂₁ [10⁻⁵ eV²] 0

2 4 6 8 10 12

∆χ2

GS98 w/o D/N GS98

AGSS09 KamLAND

NuFIT 2.0 (2014)

•

Disappearance of reactor ν̅^e’s over O(100 km) distances. Experiments: KamLAND

•

L/E dependence of ν̅^e suppression also measured

•

Compatible with solar parameters, but some tension for Δm221 measurement

KamLAND

Solar

KamLAND

θ 23 and Δm 231

From atmospheric neutrinos

Atmospheric Neutrinos

• The absolute flux uncertainty is fairly high, so people use other useful properties of the atmospheric neutrino flux:

1. !#:!e ratio: This ratio is fixed from the pion/muon cascade.

2. Zenith variation: Allows one to probe neutrinos at very different production distances (essential for oscillation signatures).

3. Compare cosmic muon flux

•

Disappearance of atmospheric νμ’s and ν̅^μ’s

•

Experiments: Kamiokande, Super-Kamiokande, etc.

•

First conclusive evidence for oscillations (1998), from zenith angle-dependent deficit

9

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

1 10 10² 10³ 10⁴

L/E (km/GeV)

Data/Prediction (null osc.)

upward- going downward-

going

Super-K

θ 23 and Δm 231

From atmospheric neutrinos

Atmospheric Neutrinos

• The absolute flux uncertainty is fairly high, so people use other useful properties of the atmospheric neutrino flux:

1. !#:!e ratio: This ratio is fixed from the pion/muon cascade.

2. Zenith variation: Allows one to probe neutrinos at very different production distances (essential for oscillation signatures).

3. Compare cosmic muon flux

•

Disappearance of atmospheric νμ’s and ν̅^μ’s

•

Experiments: Kamiokande, Super-Kamiokande, etc.

•

First conclusive evidence for oscillations (1998), from zenith angle-dependent deficit

9

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

1 10 10² 10³ 10⁴

L/E (km/GeV)

Data/Prediction (null osc.)

upward- going downward-

going

Super-K ^{= 1/2}

θ 23 and Δm 231

From long-baseline accelerator neutrinos

•

Disappearance of long-baseline νμ’s and (separately) ν̅^μ’s over O(100 km) distances

•

Experiments: K2K, MINOS, T2K, NOvA

•

Confirmation of atmospheric results, precision measurement of oscillation parameters

0.3 0.4 0.5 0.6 0.7

sin² θ

23

-3.5 -3 -2.5 -2 2 2.5 3 3.5

∆m2 32 [10-3 eV2 ] ∆m2 31

ATM

T2K

MINOS

0.015 0.02 0.025 0.03

sin²θ

13

[68.27%, 95.45% CL]

react

(no DB) DayaB

NuFIT 2.0 (2014)

Energy (GeV) Reconstructed ν

0 1 2 3 4 5

0 0.5 1

1.5 MC Best-fit

Ratio to no oscillations

>

0 1 2 3 4 5

Events/0.10 GeV

0 2 4 6 8 10 12 14 16

DATA

CCQE νµ

µ+ ν

CC non-QE νµ

µ+ ν

e CC +ν

νe

NC

0

T2K

θ 13

From medium-baseline reactor neutrinos

•

^Reactor ν̅^e disappearance over km-long baselines

•

Experiments: Double Chooz, Daya Bay, RENO

•

Most precise measurement of sin²2ϑ13 to date

11 Double Chooz

Daya Bay RENO

Daya Bay

θ 13

From long-baseline accelerator neutrinos

•

^νe appearance from νμ→νe transitions

•

Experiments: MINOS, T2K, NOvA

•

Confirmation of reactor results, degeneracy with δCP information for current-generation exps

)π ( CPδ

68% CL 90% CL Best fit

range PDG2012 1σ

>0

32

m2

∆

-1 -0.5

0 0.5

1

θ13 22 sin

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 )π ( CPδ

<0

32

m2

∆

-1 -0.5

0 0.5

1

Reactors

Reconstructed neutrino energy (MeV)

0 500 1000 1500 2000

candidate events eνNumber of

0 2 4 6

8 ^Data

Best fit

Background component

Fit region < 1250 MeV

>

T2K

Neutrino questions: mass ordering

•

Solar neutrinos measure m1 < m2, where ν1 is most electron-rich state

•

Normal mass ordering: mlight = m1 ➩ similar to quarks and charged leptons

•

Inverted mass ordering: mlight = m3 ➩ “opposite” to quarks and charged leptons

ν

1

ν

2 ^τ _μ^e

ν

3

NORMAL

ν

1

ν

2

ν

3

μ τ e

INVERTED

atm

sol

sol

atm

Normal or Inverted?

13

Neutrino questions: CP violation

{

Atmospheric Oscillations

Solar Oscillations

Interference

{

c

₂₃

= cos

₂₃

etc...

⇤

_µ^e

⇤

⇥

⌅ = ⇤ 1 0 0 0 c

₂₃

s

₂₃

0 s

₂₃

c

₂₃

⇥

⌅ ⇤ c

₁₃

0 s

₁₃

e

ⁱ

0 1 0

s

₁₃

e

ⁱ

0 c

₁₃

⇥

⌅ ⇤ c

₁₂

s

₁₂

0 s

₁₂

c

₁₂

0

0 0 1

⇥

⌅ ⇤

¹₂

3

⇥

⌅

• Source of CP violation that can be measured with oscillations: Dirac CP-odd phase δ

• δ ≠ 0, π oscillation probabilities violate CP invariance:

different probabilities for neutrinos and antineutrinos!

Is CP symmetry violated in the neutrino sector?

Neutrino questions: μ-τ symmetry and θ 23 octant

15

ν1

ν2

ν3

mass

μ τ

e sin²ϑ13 = 0.022±0.001

sin²ϑ23 = 0.452±0.052

sin²ϑ12 = 0.304±0.013

Δm221 =

(7.50±0.19)⋅10^-5 eV²

|Δm231| =

(2.46±0.05)⋅10^-3 eV²

NuFIT 2.0 (2014)

Flavour content sin²θ23

|Uμ3|² = |Uτ3|² ≡ 0.5

|Uμ3|² < |Uτ3|² < 0.5

|Uμ3|² > |Uτ3|² > 0.5

Is the ν

3

state:

• more muon-rich?

• more tau-rich?

• or equally muon/tau-rich?

• Maximal mixing (|Uμ3|² = |Uτ3|²) would be suggestive of underlying flavour symmetry

Next-generation accelerator-based experiments

Starting ~2024?

ν

^{Magnet'Coils'Forward'ECAL'End'RPCs'}

Backward'ECAL' Barrel'

ECAL' STT'Module' Barrel''

RPCs'

End' RPCs'

FD#

ND#

Hyper-Kamiokande

Next-generation atmospheric and reactor experiments

Starting ~2020?

•

PINGU, ORCA: huge atmospheric neutrino detectors with few GeV energy threshold

17 IceCube

Downwards muon bundle PINGU

DeepCore

-1500m

-2500m

South Pole Ice Cap

South Pole Surface

Fully contained

neutrino PINGU DOMs

PINGU

DeepCore PINGU

60 DOM’s

5 m spacing

X (m)

-100 -50 0 50 100 150 200

Y (m)

-150 -100 -50 0 50

100 IceCube

DeepCore PINGU

87 88 89 90 91 92 93

94

95 96

97 98

99 100

101 102

103 104

105 106

107 108

109 110

111 112

113 114

115 116

117 118

119 120

121 122

123

124 125 126

PINGU Geometry V15 (Ellett)

•

JUNO, RENO-50: reactor neutrino detectors at ~50 km baselines

Prospects for neutrino mass ordering reach

• The neutrino mass ordering will be measured in the next few years!

True NO

NOvA

LBNE 10kt JUNO

PINGU

LBNE 34kt

INO

2015 2020 2025 2030

0 1 2 3 4 5 6 7

Date

Mediansensitivity@sD

DUNE

DUNE 40

Prospects for leptonic CP violation reach

How well can we measure δ

CP

to be different from 0 or π?

19

DUNE: up to 6σ CPV sensitivity after 300 kt⋅MW⋅yr exposure (~7 yr)

-150 -100 -50 0 50 100 150

σ=√χ

2

0 2 4 6 8 10

Normal mass hierarchy

3σ 5σ

δ

CP ^[degree]

Hyper-K: up to 9σ CPV sensitivity after 7.5×10⁷ MW⋅sec beam exposure (~10 yr)

Prospects for leptonic CP violation reach

How well can we measure δ

CP

to be different from 0 or π?

DUNE: up to 6σ CPV sensitivity after 300 kt⋅MW⋅yr exposure (~7 yr)

-150 -100 -50 0 50 100 150

σ=√χ

2

0 2 4 6 8 10

Normal mass hierarchy

3σ 5σ

δ

CP ^[degree]

Hyper-K: up to 9σ CPV sensitivity after 7.5×10⁷ MW⋅sec beam exposure (~10 yr)

(popularly known as the “McDonald’s plot”)

Prospects for sin 2 θ 23 resolution

20

Chapter 3: Long-Baseline Neutrino Oscillation Physics 3–35

Exposure (kt-MW-years) 0 200 400 600 800 1000 1200 1400 Resolution 23θ2 sin

0 0.005 0.01 0.015

0.02 0.025 0.03 0.035 0.04

Resolution θ23

sin2

DUNE Sensitivity Normal Hierarchy

= 0.085 θ13

22 sin

= 0.45 θ23

sin2

Resolution θ23

sin2

Figure 3.19: The resolution of a measurement of sin² ◊₂₃ as a function of exposure assuming normal MH and sin² ◊₂₃ = 0.45 from the current global fit. The shaded region represents the range in sensitivity due to potential variations in the beam design.

Volume 2: The Physics Program for DUNE at LBNF LBNF/DUNE Conceptual Design Report

• About 5-fold improvement in

resolution over current-generation

Hyper-K after 7.5×10⁷ MW⋅sec beam exposure (~10 yr)

~7 yrs

Quarks and neutrinos are different!

Masses

• Mass hierarchy problem: m(ν) << m(other fermions)

21

14 Neutrinos: DRAFT

will be discussed in Sec. 1.7. Possible surprises include new, gauge singlet fermion states that manifest

437

themselves only by mixing with the known neutrinos, and new weaker-than-weak interactions.

438

Another issue of fundamental importance is the investigation of the status of CP invariance in leptonic

439

processes. Currently, all observed CP-violating phenomena are governed by the single physical CP-odd

440

phase parameter in the quark mixing matrix. Searches for other sources of CP violation, including the so-

441

called strong CP-phase ⇤

_QCD

, have, so far, failed. The picture currently emerging from neutrino-oscillation

442

data allows for a completely new, independent source of CP violation. The CP-odd parameter , if different

443

from zero or ⇧, implies that neutrino oscillation probabilities violate CP-invariance, i.e., the values of the

444

probabilities for neutrinos to oscillate are di fferent from those of antineutrinos! We describe this phenomenon

445

in more detail in Secs. 1.2.1, 1.3.

446

It should be noted that, if neutrinos are Majorana fermions, the CP-odd phases ⌅ and ⇥ also mediate CP-

447

violating phenomena [22] (alas, we don’t yet really know how to study these in practice). In summary,

448

if neutrinos are Majorana fermions, the majority of CP-odd parameters in particle physics — even in the

449

absence of other new physics — belong to the lepton sector. These are completely unknown and can “only”

450

be studied in neutrino experiments. Neutrino oscillations provide a unique opportunity to revolutionize our

451

understanding of CP violation, with potentially deep ramifications for both particle physics and cosmology.

452

An important point is that all modifications to the standard model that lead to massive neutrinos change it

453

qualitatively. For a more detailed discussion of this point see, e.g., [23].

454

Neutrino masses, while nonzero, are tiny when compared to all other known fundamental fermion masses in

455

the standard model, as depicted in Fig. 1-3. Two features readily stand out: (i) neutrino masses are at least

456

six orders of magnitude smaller than the electron mass, and (ii) there is a “gap” between the largest allowed

457

neutrino mass and the electron mass. We don’t know why neutrino masses are so small or why there is such

458

a large gap between the neutrino and the charged fermion masses. We suspect, however, that this may be

459

Nature’s way of telling us that neutrino masses are “different.”

e ! !

u d

c

s b

t

"

₁

"

₂

"

₃

TeV

GeV

MeV

keV

eV

meV

masses of matter particles

Figure 1-3. Standard model fermion masses. For the neutrino masses, the normal mass hierarchy was assumed, and a loose upper bound mi < 1 eV, for all i = 1, 2, 3 was imposed.

460

This suspicion is only magnified by the possibility that massive neutrinos, unlike all other fermions in the

461

standard model, may be Majorana fermions. The reason is simple: neutrinos are the only electrically-neutral

462

fundamental fermions and hence need not be distinct from their antiparticles. Determining the nature of

463

the neutrino – Majorana or Dirac – would not only help to guide theoretical work related to uncovering the

464

origin of neutrino masses, but could also reveal that the conservation of lepton number is not a fundamental

465

law of Nature. The most promising avenue for learning the fate of lepton number, as will be discussed

466

in Sec. 1.4, is to look for neutrinoless double-beta decay, a lepton-number violating nuclear process. The

467

observation of a nonzero rate for this hypothetical process would easily rival, as far as its implications for our

468

Snowmass Proceedings

(normal mass ordering assumed)

Quarks and neutrinos are different!

Mixings

1 0,2 0,004

0,2 1 0,04

0,008 0,04 1

|V

CKM

| = ( ) |V

^PMNS

|

⁼

(

^{0,80,40,4 0,50,60,6 0,20,70,7}

)

22

Quarks: small mixings

The Data: Fermion Mixing

W^± W ^± u_i

d_j

(U^CKM)_ij ^{UCKM = R1(✓23CKM)R2(✓13CKM, CKM)R3(✓12CKM)}

Quarks:

Leptons:

_UMNSP = R¹( ₂₃)R²( ₁₃, _MNSP)R³( ₁₂)P

e_j

i

Cabibbo Kobayashi

Maskawa

Pontecorvo Maki Nakagawa

Sakata

(U^MNSP)_ij NH; best fit +/-1sig (3sig range)

2 large angles, 1 “small” angle

✓₁₂^CKM = 13.0 ± 0.1

✓₂₃^CKM = 2.4 ± 0.1

✓₁₃^CKM = 0.2 ± 0.1

CKM = 60 ±14

3 “small” angles 1 large CP phase

= _C (Cabibbo angle)

phases (if Majorana) rotation matrices

fits from Gonzalez-Garcia et al. ’14, see also Forero et. al ’14, Capozzi et al. ’13

(7.85 9.10 ) (38.2 53.3 ) (31.29 35.91 )

13 = 8.50 ^+0.20_0.21

23 = 42.3 ^+3.0_1.6

12 = 33.48 ^+0.78_0.75

The Data: Fermion Mixing

W

^± W^± u_i

d_j

(U^CKM)_ij ^{UCKM = R1(✓CKM23 )R2(✓13CKM, CKM)R3(✓12CKM)}

Quarks:

Leptons:

_UMNSP = R¹( ₂₃)R²( ₁₃, _MNSP)R³( ₁₂)P

e_j

i

Cabibbo Kobayashi

Maskawa

Pontecorvo Maki Nakagawa

Sakata

(UMNSP)_ij NH; best fit +/-1sig (3sig range)

2 large angles, 1 “small” angle

✓₁₂^CKM = 13.0 ± 0.1

✓₂₃^CKM = 2.4 ± 0.1

✓^CKM₁₃ = 0.2 ± 0.1

CKM = 60 ±14

3 “small” angles 1 large CP phase

= _C (Cabibbo angle)

phases (if Majorana) rotation matrices

fits from Gonzalez-Garcia et al. ’14, see also Forero et. al ’14, Capozzi et al. ’13

(7.85 9.10 ) (38.2 53.3 ) (31.29 35.91 )

13 = 8.50 ^+0.20_0.21

23 = 42.3 ^+3.0_1.6

12 = 33.48 ^+0.78_0.75

Leptons: large mixings

Quarks and neutrinos are different!

CP violation strength

Quarks:

•

CP phase: δ = (70.3±3.5) deg

•

CPV strength: JCP = (3.12±0.09)⋅10^-5

Neutrinos:

•

CP phase: δ = [0,360] deg

•

CPV strength: JCP ≈ 3.3⋅10^-2 sinδ

0.025 0.03 0.035 0.04 J_CP^max = c₁₂ s₁₂ c₂₃ s₂₃ c²₁₃ s₁₃ 0

5 10 15

∆χ2

-0.04 -0.02 0 0.02 0.04

J_CP = J_CP^max sinδ_CP

NO IO

NuFIT 2.0 (2014)

• CP violation strength likely to be much larger for neutrinos than for quarks

Summary

24

• The neutrino oscillation revolution of the past 20 years has opened a new

perspective in flavour physics

Summary

• The neutrino oscillation revolution of the past 20 years has opened a new perspective in flavour physics

• Neutrino experimentalists are happy

• Nature’s choice of mass and mixing parameters has proven very favourable from the experimental point of view

Summary

24

• The neutrino oscillation revolution of the past 20 years has opened a new perspective in flavour physics

• Neutrino experimentalists are happy

• Nature’s choice of mass and mixing parameters has proven very favourable from the experimental point of view

• Theorists still not as happy

• “One could have imagined that neutrinos would bring a decisive boost towards the formulation of a

comprehensive understanding of fermion masses and mixings. It is frustrating that no real illumination was sparked on the problem of flavour.” (G. Altarelli, 2014)