1

Neutrino Physics, Part 1

Neutrinos in the

Standard Model, and

Why The Standard

Model is Wrong

Scott Oser

UBC

Lake Louise Winter Institute

February 2006

2

Outline

1. Neutrinos In The Standard Model

2. Neutrino Mixing And Oscillation

3. The Solar Neutrino Problem, With Solution

4. Atmospheric Neutrino Oscillations

5. Results from Long Baseline Neutrino

Experiments

3

Neutrinos in the Standard Model

A neutrino is a neutral cousin of the

electron and the other charged leptons.

νe

νe

νe

νe

e

e

W

e

e

Z

Only weak interactions — carried by very

heavy W, Z particles with short ranges

In the Standard Model, mν ≡ 0. (The

current limit on the sum of the three

masses is ∼ 0.6 eV). Neutrinos are

many orders of magnitude lighter than the

other fermions.

Why are ν ’s so light? Why 3 kinds?

What’s the relationship between leptons and quarks?

4

Different Kinds of Neutrinos: “Flavours”

Each charged lepton (e, µ, τ ) has its own kind of neutrino. For example,

in these reactions you get:

p + e− → νe + n

p + µ− → νµ + n

Note that the number of particles of each flavour type seems to be

conserved in each reaction.

Flavour is also conserved in the other direction:

νe + n → p + e−

νµ + n → p + µ−

In the Standard Model lepton flavour is rigorously conserved, but is not

protected by any symmetry of the Lagrangian.

5

The Left and the Right of the Matter

spin

momentum

ANTINEUTRINO

spin

momentum

NEUTRINO

Weak interactions only couple to left-handed ν ’s, or right-handed ν ’s

This is a pure V-A interaction (maximally parity violating). Weak current has the form:

jµ = ψγµ(1 − γ5)ψ

Right-handed ν ’s either don’t exist, or are sterile (don’t interact).

A plausible, but wrong, argument ...

1. Ockham’s Razor: the simplest solution is if right-handed ν ’s don’t exist.

2. In Standard Model, mass couples left-handed and right-handed states.

3. Therefore, to avoid right-handed states, neutrinos should have no mass.

6

Neutrino Flavour Mixing

In Standard Model, neutrinos are rather boring ... they have

no mass, and only seem to be there to conserve lepton

number, flavour number, and energy/momenta/spin.

In 1962, Maki, Nakagawa, and Sakata proposed, on the

basis of zero experimental evidence, a new phenomenon

called neutrino oscillation.

To understand what led MNS to this, let’s look at quark

mixing first.

7

Weak Interactions with Quarks

The simple version: W particle couples u ↔ d, c ↔ s, t ↔ b,

W

u

d

W

c

s

W

t

b

But this can’t be complete, since we see weak decays such as:

Λ(uds) → p(uud) + π−(du)

Somehow the strange quark in the Λ gets turned into an up quark!

8

Quark Flavour Mixing

In reality, W particle couplings mix quark generations:

W

u

d’

We say that flavour eigenstates

(eg. d,s,b) are rotated with respect

to weak eigenstates (d’,s’,b’)

u

d′

c

s′

t

b′

d′

s′

b′

=

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

d

s

b

This allows generation-mixing decays such as Λ(uds) → pπ−

9

Neutrino Mixing

W

e

νe

Since ν ’s have only weak

interactions, flavour eigenstates

are defined as those states that

couple to W

What if the flavour eigenstates are rotated relative to the mass

eigenstates (eigenstates of Hamiltonian with well-defined mass)?

νe

νµ

ντ

=

Ue1 Ue2 Ue3

Uµ1 Uµ2 Uµ3

Uτ1 Uτ3 Uτ3

ν1

ν2

ν3

10

How does superposition of mass eigenstates evolve in vacuum?

|νe〉 = cos θ |ν1〉 + sin θ |ν2〉

|νµ〉 = − sin θ |ν1〉 + cos θ |ν2〉

Each term evolves with a phase factor of ei(px−Et)

If m1 6= m2, then arguments of exponential will be different! For

example, if we consider p to be fixed, then

E =√

p2 + m2 = p√

1 + m2/p2 ≈ p + m2/(2p)

As neutrino propagates, a phase difference develops between terms!

|ν(t)〉 ∝ cos θ |ν1〉 + eiφ sin θ |ν2〉

with

φ =

(

m21

2p−

m22

2p

)

t

11

Neutrino Oscillation

Net result: at some later time, |ν(t)〉 6= |νe〉.

Probability that the original νe is detected as a νµ at some later time:

P (νe → νµ) = |〈νµ|ν(t)〉|2 = sin2 2θ sin2

(1.27∆m2L

E

)

Energy (MeV)

Osc

illat

ion

Prob

abili

ty

00.10.20.30.40.50.60.70.80.9

1

1 10

θ = neutrino mixing angle

∆m2 = m21 −m2

2 (in eV2)

L = distance ν has travelled (in km)

E = neutrino energy (in GeV)

Neutrino oscillation:

• requires at least one non-zero neutrino mass

• requires non-zero mixing elements

• results from the QM of the propagation, not from an interaction

12

Matter Effects On Neutrino Oscillation

Surprisingly the oscillation formula can be dramatically altered in matter!

id

dt

(

νe

νµ

)

=

(

−∆m2

4Ecos 2θ+

√2GF Ne

∆m2

4Esin 2θ

∆m2

4Esin 2θ ∆m2

4Ecos 2θ

)(

νe

νµ

)

The relevant process is forward scattering, in

which no momentum is exchanged. In matter,

νe ’s have a different forward scattering

amplitude than the other flavours:

e- e- e-

e-

νe

νeνx νx

WZ +

All neutrino flavors

0

Only electron neutrinos

AT SOLAR NEUTRINO ENERGIES:

This produces a matter-induced potential that

is different for νe. Effectively νe ’s have a

different “index of refraction” in matter.

The size of the potential is proportional to the

electron density Ne.

For solar ν ’s, matter effects are dominant.

Average survival probability in vacuum

Actual solar neutrino survival probability

Neutrino Energy (MeV)

Ele

ctro

n N

eutr

ino

Surv

ival

Pro

babi

lity

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10 12 14 16 18 20

13

Solar Neutrinos

The Sun is an intense source of MeV neutrinos!

4p + 2e− →4He + 2νe + 26.731 MeV

Shape of Spectra Determined By Nuclear Physics.

Solar Models Only Affect Normalization.

14

The pp Chain

99.6% 0.4%

85% 15%

99.9% 0.1%

<< 1%

p + e− + p →2H + νe

2 3He →4He + 2p 3He + p →

4He + e+ + νe

(hep)

2H + p →3He + γ

3He + 4He →7Be + γ

(7Be)

7Be + e− →7Li + νe

7Be + p →8B + γ

8B →8Be

∗

+ e+ + νe

7Li + p → 24He

8Be∗

→ 2 4He

p + p →2H + e+ + νe

(pep)

(8B)

(pp)

15

The Pioneers

The 37Cl experiment

started in the 1960’s

Ray Davis and John

Bahcall with the

tetrachloroethylene tank.

100,000 gallons of

cleaning fluid!

νe+37Cl → e−+37Ar

16

A setback ...

Predicted rate: 7.6+1.3−1.1 SNU’s

Measured rate: 2.56 ± 0.23 SNU’s

Most people reacted in two ways ...

• Experiment must be wrong. No one can look for 50 Ar atoms in 600

tons of cleaning fluid and expect to find them all!

• Theory must be wrong. The solar models are too complicated to

take seriously. The flux changes with solar temperature by T 25.

Even a tiny mistake could change fluxes greatly!

Ray Davis checked and rechecked his experiment. John Bahcall refined

astrophysical calculations. Both stuck to their guns.

Others began planning new experiments ...

17

Super-Kamiokande

Detector hall Access tunnel

1,000m

Control room

Inner Detector

Outer Detector

Photo multipliers

41m

39m

18

Water Cherenkov Detectors

ν

Neutrino-electron scattering

e

ν

e

Elastic scattering of electrons by ν ’s

Scattered electron can move faster than

light in water (since water has slowed

down light).

Get Cherenkov light—an electromagnetic

sonic boom!

• Light is blue

• Comes out in cone

• More energy→ more light!

Cherenkov cone

electron

19

Super-Kamiokande

νx + e− → νx + e−

Rate ∝ φ(νe) + 1

6φ(νµτ )

Rexp = 0.465 ± 0.005+0.014−0.012× SSM

(hep-ex/0106064, hep-ex/0206075)

z

SKDayNight Man 1Man 2Man 3Man 3 Man 4Man

4 Man 5M

an 5

CoreCore

No SKData

InnerCore

All Day

Night

Man

1

Man

2

Man

3

Man

4

Man

5

Cor

e

cosθz

Dat

a/S

SM

0.4

0.45

0.5

0.55

-1 -0.5 0 0.5

Clear directional ν signal from Sun!

0

0.1

0.2

-1 -0.5 0 0.5 1cosθsun

Eve

nt/d

ay/k

ton/

bin

20

Solar Neutrino Flux Measurements

Two Classes of Experiment (so far)

• Radiochemical

– νe interactions convert target nuclei

– Radioactive products extracted and

counted after exposure time

• Water Cerenkov

– Real-time detection of scattered

atomic e− ’s

– Mixed CC and NC sensitivity

0 1 10ENERGY (MeV)

0.00

0.50

1.00

RA

TIO

TO

SS

M P

RE

DIC

TIO

N

Ga

Cl

SK

Experiment Detection Reaction Threshold Primary Sources

Homestake νe+37Cl → e−+

37Ar 0.8 MeV 7Be,8B

Kamiokande νe,(µ,τ) + e → νe,(µ,τ) + e 7.3 MeV 8B

SAGE, GALLEX/GNO νe+71Ga → e+

+71Ge 0.23 MeV pp,7Be,8B

Super-K νe,(µ,τ) + e → νe,(µ,τ) + e 5 MeV 8B

21

The Solar Neutrino Problem

• Standard Solar Model Predictions:

• Measurements:

22

Sudbury Neutrino Observatory

2092 m to Surface

1700 Tonnes InnerShielding H2O

1000 Tonnes D2O

5300 Tonnes Outer Shield H2O

12 m DiameterAcrylic Vessel

18 m DiameterSupport Structurefor 9500 PMTs,60% coverage

Urylon Liner andRadon Seal

23

Event Display–Neutrino Event

24

Solar ν Interactions in SNO

SNO measures primarily8B neutrinos by three

interactions:

Charged Current:

νe + d → p + p + e−

Neutral Current:

νx + d → p + n + νx

Elastic Scattering:

νx + e → νx + e−

SNO CC threshold

SNO NC threshold

For the Large Mixing Angle (LMA) solution to solar neutrino problem:

|Ue2|2 ≈ sin2 θ12 ≈

φCC

φNC

25

Three Phases of the SNO Experiment

D2O Phase

(pure D20)

Nov 1999 - May 2001

n + d → t + γ

(σ = 0.0005 b)

Detect a Compton-

scattered electron from a

6.25 MeV γ

Salt Phase

(D2O + 0.2% NaCl)

July 2001 - Sept 2003

n+35Cl →36Cl +γ ’s

(σ = 44 b)

Detect Compton-scattered

electrons from multiple γ ’s

totalling 8.6 MeV

NCD Phase

(3He counters)

Dec 2004 - Dec 2006

n+3He → p + t

(σ = 5330 b)

Detect 764 keV of

ionization from the

charged particles in 3He

proportional counters

PRL 87, 071301 (2001)

PRL 89, 011301 (2002)

PRL 89, 011302 (2002)

PRD 70, 093014 (2004)

PRL 92, 181301 (2004)

PRL 92, 102004 (2004)

PRC 72, 055502 (2005)

PRD 72, 052010 (2005)

26

Signal Probability Distributions

CC ES NC

Angle

Isotropy

Radius

Energy

Fit the PDFs to the data to determine fluxes. Leave out the energy

PDFs to fit for the spectral shapes.

27

Results for the full 391-day Salt Phase

14β-0.2 0 0.2 0.4 0.6 0.8

Eve

nts/

(0.0

107)

0

20

40

60

80

100

120

140

160 DataFit result Neutrons CC ES External neutrons

(a)

θcos -1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1

Eve

nts/

(0.0

2)

0

20

40

60

80

100

120

DataFit result Neutrons CC ES External neutrons

(b)

ρ0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Eve

nts/

(0.0

5)

0

50

100

150

200

250

300

350

Fit ResultAV bkgPMT+H2O bkgd. External neutrons

DataNeutrons CC ES

(c)

=55

0 cm

R

(MeV) effT6 7 8 9 10 11 12 13 20

Eve

nts/

(0.5

MeV

)

0

100

200

300

400

500

600

700

800

900

DataFit resultNeutrons CC ES External neutrons

28

Evidence for Solar Neutrino OscillationN

eutr

ino

Flux

(×

106 c

m-2

sec

-1)

Frac

tion

of S

SM

SSM Prediction (BPB 2000)

0

1

2

3

4

5

6

7

CC ES NC0.0

0.5

1.0

SNO: Direct evidence that

φ(νe) < φ(νtot)

Phys Rev C 72, 055502 (2005)

(MeV) effT6 7 8 9 10 11 12 13

Eve

nts/

(0.5

MeV

)

0

50

100

150

200

250

300Data

Systematic uncertainties

B model shape8SSM

B model shape8LMA

No evidence of spectral distortion.

ADN = 0.037 ± 0.040

Self-consistent picture of results from

Homestake, SAGE/GALLEX/GNO, and

Super-K.

29

Evidence for Reactor Neutrino Oscillations

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Nob

s/N

exp

101 102 103 104 105

Distance to Reactor (m)

ILL Savannah River Bugey Rovno Goesgen Krasnoyarsk Palo Verde Chooz

KamLAND

KamLAND: Observation of reactor

neutrino disappearance at L/E value

where solar neutrino effect occurs.

30

Evidence for Reactor Neutrino Oscillations

(PRL 94, 081801, 2005)

(M

eV)

dela

yed

E 2

3

4

5

Fri Jun 11 11:43:30 2004 (MeV)promptE0 1 2 3 4 5 6 7 8

Eve

nts

/ 0.4

25 M

eV

0

20

40

60

80

no-oscillation

best-fit oscillation

accidentals

KamLAND data

Spectral distortion seen inreactor neutrino energy spectrum

Solar data constrains θ12, while reactor

data constrains ∆m2—extreme

complementarity!

)2 e

V-5

(10

2 m∆

5

10

15

20(a)

θ2tan

)2 e

V-5

(10

2 m∆

5

10

15

20

0 0.2 0.4 0.6 0.8 1

68% CL

95% CL

99.73% CL

(b)

ONLYSOLAR DATA

SOLAR DATA + KamLAND

31

Future Solar Neutrino Experiments

There are various ideas for precision

measurement of 7Be and pep neutrinos by

low-background scintillator detectors:

• Borexino

• KamLAND

• SNO+

• liquid noble gas detectors

Barger et al, hep-ph/0502196

Possible Motivations:

• Observe turn-up in LMA survival

probability

• Constrain solar models

• Test exotic scenarios

32

Atmospheric Neutrinos

π µ + νµ

e ν ν+ eµ+

ν

π

µ

e

ν

ν

atmosphere, making pionIncident proton strikes

p

Two muon neutrinos

electron neutrino!produced for each

Super−Kamiokandedetector

33

Super-Kamiokande Event Display

34

Super-Kamiokande Atmospheric ν Results

050

100150200250300350400450

-1 -0.5 0 0.5 1cosθ

Num

ber

of E

vent

s Sub-GeV e-like

050

100150200250300350400450

-1 -0.5 0 0.5 1cosθ

Num

ber

of E

vent

s Sub-GeV µ-like

0

20

40

60

80

100

120

140

-1 -0.5 0 0.5 1cosθ

Num

ber

of E

vent

s Multi-GeV e-like

0

50

100

150

200

250

300

350

-1 -0.5 0 0.5 1cosθ

Num

ber

of E

vent

s Multi-GeV µ-like + PC

0

0.5

1

1.5

2

2.5

3

3.5

4

-1 -0.8 -0.6 -0.4 -0.2 0cosθ

Flu

x(10

-13 cm

-2s-1

sr-1

) Upward Through Going µ

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-1 -0.8 -0.6 -0.4 -0.2 0cosθ

Upward Stopping µ

0

0.001

0.002

0.003

0.004

0.005

0.8 0.85 0.9 0.95 1

sin22θ

∆m2 (

eV2 )

Zenith angle analysis

L/E analysis

0.8 0.85 0.9 0.95 1.00.0

1.0

2.0

3.0

4.0

5.0

× 10-3

PRD 71, 112005 (2005)

Super-K sees suppression of νµ flux at

large zenith angles (distances).

νe flux is unaffected.

Looks to be νµ → ντ oscillations

First clear evidence for neutrino oscillations (1998)!

35

Neutrino Mass Hierarchy

∆m2

∆m2

∆m

2

12

3

3

12solar {

} solar

atm

osph

eric

mas

s

νe νµ τν

NORMAL INVERTEDHIERARCHYHIERARCHY

∆m2atm ≈ 2.5 × 10−3 eV2 ∆m2

sol ≈ 8 × 10−5 eV2

36

Neutrino Mixing Matrix

Adjust L/E to view oscillations at different ∆m2’s

U =

1 0 0

0 c23 s23

0 −s23 c23

︸ ︷︷ ︸

c13 0 eiδs13

0 1 0

−e−iδs13 0 c13

︸ ︷︷ ︸

c12 s12 0

−s12 c12 0

0 0 1

︸ ︷︷ ︸

Atmospheric ν ’s: Short baseline reactor ν ’s: Solar ν ’s:

θ23 ≈ π/4 θ13 < π/20 θ12 ≈ π/6

Maximal mixing! (?) Small, quark-like mixing Large, non-maximal mixing

Compare to identical parameterization of CKM matrix ...

θ23 ≈ π/76 θ13 ≈ π/870 θ12 ≈ π/14

37

Physics of Long Baseline ν Experiments

295km(Tokai)

JAERISuper Kamiokande

KEKTokyo

K2K: KEK to Kamioka

T2K: J-PARC to Kamioka

(×50 stats.)

Far detector: Super-K

Basic idea: shoot a

man-made neutrino beam

through the Earth, and study

neutrino oscillations in

controlled way

Measure Determine

P (νµ → νµ) ∆m223, θ23

P (νµ → νe) θ13

P (νµ → νµ ) CPT

P (νµ → νe ) δCP , sign(∆m223)

38

K2K: KEK to Kamiokande

250 km baseline, wide-band beam

Beam

νµ 98.2%

νe 1.3%

νµ 0.5%

K2K-I: March 1999 - July 2001

Super-K accident, reconstruction

K2K-II: December 2002 - November 2004

The first long baseline ν experiment

Goal: measure νµ disappearance at atmospheric ∆m2

39

Anatomy of a Long Baseline Experiment

10 /2.2 sec11ν 10 /2.2 sec

6 ν

ν

µπAl target

+ horns MuonMonitor

NearDetectorsDecay Pipe

PionMonitor

200 meter

300 meters

12 GeV protons

250 kilometers

SK

Target: 3cm dia × 66cm long Al cylinder

Horns: toroidal B fields, pulsed at 250 kA

Pion monitor: gas Cherenkov detector

Muon monitor: segmented ionization

chamber + array of silicon pad detectors

40

12 GeV PS Beamline

FrontDetectors

Decay pipe Horn and target station

12 GeV PS

100m0

Magnetic horns focus π’s, which decay in pipe to produce νµ

41

K2K Beam Statistics

µ1.1 sec

120 nsec

∼ 6 × 1012 p.o.t. in 9 bunches

-101234567

Jan/99Jan/99 Jan/00Jan/00 Jan/01Jan/01 Jan/02Jan/02 Jan/03Jan/03 Jan/04Jan/04

Pro

tons

/Pul

se (

10^1

2)

Date

-20

0

20

40

60

80

100

120

Acc

umul

ated

PO

T (

10^1

8)

89.1 × 1018 POT usable data

Eν

Neutrino Energy Spectrum at KEK

0 1 2 3 4 5

Measurement

Beam MC

integrated

GeV

arb

itra

ry u

nit

On-axis beamRelatively wide energy

spectrum

42

K2K Near Detectors

Scibar

43

Kiloton Water Cherenkov Detector

8.6 m diameter × 8.6 m high

cylinder

680 Super-K PMTs with

electronics—a miniature Super-K

1 kton water Cherenkov detector

normalizes beam interactions on

water target.

Measure ν spectrum and

backgrounds before oscillation

Used to predict event rate at

Super-K

44

Scibar Detector

14848 extruded scintillator strips

Read out by 1.5mm diameter WLS fibres

with multi-anode PMTs

Θµ

∆Θp

µ

p

νµ

Compare measured proton recoil

direction to quasielastic prediction to

identify or reject CCQE events

(νµ + n→ µ+ p).

45

Analysis Flowchart

NeutrinoInteractionMC

∆ 2 2m , sin 2 Θ

Beam MC

# of νpµ µ, Θ distribs

Observed:

EνΦ( )

Derived:ν xsec ratios

# of νE spectrumν

rec

Observed:# of ν

E spectrumνrec

Expectation:

AT KEK ND:

AT SK:

46

Main Interaction Types

Processes modelled with the NEUT Monte Carlo

CC Quasi-Elastic (CCQE)

• Smith & Moniz with MA = 1.1 GeV

CC Resonant Single Pion (CC-1π)

• Rein & Sehgal with MA = 1.1 GeV

CC Multiple Pion (DIS)

• GRV94 + JETSET with Bodek & Yang

correction

CC Coherent Pion

• Rein & Sehgal with cross-section

rescaling by J. Marteau

NC

+ Nuclear Effects

σ/E (10−38 cm2/GeV)

Eν (GeV)

47

Low q2 Anomaly

K2K observes a deficit of

forward-going µ relative to MC in

all near detectors

• Seen in non-QE events

Two possible explanations:

• Suppression of CC-1π at

q2 < 0.1 GeV2

• Absence of CC coherent π

production

Significant nuclear effects (poorly

understood).

Scibar data

0

50

100

150

200

250

300

350

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Entries 1726

q2

2 track non-QE

GeV2

Co

un

ts /

0.05

GeV

2

DataNCCC multi πCC coherent πCC 1πCC QE

Data favours coherent pion

suppression (PRL 95, 252301

(2005)).

Oscillation analysis is insensitive

to how q2 deficit is modelled.

48

Flux measurement with the kiloton detector

The kiloton near detector, like SK, is water Cherenkov detector. So

cross-section systematics cancel in far-near ratio.

N expSK = N obs

KT ·

[∫

dEνΦSK(Eν)σ(Eν)∫

dEνΦKT (Eν)σ(Eν)·

]

MSK

MKT

·εSK

εKT

[Far-near ratio (from MC) ≈ 1 × 10−6]

N obsSK = 107 N exp

SK = 150.9+11.5−10.1

Null oscillation probability: P = 0.0025 (3.02σ)

(PRL 94, 081802 (2005))

49

Reconstructed Neutrino Spectrum at Super-K

Reconstructed energy spectrum from 1-ring µ events

Eνrec

0

2

4

6

8

10

12

14

16

18

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5[GeV]

even

ts/0

.2[G

eV]

Kolgomorov-Smirnov test probability (no oscillation): 0.08%

Kolgomorov-Smirnov test probability (best-fit oscillation): 36%

50

Allowed K2K Mixing Parameters

Consistency with null oscillation

hypothesis:

Normalization only 0.26%

Spectrum only 0.74%

Spectrum + normalization 0.005%

Favored mixing parameters:

∆m2 = 2.8 × 10−3 eV2

sin2 2θ = 1

90% CL at sin2 2θ = 1:

1.9 − 3.6 × 10−3 eV2

K2K-I & K2K-II

10-4

10-3

10-2

10-1

0 0.2 0.4 0.6 0.8 1sin2(2θ)

∆m2

[eV

2 ]

68%90%99%

Null oscillation hypothesis rejected at 4.0σ level

(PRL 94, 081802 (2005))

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The MINOS Experiment

A beam from Fermilab’s Main Injector to

the Soudan mine located 720 km away

52

Expected MINOS Sensitivity

Goals of MINOS;

• precise measurement of ∆m2

• test alternatives of oscillation model (eg. neutrino decay)

53

Conclusions• Neutrinos have mass and oscillate. Compelling evidence from four different kinds

of experiments

1. solar neutrinos

2. reactor neutrinos

3. atmospheric neutrinos

4. long baseline neutrino beams

• Neutrino mixing opens a whole new area of lepton flavour physics. This is new

physics beyond the Standard Model, involving new fields and new fundamental

constants!

• Next time:

1. How many neutrinos are there really?

2. What are the theoretical implications?

3. How do we complete our map of the neutrino mixing matrix?

4. How might we determine the absolute mass of neutrinos?

5. Are neutrinos the reason we’re all here?