The Elementary Particles

e−

e−

γ γ

u

u

γ

d

d

The Basic Interactions of Particles

g

u, d

u, d

W+

u

d

Z0

u, d

u, dν

ν

Z0

e−

e−

Z0

e−

νe

W+

Electromagnetic Force

Strong Nuclear Force

Weak Nuclear Force

Charged Current

Neutral Current

W

e−

νe

W++u

d

+

e−

νe

This diagram represent process such as:

β decay: n → p + e− + νe

Inverse β decay: p + νe → e+ + n

Pion decay: π+ → μ+ + νμ

tim

e

u

d e+

νe

u

u d

dn

p u

μ+ νμ

dπ+

Processes Involving NeutrinosCharged Current

u

d

e− νeu

u d

d

n

p

Processes Involving NeutrinosNeutral Current

u, d, e, ν

u, d, e, ν ν

ν

Z0

particle

νν

Z0

antiparticlee− e+

LEP Collider

e+

e−

The natural width (in mass) of a short lived particle is determined in part by how many decay channels it has available to it. The Z0 width unaccounted for in seen decay modes is consistent with exactly three neutrino states.

Number of Neutrinos

Neutrino SourcesCosmic Rays

Neutrino SourcesAccelerators

Earth Shielding:

Stops particles that are not neutrinos

Decay region: →, K→

50 m decay pipeFNAL 8 GeV Booster

n

p

Toroidal Magnet

Target and toroidal focusing magnet Detector

Z

N

N=Z

U235

92

Cs140

55

Rb94

37

Typical Fission

Nuclear reactors are a very intense sources of νe coming from the b-decay of the neutron-rich fission fragments.

A commercial reactor, with 3 GW thermal power, produces 6×1020 νe/s

Neutrino Sources

Know Isotopes

Nuclear Reactors

Neutrino SourcesThe Sun

Solar Fusion Processes

The sun produces νe as a by-product of the fusion process that fuel it.

Other Neutrino Sources

Supernova produce a huge burst of neutrinos as all the protons in the star are converted to neutrons to form a neutron star.

β-decay isotopes can be used as a source of neutrinos or antineutrinos

Electron capture isotopes produce a mono-energetic beam of neutrinos

Big Bang relic neutrino are as copious as photons, but they are so low in energy that no one knows how to see them

ee NN A

1ZAZ

ee NN A1Z

AZ

ee NN A

1ZatomicAZ

Important Experiments

HOMESTAKE

Solar Neutrinos

Homestake: νe (E>814 keV) + 37Cl → e− + 37Ar

SAGE and Gallex: νe (E>234 keV) + 71Ga→ e− + 71Ge

Radiochemical solar neutrino experiments are designed to count neutrinos above the reaction threshold

The resulting isotope is chemically separated and counted when they decay.

Homestake saw only 33% of the expected solar neutrinos.

While SAGE and Gallex found about 75% of the expected neutrinos.

Important ExperimentsAtmospheric Neutrinos

Super-Kamiokande

Kamiokande and later Super-Kamiokande detect neutrinos produced by cosmic rays in the atmosphere from all around the world.

They see the Čerenkov rings produced by the charged leptons as they emerge inside the detector from the neutrino charged current interaction.

In the atmosphere, two νμ are produced for each νe. This 2:1 ratio was observed for neutrinos coming from directly above the detector where the upper atmosphere is only 30 km away, but from te other side of the Earth the rate was much lower

Oscillations and Neutrinos Mass

Remember: there are three flavors of neutrinos (νe, νμ and ντ), so we might expect three different masses (m1, m2 and m3)

But neutrinos are quantum mechanical particles → They behave in strange ways

For example: the masses and flavors don’t have to be aligned. In fact, the masses form a second basis

In quantum mechanics this happens a lot. We use the linear algebra for the rotation of vectors to handle this.

Now and

2

1

cosθsinθ

sinθcosθ

e

νμ

ν2 ν1

νeθ

21 sinθcosθ e 21 θcosθsin-

Follow the prescription of quantum mechanics:

• The ν’s are “Wave Functions”

• Their evolution in time is given by the Schrödinger Equation…

• This is the “Oscillation Probability”

• It has constant amplitude piece: sin22θ

• And an oscillatory piece:

Δm212 = m1

2-m22 (Not only need mass, but different masses!)

E

LmP e 4

θsin2sin)(21222

21 θsinθcos)0(

te

How Does Neutrino Mass Lead to Oscillations?

21 θsinθcos)( 21 tiEtiE eet

Hdt

di

Schrödinger's Equation

E

Lm

4sin

2122

ν

ν

pmpE ii 2

Ep

ν

ν

2)(tP

ν

ν

ctL

3

2

1

τ3τ2τ1

μ3μ2μ1

e3e2e1

τ

μ

e

ν

ν

ν

UUU

UUU

UUU

ν

ν

ν

100

0θcosθsin

0θsinθcos

θcos0θsin

010

θsin0θcos

θcosθsin0

θsinθcos0

001

1212

1212

1313

1313

2323

2323

i

i

MNS

e

e

U

Generalizing for Three Neutrinos

For three neutrinos just add another dimension to the mixing matrix

It can be parameterized in terms of three rotation (mixing) angles: θ12, θ13 and θ23

There are three corresponding mass squared differences: Δm12

2, Δm132 and Δm23

2

Important ExperimentsMore Solar Neutrinos

SNO used a heavy water (D2O) target to measure the solar flux with neutral current (NC), charges current (CC) and elastic scattering (mixed NC and CC)

CC: νe + d → e− + p + p

NC: ν + d → ν + p + n

ES: ν + e− → ν + e−

They definitively showed that some of the solar neutrinos, which began life as νe, where interacting in the SNO detector as νμ and ντ.

ν-e Elastic Scattering

νe

νee−

e−

W−

ν

Z0

ν e−

e−

For electron neutrinos elastic scattering is part charged current and part neutral current, while for νμ and ντ it is pure neutral current. This results in a 6 times larger probability of elastic scattering for νe.

Elastic scattering with a very low momentum transfer (forward scattering) has a very high probability. This causes a “drag” on neutrinos as they pass through matter. This drag is greater on νe causing accelerated mixing which is a function of electron density. This is know as the matter effect (or MSW effect) and it is the dominant oscillation effect in the dense solar core.

Important ExperimentsMore “Solar” Neutrinos

The KamLAND experiment used neutrinos from all of the nuclear reactors in Japan and Korea (flux averaged baseline of 180 km and average energy of 3 MeV) to study oscillations at the solar neutrino Δm2.

Neutrinos were detected with inverse β-decay in scintillator.

Neutrino Oscillation Data

sin22θ

Δm

2 (

eV2 )

Atmospheric (θ23)

Solar (θ12)

7.07.0

6.06.0

4.0

4.0

2.05.0

~

8.0MNSU

Two of the three mixing angles are known. Only θ13 is unknown.

ν3

ν2ν1

Dm232

Dm122

Dm132 ≈ Δm12

2 + Δm232

ν3

ν2ν1

Dm22

Dm12

mas

s2

Other Unknowns and Big QuestionsThe absolute mass scale:

Oscillation experiment are sensitive to the differences between mass2, but not the actual masses

ν3

Dm22

ν2ν1

Dm12

mas

s2

Other Unknowns and Big QuestionsThe mass hierarchy:

Not knowing the absolute mass of the mass eigenstates means that we don’t know which is heaviest

ν3

Dm22

ν2ν1

Dm12

mas

s2

ν3

Dm22

ν2ν1

Dm12

mas

s2

Normal Hierarchy Inverted Hierarchy