Neutrino Oscillation

Nguyen Thanh Phong

Yonsei Univ., May 19, 2008

Outline

1. Brief History of the Neutrino

2. The evidence of the oscillations of neutrinos

3. Theory of neutrino oscillation

4. Summary

1. Brief History of the Neutrino

1) 1896: Henri Becquerel discovers natural radioactivity while studying phosphorescent properties of uranium salts.

rays: easy to absorb, hard to bend, positive charged, mono-energetic;

ray: harder to absorb, easy to bend, negative charge, spectrum?;

rays: no charge, very hard to absorb.

2) 1897: J.J. Thompson discovers the electron.

3)1911: Lise Meitner and Otto Hahn first shown that the energies of electrons mitted by beta decay had a continuous rather than discrete spectrum.

4) 1914: Chadwick presented definitive evidence for a continuous beta-ray spectrum.

F. A. Scott, Phys. Rev. 48, 391 (1935)

Instead ofdiscrete

spectra were continuous

Origin continuous -ray spectrum was unknown. Different options include several different energy loss mechanisms.

It took 15 years more to decide that the “real” beta-ray spectrum was really continuous. Reason for continuous spectrum was a total mystery:

+ QM: Spectra are discrete;

+ Energy-momentum conservation: N → N’ + e-

electron energy and momentum well defined

Nuclear physics before 1930: nucleus = nPP + nee-

Example: 4He = 4P +2e- work well.

However: 14N = 14P +7e- is expected to be a fermion, but it was experimentally known that is a boson!

There was also a problem with the magnetic moment of nuclei:

N, P e (=eh/4mc). How can the nuclear magnetic moment

be so much smaller than the electron one if the nucleus contains

electrons?

SOLUTION: bound, nuclear electrons are very weird!

+ This can also be used to solve the continuous -ray spectrum:

energy need not to be conserved in nuclear processes! (N. Bohr)

“…This would mean that the idea of energy and its conservation fails in dealing with processes involving the emission and capture of nuclear electrons. This does not sound improbable if we remember all that it has been said about peculiar properties of electrons in the nucleus.” (G. Gamow, 1931)

Enter the neutrino…

Weakly interacting massless neutral fermion

1930: Postulated by Pauli: the "neutron", a new spin 1/2 particle with small mass and no electric charge in order that: + resolve the problem of continuous beta-ray spectra, + reconcile nuclear model with spin-statistics theorem.

1932: Chadwick discovered the neutron.Chadwick’s neutron if different from Pauli’s neutron = neutrino (Fermi).

Adapted summary of an English translation to Pauli’s letter dated December 4, 1930

observing the unobservable…

1) 1956: “Discovery” of the electron neutrino (Reines and Cowan) in the Savannah River Nuclear Reactor site.

2) 1962, the second neutrino: e (Lederman, Steinberger, Schwarts at Brookhaven National Laboratory-BNL). First neutrino beam:

3) 2001: directly observed (DONUT experiment at FERMILAB. Same strategy:

2. The evidence of the oscillations of neutrinos

A. Solar neutrinos

B. Atmospheric neutrinos

C. Nuclear reactor neutrinos

A. Solar neutrinos

•How the Sun burns

Solar neutrino deficit is now understood as a consequence of neutrinos oscillation.

A. Atmospheric neutrinos

Atmosphere

(Sign of the particles are neglected in this figure.)

A half of lost !!

B. Nuclear reactor neutrinos

Reactor Long Baseline Experiment 150 - 210 km

( Epr > 2.6 MeV )

3. Theory of neutrino oscillation

A. Neutrino oscillation in vacuum

B. Neutrino oscillation in matter

Neutrinos come from at least three flavors

The known three flavors:

Each of these is associated with the corresponding charged-lepton flavor:

The meaning of this association

Over short distance, neutrinos do not change flavor:

Does not occur

But if neutrinos have masses, and leptons mix, neutrino flavor changes do occur during

long journeys

Let us assume neutrino have mass and leptons mix

When W+ decays:

The produced neutrino state |> is

Neutrino of flavor Neutrino of definite mass mi

Lepton mixing matrix

Another way to look at W boson decay

A given l+ can be accompanied by any i, and

The neutrino state |> produced together with l+ is

According to the Standard Model, extended toinclude neutrino mass and leptonic mixing

The number of different i is the same as thenumber of different l (3).

The mixing matrix U is 3 x 3 and unitary: UU† = U†U = 1

From |> = ΣiU*i|i> and the unitarity of U,

The flavor-α fraction of i is

Neutrino Flavor Change (Oscillation) in Vacuum

What is Propagator (i) Prop(i)?

|i,L = exp[ -i(Eit - piL)] |I,o

Neutrino sources are ~ constant in time.

Averaged over time of the interference

is

Unless E1 = E2

Only neutrino mass eigenstates with a commonenergy E are coherent.

For each mass eigenstate

|i,L = exp[-imi2L/2E)] |I,o

Probability for Neutrino Oscillation in Vacuum

For Antineutrinos: We assume the world is CPT invariant.

— Comments —

1. If all mi = 0, so that all Δmij2 = 0,

Flavor changes mass

2. If there is no mixing,

Flavor changes Mixing⇒

3. P ( → ) depends only on squared-masssplittings. Oscillation experiments cannot tell us

4. Neutrino flavor change does not change the total flux in a beam. It just redistributes it among flavors

When There are Only Two Flavorsand Two Mass Eigenstates

The oscillations of neutrinos in matter

Hamiltonian of a neutrino in a medium:

H = H0 + V, V = VNC + VCC const.*I + Ve

CC

(Up to small higher-order corrections)

2 oscillation in constant-density matter

— Comments —

1) Mikheyev - Smirnov - Wolfenstein (MSW) resonance:

2) For anti-neutrinos, VeCC changes sign, hence

there is no MSW resonance for anti-neutrinos

3) Matter effects induces the CP violation for 2 oscillation in a medium.

Summary

The history of neutrino is briefly introduced.

Some evidences of the oscillations of solar neutrino, atmospheric neutrino and nuclear reactor neutrino are shown.

The theory of neutrino oscillation in vacuum is derived. The interaction of neutrinos with medium is introduced, and 2-family neutrinos oscillation in constant density matter is considered. We see that the CP-violation can induced from the effect of matter which is absented in vacuum.