1

Neutrino Neutrino

PhenomenologPhenomenolog

yy Boris KayserScottish Summer

SchoolAugust 9, 2006 +

2

The Neutrino Revolution(1998 – …)

Neutrinos have nonzero masses!

Leptons mix!

3

These discoveries come from

the observation of neutrino oscillationneutrino oscillation.

4

The Physics of The Physics of Neutrino Oscillation Neutrino Oscillation

The Physics of The Physics of Neutrino Oscillation Neutrino Oscillation

5

Neutrinos Come in at Least Three Flavors

The known neutrino flavors: e ,

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

6

The Meaning of this Association

e Detectore

e

W boson

Short Journey

e

W

W

7

Over short distances, neutrinos do not change flavor.

W

Short Journey

Does Not Occur

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

do occur during long journeys.

8

Let Us Assume Neutrino Masses and Leptonic

MixingNeutrino mass —

There is some spectrum of 3 or more neutrino mass eigenstates i:

(Mass)2

12

34

Mass (i) mi

9

Leptonic mixing —

When W+ l+ + ,

the produced neutrino state |> is

|> = U*i |i> .

Neutrino of flavor Neutrino of definite mass mi

Leptonic Mixing Matrix

le e, l , l

e, , or

i

10

Another way to look at W decay:

A given l+ can be accompanied

by any i.Amp(W+ l+ + i) = U*i

is |> = U*i |i> .

The neutrino state |> produced together with l

+ i

11

According to the Standard Model, extended to include neutrino mass and leptonic mixing — The number of different i is the same as the number of different l.

The mixing matrix U is 3 x 3 and unitary:

UU† = U†U = 1.Some models include “sterile” neutrinos — neutrinos that experience none of the known forces of nature except gravity.

In such models, there are N > 3 i, and U is N x N, but still unitary.

12

Just as each neutrino of definite flavor is a superposition of mass eigenstates i, so each mass eigenstate is a superposition of flavors .

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

|i> = Ui | > .

The flavor-fraction of i is —

|<|i>|2 = |Ui|2 .

13

The Standard Model (SM) description of neutrino interactions (not masses or leptonic mixing) is well-confirmed.

We will assume it is true, and extend it to include mixing.

For the lepton couplings to the W boson, we then have —

€

LSM = −g

2l Lα γ λ ν LαWλ

− + ν Lα γ λ l LαWλ+

( )α =e,μ ,τ

∑

= −g

2l Lα γ λ Uαiν LiWλ

− + ν Liγλ Uαi

*l LαWλ+

( )α =e,μ ,τi = 1,2,3

∑

Left-handed

Taking mixing into account

14

Insert Insert Explanation of Explanation of

Neutrino Neutrino OscillationOscillation

15

Experimental Experimental EvidenceEvidence

16

Evidence For Flavor Change

Neutrinos

Solar Reactor

(L ~ 180 km)

AtmosphericAccelerator

(L = 250 and 735 km)

Stopped Decay LSND

L 30 m

Evidence of Flavor Change

CompellingCompelling

CompellingCompelling

Unconfirmed

( )

17

Solar e is now well established.

The mechanism for this flavor conversion is the —

Large Mixing Angle version of the —

Mikheyev Smirnov Wolfenstein

— Effect.

This occurs as the neutrinos stream outward through solar material. It

requires both interactions with matter and neutrino mass and mixing.

What Happens To Solar Neutrinos

18

How Does the Large Mixing Angle

MSW Effect Work?The solar matter effect is important for the high-energy 8B neutrinos, not the low-energy pp neutrinos.

Since 3 couples at most feebly to electrons (to be discussed), and solar neutrinos are born e, the solar neutrinos are mixtures of just 1 and 2. (Convention: 2 heavier than 1).

This is a 2-neutrino system.Solar neutrino flavor change is e x, where x is some combination of and .

19

In the sun,

At the center of the sun,

√2GFNe ≈ 0.75 × 10-5 eV2 / MeV .

For Δm2sol ≈ 8 × 10-5 eV2 and typical 8B

neutrino energy of ~ 8 MeV,

Δm2sol / 4E ≈ 0.25 × 10-5 eV2 /

MeV .

The interaction term in H dominates, and e is approximately an eigenstate of H.*

€

H =Δmsol

2

4E

−cos2θsol sin2θsol

sin 2θsol cos2θsol

⎡

⎣ ⎢

⎤

⎦ ⎥+ 2GF Ne

1 0

0 0

⎡

⎣ ⎢

⎤

⎦ ⎥

e x

e

x

*For the (E ~ 0.2MeV) pp neutrinos, HVac

dominates.

20

The 88B solar neutrino propagates outward adiabatically.

It remains the slowly - changing heavier eigenstate of the slowly - changing H.

It emerges from the sun as the heavier eigenstate of HVac, 2.*

It stays 2 until it reaches the earth. Nothing “oscillates”!

Since 2 = esinsol + xcossol, (See 2 2 U matrix)

Prob[See e at earth] = sin2sol.

*Good to 91% (Nunokawa, Parke, Zukanovich-Funchal)