Neutrinos Theory

1
Neutrinos Theory

• Carlos Pena Garay
• IAS, Princeton

2
Plan

• I. Neutrinos as Dirac Particles
• Neutrinos from earth and heavens
• Neutrinos as Majorana Particles

3
Plan

• I. Neutrinos as Dirac Particles
• Making Neutrinos
• Neutrinos as Majorana Particles

4
Nuclear b-decay

5
Neutrinos are left-handed

6
Neutrinos must be massless

Helicity Chirality (massless)
All neutrinos left handed gt massless
If neutrinos are massive
neutrino right-handed gt Contradiction!
7
Standard Model

Exact Lepton number symmetry terms never
arise in perturbation theory Renormalizability
All gauge currents satisfy anomaly
cancellation What about global symmetries L is
broken non perturbatively through the anomaly,
but B-L is conserved to all orders terms
never arise in the Standard Model
8
Anti-neutrinos are right-handed

-
CPT nL gt nR
9
3 neutrino families (flavors)

10
Standard Model

11
Global symmetries

The results of charged-current experiments (until
recently) were consistent with the existence of
three different neutrino species with the
separate conservation of Le, Lm and Lt.
12
Massive Neutrinos Dirac

n(p,h)
n(p,-h)
CPT
Boost, if m ? 0
Boost, if m ? 0
n(p,-h)
n(p,h)
CPT
13
Standard Model right handed

14
Standard Model right handed

15
Standard Model right handed

Masses Several distinctive features I am
going to concentrate today is neutrino
oscillations
16
Parameters Dirac

Exercise
17
Neutrino Oscillations

W
X
nj
lk
li
Uij
Ujk
18
Neutrino Oscillations in Vacuum

Due to different masses, different phase
velocities
Osc. Length distance to come back to the
initial state
19

Production, propagation and detection as a unique
process, where neutrinos are virtual particles
propagating between production and detection
Neutrinos are described by propagators S
(xP-xD) Consider finite production and detection
regions and finite energy and momentum resolution
20

If
neutrinos can be considered real (on shell) and
production, propagation, and detection can be
treated separately Match initial and final
conditions Wave packet formalism
21

Correct calculation of the phase
Phases calculated in the same space-time
point Second summand is small by either one
and/or the other term gt standard result
Oscillation effects disappear if neutrino masses
are all equal
22

Exercise Write Pee, Pem
Exercise Minimal number of Pab to know all
the others
23
One example

24
Some real cases

25

Neutrino Oscillations in matter
After a plane wave pass through a slab, the phase
is shifted p (x(n-1)R) Net effect

26

Only the difference of potential is
relevant Net effect

27

Two Neutrino Oscillations in matter
Dm2 2E
Dm2 4E
- cos 2q Ve sin 2q
sin 2q
0
ne nm
ne nm
d dt
i
Dm2 4E
sin22q
sin22qm
( cos2q - 2 2GFNeE/Dm2)2 sin 22q
Difference of the eigenvalues
Dm2 2E
( cos2q - 2 2GFneE/Dm2)2 sin 22q
H2 - H1
28

Resonance
sin2 2qm
n
n
In resonance
sin2 2qm 1
sin2 2q 0.08
sin2 2q 0.825
Flavor mixing is maximal Level split is minimal
ln l0 cos 2q

Vacuum oscillation length

Refraction length
ln / l0
n E
Resonance width DnR 2nR tan2q
Resonance layer n nR DnR
29

Level crossing
sin2 2q 0.08
sin2 2q 0.825
ne
ne
n2m
n2m
nm
nm
ln / l0
n1m
ln / l0
n1m
Small mixing
Large mixing
-if(t)
n (t) cosqa n1m sinqa n2m e
30

Graphical interpretation
n (Re nenm, Im nenm, nene - 1/2)
elements of density matrix
2p lm
B (sin 2qm, 0, cos2qm)
lm 2p/ D H
oscillation length
Evolution equation
dn dt
( B x n )
Coincides with equation for the electron spin
precession in the magnetic field
f 2pt/ lm
- phase of oscillations
P nene nZ 1/2 cos2qZ/2
31

A real case solar neutrinos
32
The Neutrino Matrix SM n mass

ALL oscillation neutrino data BUT LSND