1. Pontecorvo’s idea An introductory course on neutrino physics (IV)
J.J. Gómez-Cadenas
IFIC-Valencia
Summer Student School
CERN, July,2006

2. Una puerta que no es una puerta…
Or is it… ?

3. Fermion masses
A fermion mass can be thought as a coupling constant between a left and a right handed helicity state.
This, however would break gauge invariance (since right and left handed states have different weak charges).
But the the SM uses the same ghost that gives masses to the Z and W to provide fermion masses

4. Weak and Mass States Mass States: Objects that couple to Higgs.
Weak States: Objects that couple to weak bosons.
Are those two types of objects identical?

5. Mixing in two families What if they are not?
Assume instead that weak and mass states are connected by a simple two-dimensional rotation (assume, for simplicity two families)
Then mass and weak states are connected by means of an unitary transformation, the PMNS mixing matrix, which depends of a single parameter, the mixing angle q

6. Neutrino oscillations
detection
source ne
propagation L
The weak interaction
produces neutrinos
of a given flavor
The mass eigenstates
Propagate at different velocities
Detection again via
weak interaction

7. Oscillation Probability

8. Atmospheric n oscillationsne nm nm

9. Is God fine-tuning physics?
detection
source ne
propagation L

10. Neutrino oscillations in Matter
ne,nm, nt interact with e, p and n of matter via NC.interactions (Z). Only ne interact via (CC) with the electrons of the medium
Oscillation probability change in matter. There can be a resonant enhancement of the oscillation probability. The Mikheyev-Smirnov-Wolfenstein (MSW) effect.
Poscmatter can be large (1) even if mixing angle in vacuum is small.
In practice this implies that (if MSW is at work) ne can oscillate to nm, nt BEFORE exiting the sun

11. Oscillation Probability in matter
The probability of oscillation in matter has the same form as in vacuum

12. MSW resonance condition
For constant matter density there is an energy such that mixing in matter is maximal independently from the vacuum value.
Thus the probability of neutrino transition in matter can be large even if the mixing angle is small

13. Adiabatic approximation

14. Solar oscillations
Neutrinos produced at the sun (ne) oscillate to other neutrinos via matter-enhanced MSW.
Dm2 =8 x 10-5 eV2
q300

15. Solar neutrino oscillations
Matter effect on e from Sun to Earth
The LMA solar solution +
matter effects
explain beautifully
all solar neutrino experiments

16. Oscillations revisited
Normal
Inverted

17. The PNMS matrix
Unless the other two angles q13 is small (experimental upper limit q13 <100)
If d 0,p,2p…then weak interactions violate CP symmetry in the lepton sector (as in the quark sector)
CP violation phase
solar
Links atmospheric & solar sectors
atmospheric

18. The last anomaly LSND Does not fit in a 3 family scenario 2 m2
MiniBooNE (Fnal )
Testing it …
If it is confirmed (2005)!?
Change our vision of 
(has happened before…)