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

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

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

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?

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

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

Oscillation Probability

Atmospheric n oscillations ne nm nm

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

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

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

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

Adiabatic approximation

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

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

Oscillations revisited Normal Inverted

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

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…)