J.J. Gómez-Cadenas IFIC-Valencia Summer Student School CERN, July,2006 The Image of the Vampire An introductory course on neutrino physics (II) J.J. Gómez-Cadenas IFIC-Valencia Summer Student School CERN, July,2006

When a Vampire faces a a mirror? What happens… When a Vampire faces a a mirror?

Parity Parity  Invariance under left  right (symmetry of mirror image and object) Parity operation (space inversion) P, changes the sign of any true (polar) vector x y -x -y -P P J Axial vectors such as angular momentum remain unchanged

The heretics 1950, Lee & Yang To decide univocally whether parity is conserved in weak interactions one must perform an experiment to determine whether weak interactions differentiate the right from the left. A relatively simple possibility is to measure the angular distributions of the electrons coming from beta decays of oriented nuclei… an asymmetry of the distribution… constitutes an unequivocal proof that parity is not conserved in beta decays

b decay of cobalt (concept) J P2 P1 I2 I1 z P Concept of the 1956 Wu and Ambler experiment: A polarized nucleus emits electrons with momenta p1 and p2. If parity is conserved the original situation and its mirror transformed cannot be distinguished I1 = I2

b decay of cobalt B Cerium-magnesium nitrate cristal Cryostat Source counter magnetic field & low temperature so that the Co60 spins where aligned along the magnetic field. Reverse the magnetic field to change polarization (J to -J) There were more electrons ejected in the direction opposite to the Co60 spins, than in the direction along the spins, showing parity violation.

The Goldhaber experiment 1958: To measure the neutrino helicity Goldhaber, Grozins & Sunyar studied the decay of 152Eu into 152Sm in which the nucleus captures an electron and emits a neutrino The nucleus of Sm recoils from the n conserving momentum and helicity. Thus a measurement of the nucleus’s helicity provides that of the neutrino

Results of Goldhaber experiment

Another example: pion decay

Pion decay and CP Antineutrinos are right handed!

Neutrino polarization

What if neutrinos are massive? Suppose the neutrino has a tiny mass (more on that later) Then it cannot go at the speed of light and the neutrino can exist in two helicity states. (jump into a reference system moving faster than n to see its helicity flip) Who is this nR state?

Dirac versus Majorana nR is a distinct state Yn = nL + nR forming a Dirac spinor (like the other fermions) nR is the nL antineutrino Yn = nL + nLC Any charge carried by the neutrino is violated (since particle and antiparticles carry opposite charges)

V-A Theory: Feynman & Gellmann 1958

The W boson To preserve the unitarity bound and control divergences in higher order processes one needs to introduce an “intermediate” carrier (as in QED) replacing G by an effective constant which would depend on momentum transfer

Neutral currents (Gargamelle, 1973) Events induced by a (conventional) neutrino beam in which no lepton was present

Standard Model predicts Charged and Neutral Currents

The mass of the neutrino It was clear right from Pauli’s postulate that the mass of the neutrino was either very light or exactly zero. In his great 1934 paper, Fermi already shows how a massive neutrino would affect the end-point of the electron spectrum in nuclear b-decay.

Kurie Plot Spectrum of electrons emitted in b decay for masless neutrinos

Kurie Plot for a massive neutrino -3 -2 -1 0 Ee-E0 [eV] 1 0.8 0.6 0.4 0.2 rel. rate [a.u.] theoretical b spectrum near endpoint mn = 0eV mn = 1eV Only 10-10 of all decays here

Direct Measurement of the neutrino mass Mainz/Katrin (Future) mn < 0.2eV (90%CL)

SM neutrino interactions neutrinos only couple to the weak bosons Z and W