Selected topic in neutrino physics Petr Vogel, Caltech

1. Selected topic in neutrino physicsPetr Vogel, Caltech • Overview of oscillation phenomenology • KamLAND, a culmination of half century of reactor neutrino studies • Neutrinoless double beta decay: from rates to Majorana masses • Mechanism of lepton number violation • An example of model building

2. New era of neutrino physics • Atmospheric neutrino oscillations (in particular zenith angle dependence of the muon neutrino flux, confirmed by K2K) 2.Solar neutrino deficit (in particular the difference in neutrino fluxes deduced from the charged and neutral current reaction rates) 3. KamLAND (reactor nedisappearance, oscillations seen with the terrestrial sources) 4. LSND oscillation observations (unconfirmed, but soon to be checked; if correct all bets are off)

3. Consequences: This is a first clear manifestation of “physics beyond the Standard model”. • At least some neutrinos are massive. Lower limits are 50 and 10 meV, upper limit ~ 2 eV from tritium b decay, or alternatively, Smn < 1 eV from cosmology and astrophysics. • Mixing exists. Two mixing angles are large, one is small) • But we do not know the absolute mass scale • We do not know the behavior under charge conjugation • We know nothing about CP symmetry of leptons

4. (entries evaluated for Ue3 = 0.1, near the middle of allowed range)

5. Neutrino mass and oscillations:An overview In the standard electroweak model neutrinos are massless and the lepton flavors are exactly conserved. Formally this is a consequence of the absence of the right-handed weak singlet components. Neutrino masses do not arise even through loop effects. Charged lepton and neutrino fields form doublets in SU(2)L: From the width of Z it follows that Nn = 2.984 +- 0.008. BBN is compatible with 3 flavors and disfavors 4.

6. Neutrino mass is generated by a phenomenological mass term, connecting the left and righthanded fields: Themass is analogous to the mass term of charged leptons, it might violate flavor, but conserves the lepton number. The Majorana mass might exist if there are no additive conserved charges. It violates the total lepton number. For N lefthanded neutrinos ni and n sterile nj Mnhas N + n Majorana eigenstates nkc = nk. For N lefthanded neutrinos there are N masses, N(N-1)/2 mixing angles, (N-1)(N-2)/2 CP phases, and (N-1) Majorana phases.

7. NxN unitary mixing matrix has 2N2 real parameters. N is used for normalization, N(N-1) for orthogonality, N is absorbed by charged lepton phases. Thus N2 is left. N phases can be eliminated by choosing the phases of the charged lepton fields. There are N(N-1) parameters left. (N-1)(N-2)/2 CP phases + (N-1) Majorana phases =N(N-1)/2 phases altogether N(N-1)/2 angles Altogether N(N-1) mixing parameters + N-1 mass differences + 1 mass scale

8. Basic formulae for vacuum oscillations:

9. Parametrization of the 3x3 mixing (MNS or PMNS) matrix: Majorana phases ai do not affect flavor oscillations Since q13 is small, q12 ~ qsolar, and q23 ~ qatm (or En in MeV and Losc in m)

10. The magnitude of CP or T violation in flavor oscillations is sind where Dij = (mi2 – mj2)L/4E. Thus the size of the effect is the same in all channels. CP violation is possible only when all three angles and all three mass differences are nonvanishing.

11. Oscillations in matter: When neutrinos propagate in matter, additional phase appears, due to effective neutrino-matter interaction with electrons (only for electron neutrinos and antineutrinos): And with nucleons for all active neutrinos:

12. The additional phase is then And the corresponding oscillation length is

13. The equations of motion can be rewritten either in the vacuum mass eigenstate basis, Or in the flavor eigenstate basis In either case the matter eigenstates depend on L0, Losc, and on the vacuum mixing angle q

14. There is a resonance, i.e. maximum mixing, if Losc/Locos2q = 1. In practical units the ratio Losc/Lo is

15. We can thus consider several special cases:

18. Why is the survival probability increasing again for large En? At resonance the two eigenvalues are essentially degenerate, and there is a probability Px for jumping from one eigenstate to another. Since cos2qm(rmax) ~ -1, and at high energies Px ~ 1, <P(ne -> ne)> -> cos2q.

20. Thus solar neutrinos (from 8B decay observed in SK and SNO) actually “do not oscillate”. They are born as the heavier eigenstate n2, and propagate like that all the way to a detector. The fact that the oscillation parameters derived from the solar n and reactor ne agree is a sign of not only CPT invariance but test the whole concept of vacuum and matter oscillations.

21. Atmospheric neutrinos. Best fit Dm322 ~ 2x10-3eV2, sin22q23 > 0.94

22. Allowed regions of parameter space (2003)

23. Present status of our knowledge of oscillation parameters 8.2-0.5+0.6x10-5(2004)

24. LSND – fly in the ointment L = 30 m, En = 20-50 MeV, “decay at rest spectrum” Oscillations nm-> ne, 87.9 +- 22.4 +- 6.0 events, oscillation probability 0.264 +- 0.067 +- 0.45 % Most of the parameter range excluded by reactor and KARMEN experiments, but a sliver with 0.2 < Dm2 < 10 eV2 remains. Requires existence of sterile neutrinos !!! At present tested by Mini-BOONE at Fermilab, wait and see……(until 2005 at least)

26. Reminder, direct neutrino mass mesurement 1) Time of flight – not sensitive enough 2) Two body decays, e.g. p+ -> m+ + nm, not sensitive enough 3) Three body decay (b decay of 3H) This is essentially model independent, based on kinematics only. Incoherent sum, mn = (S |Uei|2 mi2)1/2 is determined. Present limit 2.5 – 2.8 eV, planned sensitivity ~0.3eV (KATRIN).

28. Cosmological constraints The presently observed distribution of matter (through high resolution galaxy surveys) and CMB are both affected by the presence of massive neutrinos in the early Universe. Combined analysis issensitive to Smi.