1. March 12, 2005Benasque Neutrinos Theory Neutrinos Theory Carlos Pena Garay IAS, Princeton ~

2. 1 kton water + Gd guided by KamLAND KamLAND 1kton LS, 2000 PMT, 33% cov (1.4 yr, 90%) Supernova (8.5 kpc) : 300 events Relic Supernova (E>6MeV) ~ 0.4 events/yr bck React Geo Bin1 125.2 (24.6) 2.3 6.3 Bin2 24.6 (19.8) 19.5 7.4 Bin3 12.9 ( 9.8) 35.1 3.9 Bin4 5.9 ( 3.9) 36.1 2.8

3. 1 kton water + Gd guided by KamLAND Gd-1kton, 2000 PMT, 33% cov (1.4 yr, 90%) Supernova (8.5 kpc) : 300 events Relic Supernova (E>5MeV) ~ 0.5 events/yr bck React Geo Bin1 125.2 (24.6) ~0 ~7 Bin2 24.6 (19.8) ~1 ~8.5 Bin3 12.9 ( 9.8) ~2 ~4.5 Bin4 5.9 ( 3.9) ~2 ~3

4. Neutrino mass : Direct methods

6. Plan I. Neutrinos as Dirac Particles II. Making Neutrinos III. Neutrinos as Majorana Particles

7. Massive Neutrinos : Dirac (p,h) (p,-h) CPT (p,h) (p,-h) CPT Boost, if m ≠ 0 Chirality vs Helicity

9. Massive Neutrinos : Majorana (p,h) (p,-h) CPT (p,h) (p,-h) CPT Boost, if m ≠ 0

10. Massive Neutrinos : Majorana (p,h) (p,-h) CPT (p,h) (p,-h) CPT Boost, if m ≠ 0

11. Parameters : Majorana Majorana phases only relevant in processes involving Lepton Number Violation (     Previous discussion on neutrino osc. is valid for Majorana ! Helicity suppressed by smallness of neutrino masses 

12. Majorana vs Dirac : 0  decay 0  : nn  ppe – e – (without neutrinos) m e | | = (  1/2 F  ) 1/2 F  = G 0  |M 0 f – (g A / g V ) 2 M 0 GT | 2 searchingobserved

13. Normal Hierarchy Inverted Hierarchy Degenerate Connection with neutrino parameters : j | | = |  m j U ej 2 | = |  m j | U ej | 2 e i  | | | = |  m j U ej 2 | = |  m j | U ej | 2 e i  |

14. From Osc. Data :

15. Signal : Energy Resolution required Summed electron energy in units of the kinematic endpoint (Q)

16. nuclear matrix elements? Observed : Neutrinos are Majorana Not observed : Hard to extract neutrino parameters, and exclude Dirac. Nuclear Physics methods : QRPA, SM Next Generation experiments :

17. Positive signal ? 214 Bi  ? Klapdor et al (part of HM) 28.8 (6.9)  3-4  Bckg ~ 60 ev.

18. Present Limits : Candidate Detector Present (eV) nucleus type (kg yr) T 1/2 0νββ (yr) 48 Ca >9.5*10 21 (76%CL) 76 Ge Ge diode ~30 >1.9*10 25 (90%CL) <0.39 +0.17 -0.28 82 Se >9.5*10 21 (90%CL) 100 Mo >5.5*10 22 (90%CL) 116 Cd >7.0*10 22 (90%CL) 128 Te TeO 2 cryo ~3 >1.1*10 23 (90%CL) 130 Te TeO 2 cryo ~3 >2.1*10 23 (90%CL) <1.1 - 2.6 136 Xe Xe scint ~10 >1.2*10 24 (90%CL) <2.9 150 Nd >1.2*10 21 (90%CL) 160 Gd >1.3*10 21 (90%CL)

19. Projected/proposed ExperimentNucleusDetector T 0 ν (y) eV CUORE 130 Te.77 t of TeO 2 bolometers (nat) 7 x 10 26.014-.091 EXO 136 Xe10 t Xe TPC + Ba tagging1 x 10 28.013-.037 Gertha 76 Ge1 t Ge diodes in LN1 x 10 28.013-.050 Majorana 76 Ge1 t Ge diodes4 x 10 27.021-.070 MOON 100 Mo34 t nat.Mo sheets/plastic sc. 1 x 10 27.014-.057 DCBA 150 Nd20 kg Nd-tracking2 x 10 25.035-.055 CAMEO 116 Cd1 t CdWO 4 in liquid scintillator > 10 26.053-.24 COBRA 116 Cd, 130 Te 10 kg of CdTe semiconductors 1 x 10 24.5-2. Candles 48 CaTons of CaF 2 in liq. scint.1 x 10 26.15-.26 GSO 116 Cd2 t Gd 2 SiO 5 :Ce scint in liq scint 2 x 10 26.038-.172 Xmass 136 Xe1 t of liquid Xe3 x 10 26.086-.252

20. Theorem 0    Majorana in gauge theories with SSB

21. Seesaw mechanism   L R R L   x Integrating out the heavy field R m R >> : Equivalenly, diagonalize the mass matrix in L - R basis

22. Leptogenesis Generate L asymmetry from direct CP violation in right handed decay Net effect (2 families needed): Convert L into B via anomaly  Matter- Antimatter asymmetry

23. Summary Neutrinos oscillate, refract, decohere,…  > test sources and explore mixing matrix The field is open with a well defined program : - Complete the mixing matrix :  13 and  CP - 0  Dirac vs Majorana - Test sources ( Solar luminosity with neutrinos,… ) Expand to discovery regions : -Low energies : solar, ( s. DM searches), terrestrial, SN, … -High energies : hadronic acceleration sources, CR connection Be ready for surprises