1. Jose Bernabeu U. Valencia and IFIC XIII International Workshop on Neutrino Telescopes March 2009 CP Violation in Neutrino Oscillations without Antineutrinos: Energy Dependence

2. Programme  What is known, what is unknown in Neutrino Oscillations  Third Generation of Neutrino Experiments: CP Violation  The CP phase with neutrinos only: Energy Dependence  A combined BB and EC experiment for the same ion Ytterbium  Comparison between i) low energy (E p (SPS) ≤ 450 GeV, Frejus and Canfranc) i) low energy (E p (SPS) ≤ 450 GeV, Frejus and Canfranc) ii) high energy (E p (SPS) ≤ 1000 GeV, Canfranc and Boulby) ii) high energy (E p (SPS) ≤ 1000 GeV, Canfranc and Boulby)  CP-Violation Discovery Potential and Mass Hierarchy Determination  Conclusions

3. Neutrino flavour oscillations  Neutrino flavour oscillations ? Majorana neutrinos ?  0: masses and phases Absolute neutrino masses ?  3 H beta, Cosmology Form of the mass spectrum  Matter effect in neutrino propagation What is known, What is known, what is unknown what is unknown, A hint ?

4. The Pontecorvo MNS Matrix  For Flavour oscillations U: 3 mixings, 1 phase  Atmospheric  KEK, MINOS, OPERA Appearance   e ! Reactors Matter effects Solar KAMLAND Borexino Even if they are Majorana After diagonalization of the neutrino mass matrix,

5. Three Generations of Experiments Three Generations of Experiments  0. Only three?  MiniBoone  I. Solar Sector, Atmospheric Sector   II. Connection between both Sectors   III. CP-Violating Interference  δ Super-Beams? Beta / EC Beams ? Neutrino Factory? Δ Δm 2 12, θ 12 │Δm 2 23 │, θ 23 Borexino MINOS, OPERA θ θ 13, Sign (Δm 2 23 ) Double CHOOZ, Daya Bay, T2K, NOVA, …

6.  European Strategy Plan demands for ~ 2012 a CDR with the alternatives: SuperBeams, Beta/EC Beams, Neutrino Factory.  SuperBeam: no pure Flavour, uncertain continuous Spectrum.  Beta Beam: pure Flavour, known continuous Spectrum.  EC Beam: pure Flavour, known single Monochromatic Beam.  Neutrino Factory: pure Flavour iff detector with charge discrimination, known continuous Spectrum. Frejus CPV can be observed either by an Asymmetry between Neutrinos and Antineutrinos or by Energy Dependence (CP phase as a phase shift) in the Neutrino channel, or both. Third Generation Experiments: CP Violation

7. Why Energy Dependence ? A theorem CP violation : CPT invariance + CP violation = T non-invariance No Absorptive part  Hermitian Hamiltonian  CP odd = T odd = is an odd function of time = L ! In vacuum neutrino oscillations In vacuum neutrino oscillations for relativistic neutrinos  L/E dependence, so CP-even (odd) terms in the appearance probability  Even (odd) functions of energy. Then ENERGY DEPENDENCE disentangles the CP-even and CP-odd terms

8. Interest of energy dependence in suppressed neutrino oscillations Appearance probability : |Ue3| gives the strength of P(ν e → ν μ ) CP odd term is odd in E/L δ gives the interference pattern: CP odd term is odd in E/L δ acts as a phase shift  This suggests the idea of either a monochromatic neutrino beam to separate δ and |Ue3| by energy dependence with different boosts, or a combination of channels with different neutrino energies in the same boost CP violation accessible in suppressed appearance experiments, in order to have access to the interference between the atmospheric and solar probability amplitudes

9. Neutrinos from electron capture Electron capture: From the single energy e - -capture neutrino spectrum, we can get a pure and monochromatic beam by accelerating ec-unstable ions and choosing forward ν’s  One can concentrate all the intensity at the most appropriate energy for extracting the neutrino parameters ● 2 body decay!In the CMsingle discrete energy ● 2 body decay!  In the CM, a single discrete energy if a single final nuclear level is populated How can we obtain a monochromatic neutrino beam? Forward direction Z protons N neutrons Z-1 protons N+1 neutrons boost J. B., C. E. et al EνEν

10. A combined beta-beam and EC neutrino experiment A combined beta-beam and EC neutrino experiment ( 156 Yb) Suppressed appearance probabilities for the CERN-Frejus (130 Km, red line) and CERN-Canfranc (650 Km, blue line) baselines. The unoscillated neutrino flux is shown for γ=166 Suppressed appearance probabilities for the CERN- Canfranc (650 Km, blue line) and CERN-Boulby (1050 Km, red line) baselines. The unoscillated neutrino flux is shown for γ=369

11. Similarities and Differences between Beta beam and EC neutrinos - In proton rich nuclei (to restore the same orbital angular momentum for protons and neutrons )  Superallowed Gamow-Teller transition a SINGLE Gamow-Teller resonance. ● The “breakthrough” came thanks to the recent discovery of isotopes with small half-lives of one minute or less, which decay in neutrino channels near 100% to a SINGLE Gamow-Teller resonance. Nuclear A Facility with an EC channel would require a different approach to acceleration and storage of the ion beam compared to the standard beta- beam, as the atomic electrons of the ions cannot be fully stripped A Facility with an EC channel would require a different approach to acceleration and storage of the ion beam compared to the standard beta- beam, as the atomic electrons of the ions cannot be fully stripped Partly charged ions have a short vacuum life-time against collisions. The interesting isotopes have to have Partly charged ions have a short vacuum life-time against collisions. The interesting isotopes have to have half-life < vacuum half-life ~ few min.

12. Electron neutrino fluxes from EC and BB  Distribution of neutrino energy per unit surface at the detector in the forward direction: Notice: i) All Nuclear Physics input is under control ii) The Intensity increases like γ 2 with the Lorentz factor. Monochromatic lineE=2γE 0 2γ MeV to the end point of iii) The Monochromatic line E=2γE 0 is higher by 2γ MeV to the end point of the β + the β + spectrum EC: BB:, and

13. Experimental Setups for the combined experiment  Appearance Experiment : Electron Neutrino Flux × Oscillation Probability to muon neutrinos × CC Cross Section for muon production. I: CERN-Frejus (130 Km), γ=166  SPS II: CERN-Canfranc (650 Km), γ=166  SPS III and III-WC: CERN-Canfranc (650 Km), γ=369  Upgraded SPS IV and IV-WC: CERN-Boulby (1050 Km), γ=369  Upgraded SPS Detectors: LAr or TASD, 50 kton  Neutrino spectral information from CC muon events Water Cerenkov, 0.5 Mton  Neutrino energy from QE events only + inelastic events in a single bin, with 70% efficience The separation between the energy of the EC spike and the end point energy of the beta-spectrum is possible: if E ν (QE)>2γE o (β), since E ν (true)> E ν (QE), the event must be attributed to the EC flux and hence, it is not necessary to reconstruct the true energy

14. Comparing baselines I and II  For the combined BB + EC fluxes with θ 13 =1 0 and δ=90 0 The BB channel contributes very little to the overall sensitivity of the setup, due to the γ 2 dependence. The bulk of the sensitivity is due to the EC channel placed on the first oscillation maximum

15. Comparing energies II and III with the same baseline  Combination of BB and EC fluxes for θ 13 =1 0 and δ=90 0 γ=166 γ=369 The sensitivity is better with the upgraded SPS energy The relative role of the two BB and EC components is exchanged when going from II to III

16. Setup III: The virtues of combining energies from BB and EC Setup III: The virtues of combining energies from BB and EC Setup III: θ 13 =3 0, δ=90 0 BB EC BB+EC The power of the combination of the two channels is in the difference in phase and in amplitude between the two fake sinusoidal solutions, selecting a narrow allowed region in the parameter space

17. Set up III-WC : Disentangling Set up III-WC : Disentangling θ 13 and δ θ 13 and δ Solutions, from discrete degeneracies included, for θ 13 =1 0, 3 0 and for different values of the CP phase The increase in event rates improves the results substantially with respect to those results for Setup III, although not as much as the size factor between the two detectors. The effects of the hierarchy clon solution are taken into account. The mass ordering can be determined for large values of the mixing angle. The hierarchy degeneracy worsen the ability to measure δ for negative true values of δ.

18. Comparing III-WC and IV-WC  Boulby provides a longer baseline L=1050 km than Canfranc L=650 km. This has two contrasting effects on the sensitivity to measure CP violation: i) Sufficient matter effects to resolve the hierarchy degeneracy for small values of θ 13 ; ii) It decreases the available statistics The smaller count rate results in a poorer resolution. The longer baseline allows for a good determination of the mass ordering, eliminating more degenerate solutions.

19. CP Discovery Potential for WC  Comparing the two locations of the WC detector, the Canfranc baseline has a significally (slightly) better reach for CP violation at negative (positive) values of δ than the Boulby baseline. CanfrancBoulby

20. Mass hierarchy determination  Fraction of δ for which the neutrino mass hierarchy can be determined III-WC with present priors in the known parameters III-WC with negligible errors in the known parameters IV-WC with present priors in the known parameters The Boulby baseline, with its larger matter effect, is better for the determination of the mass hierarchy

21. Conclusions  The two separate channels BB and EC have a limited overlap of the allowed regions in the (θ 13, δ) plane, resulting in a good resolution on the intrinsic degeneracy.  The CP phase sensitivity is obtained by only using neutrinos, thanks to the Energy Dependence of the oscillation probability with the combination of the two BB and EC channels.  THE SPS UPGRADE TO HIGHER ENERGY (Ep = 1000 GeV) IS CRUCIAL TO HAVE A BETTER SENSITIVITY TO CP VIOLATION (the main objective of the third generation neutrino oscillation experiments) IFF ACCOMPANIED BY A LONGER BASELINE ( Canfranc or Boulby).  THE BEST E/L FOR HIGHER SENSITIVITY TO THE MIXING U(e3) IS NOT THE SAME THAN THAT FOR THE CP PHASE. Like the phase- shifts, the effect of δ is easier to observe by going to the region of the second oscillation.

22. Conclusions  Setups III and III-WC, with the Canfranc baseline, have larger counting rates and a better tuning of the beam to the oscillatory pattern, resulting in a very good ability to measure the parameters. These setups provide the best sensitivity to CP violation for positive values of δ.  For negative δ, the type of hierarchy cannot be resolved in some cases for these setups.  Setups IV and IV-WC, with the Boulby baseline, provide a better determination of the hierarchy and a good reach to CP violation for negative δ, even if the mass ordering is unknown. THE COMBINATION OF THE TWO BB AND EC BEAMS FROM A SINGLE DECAYING ION AND A FIXED γ BOOST ACHIEVES REMARKABLE RESULTS

23. Acknowledgements  Thanks to many colleagues and, particularly, to my collaborators: J. Burguet-Castell, C. Espinoza, M. Lindroos, C. Orme, S. Palomares-Ruiz and S. Pascoli.  Thank you very much for your attention…