CP Violation in Neutrino Oscillations without Antineutrinos: Energy Dependence

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

2. 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 (Ep(SPS) ≤ 450 GeV, Frejus and Canfranc) ii) high energy (Ep(SPS) ≤ 1000 GeV, Canfranc and Boulby) • CP-Violation Discovery Potential and Mass Hierarchy Determination • Conclusions Programme

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

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

5. 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? │Δm223│, θ23 Δm212, θ12 Δ MINOS, OPERA Borexino θ13, Sign (Δm223) Double CHOOZ, Daya Bay, T2K, NOVA, … θ

6. Third Generation Experiments: CP Violation • 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.

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 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. Appearance probability: • 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 Interest of energy dependence in suppressed neutrino oscillations • CP violation accessible in suppressed appearance experiments, in order to have access to the interference between the atmospheric and solar probability amplitudes • |Ue3| gives the strength of P(νe→νμ) • δ gives the interference pattern: CP odd term is odd in E/L • δ acts as a phase shift

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

10. A combined beta-beam and EC neutrino experiment (156Yb) • 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 • 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 • 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: EC: BB: , and • Notice: • i) All Nuclear Physics input is under control • ii) The Intensity increases like γ2 with the Lorentz factor. • iii) The Monochromatic lineE=2γE0 is higher by 2γ MeV to the end point of • the β+ spectrum

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 Eν(QE)>2γEo(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 θ13=10 and δ=900 • The BB channel contributes very little to the overall sensitivity of the setup, due to the γ2 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 θ13=10 and δ=900 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: θ13=30, δ=900 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 θ13 and δ • Solutions, from discrete degeneracies included, for θ13=10 , 30 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 θ13; 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. Canfranc Boulby

20. Mass hierarchy determination • Fraction of δ for which the neutrino mass hierarchy can be determined • IV-WC with present priors in the known parameters • III-WC with present priors in the known parameters • III-WC with negligible errors 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 (θ13, 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…