1. CP violation and mass hierarchy searches Neutrinos in particle physics and astrophysics (lecture) June 2009 Walter Winter Universität Würzburg TexPoint fonts used in EMF: AAAAA A A A

2. 2 Contents  Phenomenology  Simulation tools  Experiments and CP violation measurement  CP precision measurement  CPV from non-standard physics?  Mass hierarchy measurement  Summary

3. Phenomenology (partly repetition from lecture)

4. 4 Neutrino mixing with three flavors ( ) ( ) ( ) =xx (s ij = sin  ij c ij = cos  ij ) Potential CP violation From observations:  23,  12 large  13 small,  unknown Atmospheric mixingReactor mixingSolar mixing

5. 5 Neutrino masses: three flavors  Normal or inverted mass ordering  Neutrino oscillations driven by |  m 31 2 | (atm.) >>  m 21 2 (solar)  Flavor content in mass eigenstate i given by |U  i | 2  Absolute mass scale unknown (< eV):  Tritium endpoint  Neutrinoless double beta decay  Cosmology 8 8 NormalInverted |U e3 | 2 ~ s 13 2

6. 6  Three Flavors: six parameters (three angles, one phase; two independent mass squared differences)  Describes atmospheric, solar, reactor data in two flavor limits: Neutrino oscillations Coupling :  13 Atmospheric oscillations: Amplitude:  23 Frequency :  m 31 2 Solar oscillations : Amplitude:  12 Frequency :  m 21 2 Suppressed effect :  CP (Super-K, 1998; Chooz, 1999; SNO 2001+2002; KamLAND 2002)

7. 7 Two flavor limits (lecture!)  Atmospheric neutrinos  Solar neutrinos Adiabatic evolution (MSW), mostly sensitive to  12  Reactor experiments  Atmospheric oscillation length (L ~ 1-2 km)  Solar oscillation length (L ~ 30-100 km)

8. 8 Three flavor effects With the following definitions expand to second order in small quantities  and  13 : Test: for  = 0,  13 = 0: P e  = 0 Problem: The info has to be disentangled from this expression! Mass hierarchy! Quantities of interest Spectral terms

9. 9 CP violation (CPV)  CP violation: Matter and antimatter behave „differently“ (in a well defined way including the peculiarities of the Standard Model, i.e., V-A interactions)  Necessary requirement for baryogenesis  Here: CP violation ~ Im (e i  ) ~ sin  CP  Define: we discover CP violation if we can exclude  CP = 0 and  (where sin  CP =0, or U is real) at the chosen confidence level

10. 10 Terminology  Any value of  CP (except for 0 and  ) violates CP  Sensitivity to CPV: Exclude CP-conserving solutions 0 and  for any choice of the other oscillation parameters in their allowed ranges

11. 11 CPV - statistics   2 (  12,  13,  23, ,  m 21 2,  m 31 2 )  For future experiments: we have to simulate data (O i ) assuming a set of (  12,  13,  23, ,  m 21 2,  m 31 2 ) implemented by nature: „true values“, „simulated values“ Mostly the unknown  13 and  relevant  Compute  2 (  13,  )=Min  12,  13,  23,  m212,  m312  2 (  12,  13,  23,0/ ,  m 21 2,  m 31 2,  13,  ) (marginalization over unwanted parameters)  Discovery potential as a function of (  13,  ) Our „theory“ (fit values), describe T i

12. 12 CPV discovery reach … in (true) sin 2 2  13 and  CP Sensitive region as a function of true  13 and  CP  CP values now stacked for each  13 Read: If sin 2 2  13 =10 -3, we expect a discovery for 80% of all values of  CP No CPV discovery if  CP too close to 0 or  No CPV discovery for all values of  CP 33 Best performance close to max. CPV (  CP =  /2 or 3  /2)

13. 13 Measurement of CPV (Cervera et al. 2000; Freund, Huber, Lindner, 2000; Huber, Winter, 2003; Akhmedov et al, 2004)  Antineutrinos:  Magic baseline:  Silver:  Platinum, Superb.:

14. 14 Degeneracies  CP asymmetry (vacuum) suggests the use of neutrinos and antineutrinos Burguet-Castell et al, 2001)  One discrete deg. remains in (  13,  )-plane (Burguet-Castell et al, 2001)  Additional degeneracies: (Barger, Marfatia, Whisnant, 2001)  Sign-degeneracy (Minakata, Nunokawa, 2001)  Octant degeneracy (Fogli, Lisi, 1996) Best-fit Antineutrinos Iso-probability curves Neutrinos

15. 15 Intrinsic vs. extrinsic CPV  The dilemma: Strong matter effects (high E, long L), but Earth matter violates CP  Intrinsic CPV (  CP ) has to be disentangled from extrinsic CPV (from matter effects)  Example:  -transit Fake sign-solution crosses CP conserving solution  Typical ways out:  T-inverted channel? (e.g. beta beam+superbeam, platinum channel at NF, NF+SB)  Second (magic) baseline (Huber, Lindner, Winter, hep-ph/0204352) NuFact, L=3000 km Fit True  CP (violates CP maximally) Degeneracy above 2  (excluded) True Critical range

16. 16 The magic baseline

17. Simulation tools

18. 18 GLoBES AEDL „Abstract Experiment Definition Language“ Define and modify experiments AEDL files User Interface C library, loads AEDL files Functionality for experiment simulation Simulation of future experiments http://www.mpi-hd.mpg.de/ lin/globes/ (Huber, Lindner, Winter, 2004; Huber, Kopp, Lindner, Rolinec, Winter, 2006) Application software linked with user interface Calculate sensitivities etc.

19. 19 Event rate engine In practice: Secondary particles integrated out  Detector response R(E,E´) EE´ E: Incident neutrino energy E‘: Reconstructed energy E: Secondary particle energy (e.g. muon)

20. Experiments and CP violation measurement

21. 21 There are three principle possibilities to artificially create neutrinos:  Beta decay:  Example: Nuclear fission reactors  Pion decay:  From accelerators:  Muon decay:  The muons are produced by pion decays! Muons, Neutrinos Reminder: „man-made“ neutrinos Protons TargetSelection, Focusing Pions Decay tunnel Absorber Neutrinos

22. 22 Next generation experiments  Perspectives to constrain  13 and find CPV relatively weak  Focus on next-to-next generation! Example: Neutrino factory (Huber, Lindner, Schwetz, Winter, in prep.)  CL

23. 23 Neutrino factory: International design study IDS-NF:  Initiative from ~ 2007- 2012 to present a design report, schedule, cost estimate, risk assessment for a neutrino factory  In Europe: Close connection to „Euro us“ proposal within the FP 07  In the US: „Muon collider task force“ ISS (Geer, 1997; de Rujula, Gavela, Hernandez, 1998; Cervera et al, 2000) Signal prop. sin 2 2  13 Contamination Muons decay in straight sections of a storage ring

24. 24 IDS-NF baseline setup 1.0  Two decay rings  E  =25 GeV  5x10 20 useful muon decays per baseline (both polarities!)  Two baselines: ~4000 + 7500 km  Two MIND, 50kt each  Currently: MECC at shorter baseline (https://www.ids-nf.org/)

25. 25 NF physics potential  Excellent  13, MH, CPV discovery reaches (IDS-NF, 2007)  Robust optimum for ~ 4000 + 7500 km  Optimization even robust under non-standard physics (dashed curves) (Kopp, Ota, Winter, arXiv:0804.2261; see also: Gandhi, Winter, 2007)

26. 26 Experiment comparison  The sensitivities are expected to lie somewhere between the limiting curves  Example: IDS- NF baseline (~ dashed curve) (ISS physics WG report, arXiv:0810.4947, Fig. 105)

27. 27 On near detectors@IDS-NF  Define near detectors including source/detector geometry:  Near detector limit: Beam smaller than detector  Far detector limit: Spectrum similar to FD  Compute spectrum, study systematical errors, study impact of physics (Tang, Winter, arXiv:0903.3039) ~ND limit~FD limit

28. 28 Example: Systematics (Tang, Winter, arXiv:0903.3039)

29. CP precision measurement

30. 30 Performance indicator: CP coverage  Problem:  CP is a phase (cyclic)  Define CP coverage (CPC): Allowed range for  CP which fits a chosen true value  Depends on true  13 and true  CP  Range: 0 < CPC <= 360   Small CPC limit: Precision of  CP  Large CPC limit: 360  - CPC is excluded range

31. 31 CP pattern  Performance as a function of  CP (true)  Example: Staging. If 3000-4000 km baseline operates first, one can use this information to determine if a second baseline is needed (Huber, Lindner, Winter, hep-ph/0412199) Exclusion limitPrecision limit

32. CPV from non-standard physics?

33. 33 ~ current bound CPV from non-standard interactions  Example: non-standard interactions (NSI) in matter from effective four-fermion interactions:  Discovery potential for NSI-CPV in neutrino propagation at the NF Even if there is no CPV in standard oscillations, we may find CPV! But what are the requirements for a model to predict such large NSI? (arXiv:0808.3583) 33 IDS-NF baseline 1.0

34. 34  Effective operator picture: Describes additions to the SM in a gauge-inv. way!  Example: NSI for TeV-scale new physics d=6: ~ (100 GeV/1 TeV) 2 ~ 10 -2 compared to the SM d=8: ~ (100 GeV/1 TeV) 4 ~ 10 -4 compared to the SM  Current bounds, such as from CLFV: difficult to construct large (= observable) leptonic matter NSI with d=6 operators (except for   m, maybe) (Bergmann, Grossman, Pierce, hep-ph/9909390; Antusch, Baumann, Fernandez-Martinez, arXiv:0807.1003; Gavela, Hernandez, Ota, Winter,arXiv:0809.3451)  Need d=8 effective operators!  Finding a model with large NSI is not trivial! Models for large NSI? mass d=6, 8, 10,...: NSI

35. 35 Systematic analysis for d=8  Decompose all d=8 leptonic operators systematically  The bounds on individual operators from non- unitarity, EWPD, lepton universality are very strong! (Antusch, Baumann, Fernandez-Martinez, arXiv:0807.1003)  Need at least two mediator fields plus a number of cancellation conditions (Gavela, Hernandez, Ota, Winter, arXiv:0809.3451) Basis (Berezhiani, Rossi, 2001) Combine different basis elements C 1 LEH, C 3 LEH Cancel d=8 CLFV But these mediators cause d=6 effects  Additional cancellation condition (Buchmüller/Wyler – basis) Avoid CLFV at d=8: C 1 LEH =C 3 LEH Feynman diagrams

36. Mass hierarchy (MH)

37. 37 Motivation  Specific models typically come together with specific MH prediction (e.g. textures are very different)  Good model discriminator (Albright, Chen, hep-h/0608137) 8 8 NormalInverted

38. 38  Magic baseline:  Removes all degeneracy issues (and is long!)  Resonance: 1-A  0 (NH:, IH: anti- ) Damping: sign(A)=-1 (NH: anti-, IH: )  Energy close to resonance energy helps (~ 8 GeV)  To first approximation: P e  ~ L 2 (e.g. at resonance)  Baseline length helps (compensates 1/L 2 flux drop) Matter effects (Cervera et al. 2000; Freund, Huber, Lindner, 2000; Huber, Winter, 2003; Akhmedov et al, 2004) Lecture:

39. 39 Baseline dependence  Comparison matter (solid) and vacuum (dashed)  Matter effects (hierarchy dependent) increase with L  Event rate (, NH) hardly drops with L  Go to long L! (Freund, Lindner, Petcov, Romanino, 1999) (  m 21 2  0) Event rates (A.U.) Vacuum, NH or IH NH matter effect

40. 40 Mass hierarchy sensitivity  For a given set of true  13 and  CP : Find the sgn-deg. solution  Repeat that for all true true  13 and  CP (for this plot)

41. 41 Small  13 optimization: NF  Magic baseline good choice for MH  E  ~ 15 GeV sufficient (peaks at 8 GeV) (Huber, Lindner, Rolinec, Winter, 2006) (Kopp, Ota, Winter, 2008) E  -L (single baseline)L 1 -L 2 (two baselines)

42. 42 Summary  CP violation measurement requires next-to- next generation of experiments  Example: Neutrino factory  Other relevant quantities:  CP precision measurement  CP violation from non-standard physics  Mass hierarchy  CP violation discovery in the lepton sector may be an interesting hint for leptogenesis! This talk at: http://www.physik.uni-wuerzburg.de/~winter/Teaching/neutrinos.html