1. CP violation and mass hierarchy searches with Neutrino Factories and Beta Beams NuGoa – Aspects of Neutrinos Goa, India April 10, 2009 Walter Winter Universität Würzburg TexPoint fonts used in EMF: AAAAA A A A

2. 2 Contents  Motivation from theory: CPV  CPV Phenomenology  The experiments  Optimization for CPV  CP precision measurement  CPV from non-standard physics  Mass hierarchy measurement  Summary

3. Motivation from theory

4. 4 Where does CPV enter?  Example: Type I seesaw (heavy SM singlets N c ) Charged lepton mass terms Eff. neutrino mass terms Block-diag. CC Primary source of CPV (depends BSM theory) Effective source of CPV (only sectorial origin relevant) Observable CPV (completely model-indep.) Could also be type-II, III seesaw, radiative generation of neutrino mass, etc.

5. 5  From the measurement point of view: It makes sense to discuss only observable CPV (because anything else is model-dependent!)  At high E (type I-seesaw): 9 (M R )+18 (M D )+18 (M l ) = 45 parameters  At low E: 6 (masses) + 3 (mixing angles) + 3 (phases) = 12 parameters Connection to measurement There is no specific connection between low- and high-E CPV! But: that‘s not true for special (restrictive) assumptions! CPV in 0  decay LBL accessible CPV:  If  U PMNS real  CP conserved Extremely difficult! (Pascoli, Petcov, Rodejohann, hep-ph/0209059)

6. 6 Why is CPV interesting?  Leptogenesis: CPV from N c decays  If special assumptions (such as hier. M R, NH light neutrinos, …) it is possible that  CP is the only source of CPV for leptogensis! (N c ) i ~ M D (in basis where M l and M R diagonal) (Pascoli, Petcov, Riotto, hep-ph/0611338 ) Different curves: different assumptions for  13, …

7. 7 How well do we need to measure?  We need generic arguments Example: Parameter space scan for eff. 3x3 case (QLC-type assumptions, arbitrary phases, arbitrary M l ) The QLC-type assumptions lead to deviations O(  C ) ~ 13   Can also be seen in sum rules for certain assumptions, such as (  : model parameter)  This talk: Want Cabibbo-angle order precision for  CP ! (Niehage, Winter, arXiv:0804.1546) (arXiv:0709.2163)

8. CPV phenomenology

9. 9 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

10. 10 Measurement of CPV (Cervera et al. 2000; Freund, Huber, Lindner, 2000; Huber, Winter, 2003; Akhmedov et al, 2004)  Antineutrinos:  Magic baseline:  Silver:  Platinum, Superb.:

11. 11 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

12. 12 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

13. 13 The magic baseline

14. 14 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 ~ Cabibbo-angle precision at 2  BENCHMARK! Best performance close to max. CPV (  CP =  /2 or 3  /2)

15. The experiments

16. 16 More recent modifications:  Higher  (Burguet-Castell et al, hep-ph/0312068)  Different isotope pairs leading to higher neutrino energies (same  ) Beta beam concept … originally proposed for CERN ( http://ie.lbl.gov/toi )  Key figures (any beta beam): , useful ion decays/year?  Often used “standard values”: 3 10 18 6 He decays/year 1 10 18 18 Ne decays/year  Typical  ~ 100 – 150 (for CERN SPS) (CERN layout; Bouchez, Lindroos, Mezzetto, 2003; Lindroos, 2003; Mezzetto, 2003; Autin et al, 2003) (Zucchelli, 2002) (C. Rubbia, et al, 2006) 

17. 17 Current status: A variety of ideas “Classical” beta beams:  “Medium” gamma options (150 <  < ~350) -Alternative to superbeam! Possible at SPS (+ upgrades) -Usually: Water Cherenkov detector (for Ne/He) (Burguet-Castell et al, 2003+2005; Huber et al, 2005; Donini, Fernandez-Martinez, 2006; Coloma et al, 2007; Winter, 2008)  “High” gamma options (  >> 350) -Require large accelerator (Tevatron or LHC-size) -Water Cherenkov detector or TASD or MID? (dep. on , isotopes  (Burguet-Castell et al, 2003; Huber et al, 2005; Agarwalla et al, 2005, 2006, 2007, 2008, 2008; Donini et al, 2006; Meloni et al, 2008)  Hybrids:  Beta beam + superbeam (CERN-Frejus; Fermilab: see Jansson et al, 2007)  “Isotope cocktail” beta beams (alternating ions) (Donini, Fernandez-Martinez, 2006)  Classical beta beam + Electron capture beam (Bernabeu et al, 2009) ……  The CPV performance depends very much on the choice from this list! Often: baseline Europe-India

18. 18 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

19. 19 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/)

20. 20 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)

21. Optimization for CPV

22. 22  Small  13 : Optimize discovery reach in  13 direction  Large  13 : Optimize discovery reach in (true)  CP direction ~ Precision!  What defines “small” vs “large  13 ”? A Double Chooz, Day Bay, T2K, … discovery? Optimization for CPV Optimization for small  13 Optimization for large  13

23. 23 Large  13 strategy  Assume e.g. that Double Chooz discovers  13  Minimum wish list easy to define:  5  independent confirmation of  13 > 0  3  mass hierarchy determination for any (true)  CP  3  CP violation determination for 80% (true)  CP (~ 2  sensitvity to a Cabibbo angle-size CP violation) For any (true)  13 in 90% CL D-Chooz allowed range!  What is the minimal effort for that?  NB: Such a minimum wish list is non-trivial for small  13 (arXiv:0804.4000Sim. from hep-ph/0601266; 1.5 yr far det. + 1.5 yr both det.) (arXiv:0804.4000; Sim. from hep-ph/0601266; 1.5 yr far det. + 1.5 yr both det.)

24. 24 Example: Minimal beta beam  Minimal effort =  One baseline only  Minimal   Minimal luminosity  Any L (green-field!)  Example: Optimize L-  for fixed Lumi:  CPV constrains minimal    as large as 350 may not even be necessary! (see hep-ph/0503021)  CERN-SPS good enough? (arXiv:0804.4000) Sensitivity for entire Double Chooz allowed range! 5yr x 1.1 10 18 Ne and 5yr x 2.9 10 18 He useful decays

25. 25  Assume that Double Chooz … do not find  13  Example: Beta beam in  13 -direction (for max. CPV)  „Minimal effort“ is a matter of cost! Small  13 strategy Example: Beta beams (Huber et al, hep-ph/0506237)(Agarwalla et al, arXiv:0802.3621) 50 kt MID L=400 km LSF ~ 2 (LSF)

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. CP precision measurement

28. 28  Theoretical example Large mixings from CL and sectors? Example:  23 l =  12  =  /4, perturbations from CL sector (can be connected with textures) (Niehage, Winter, arXiv:0804.1546; see also Masina, 2005; Antusch, King 2005 for similar sum rules)  The value of  CP is interesting (even if there is no CPV)  Phenomenological example Staging scenarios: Build one baseline first, and then decide depending on the outcome  Is  CP in the „good“ (0 <  CP <  ) or „evil“ (  <  CP < 2  ) range? (signal for neutrinos ~ +sin  CP ) Why is that interesting?  12 l dominates  13 l dominates  12 ~  /4 +  13 cos  CP  12 ~  /4 –  13 cos  CP   13 > 0.1,  CP ~    13 > 0.1,  CP ~   23 ~  /4 – (  13 ) 2 /2  23 ~  /4 + (  13 ) 2 /2  CP and octant discriminate these examples!

29. 29 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

30. 30 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

31. CPV from non-standard physics?

32. 32 ~ 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

33. 33 CPV discovery for large NSI  If both  13 and |  e  m | large, the change to discover any CPV will be even larger: For > 95% of arbitrary choices of the phases  NB: NSI-CPV can also affect the production/ detection of neutrinos, e.g. in MUV (Gonzalez-Garcia et al, hep-ph/0105159; Fernandez-Martinez et al, hep-ph/0703098; Altarelli, Meloni, 0809.1041; Antusch et al, 0903.3986) (arXiv:0808.3583) 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)

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 Small  13 optimization: BB  Only B-Li offers high enough energies for „moderately high“   Magic baseline global optimum if  >=350 (B-Li)  Recently two-baseline setups discussed (Coloma, Donini, Fernandez-Martinez, Lopez-Pavon, 2007; Agarwalla, Choubey, Raychaudhuri, 2008) (Agarwalla, Choubey, Raychaudhuri, Winter, 2008)

43. 43 Optimization for large  13  Performance as defined before (incl. 3  MH)  L > 500 km necessary  Large enough luminosity needed  High enough  necessary  Ne-He: limited to  > 120  B-Li: in principle, smaller  possible  High  = high E = stronger matter effects! (arXiv:0804.4000)

44. 44 Physics case for CERN-India? (neutrino factory)  MH measurement if  13 small (see before; also de Gouvea, Winter, 2006)  Degeneracy resolution for 10 -4 ≤ sin 2 2  13 ≤ 10 -2 (Huber, Winter, 2003)  Risk minimization (e.g.,  13 precision measurement) (Gandhi, Winter, 2007)  Compementary measurement (e.g. in presence of NSI) (Ribeiro et al, 2007)  MSW effect verification (even for  13 =0) (Winter, 2005)  Fancy stuff (e.g. matter density measurement) (Gandhi, Winter, 2007)

45. 45 Summary  The Dirac phase  CP is probably the only realistically observable CP phase in the lepton sector  Maybe the only observable CPV evidence for leptogenesis  This and  1,  2 : the only completely model-inpendent parameterization of CPV  What precision do we want for it? Cabibbo-angle precision?  Relates to fraction of „  CP “ ~ 80-85%  For a BB or NF, the experiment optimization/choice depends on  13 large or small  Other interesting aspects in connection with CPV: CP precision measurement, NSI-CPV  MH for small  13 requires magic baseline