1. Long baseline neutrino oscillations: Theoretical aspects NOW 2008 Conca Specchiulla, Italy September 9, 2008 Walter Winter Universität Würzburg TexPoint fonts used in EMF: AAAAA A A A

2. 2 Contents  Theoretical motivation: Quantities of interest  How to measure these? - Phenomenology  Experiment choice and optimization  Neutrino factory: what can we expect?  The potentially unexpected  Summary

3. Quantities of interest

4. 4 Theoretical motivation  Mass models describe masses and mixings (mass matrices) by symmetries, GUTs, anarchy arguments, etc.  From that: predictions for observables  Example: Literature research for  13   13 as performance indicator for models (Albright, Chen, 2006) Talk: Mu-Chun Chen, Friday

5. 5  Large mixings from CL and sectors? Example:  23 l =  12  =  /4, perturbations from CL sector (can be connected with textures) (Niehage, Winter, 2008)  Another example: QLC+Flavor symmetries lead e.g. to Modern QLC scenarios do not have an exact factor k=1 there (depends on model) (e.g. Plentinger, Seidl, Winter, 2008; see also: Frampton, Matsuzaki, 2008) Some other examples  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! k as performance indicator for QLC models k

6. 6 Perform. indicators for theory What observables test the theory space most efficiently?  Magnitude of  13 (see before!)  Mass hierarchy (strongly affects textures)  Deviations from max. mixing (  -  symmetry?)   23 octant  |sin 2  12 -1/3| (tribimaximal mixings?)  |sin  CP -1| (CP violation) (leptogenesis?)  Value of  CP  k  C +  12 ~  /4 ~  23 (k as indicator for quark-lepton unification models?)  Dev. from std. osc. framework (Antusch et al, hep-ph/0404268) Most important for LBL experiments

7. Long baseline phenomenology

8. 8 Why GeV energies? Unoscillated flux  Cross sections ~ E (DIS regime)  Flux ~ E 2 (beam collimation)  For fixed L: unoscillated event rate ~ E 3 Oscillated flux  Adjust baseline to stay on osc. maximum Flux ~ 1/L 2, L ~ E on oscillation maximum  Event rate ~ E on oscillation maximum  In addition: Matter effects (resonance energy ~ 10 GeV in Earth‘s mantle)  Measure mass hierarchy, Flux(L) ~ const. at resonance

9. 9 GeV Long baseline experiments Contamination SourceProduction … and DetectionLimitationsL Beam, Super- beam Intrinsic beam BGs, systematics 100- 2,500 km ~ 0.5 – 5 GeV Neutrino factory Charge identification, NC BG 700- 7,500 km 2-25 GeV  -beam Source luminosity 100- 7,500 km 0.3 – 10 GeV For leading atm. params Signal prop. sin 2 2  13

10. 10 Channels of interest  Disappearance for  m 31 2,  23 :    NB: We expand in  Appearance for  13, CPV, MH:  Golden: e   (NF/BB) or    e  (SB) (e.g., De Rujula, Gavela, Hernandez, 1999; Cervera et al, 2000)  Silver: e   (NF – low statistics!?) (Donini, Meloni, Migliozzi, 2002; Autiero et al, 2004)  Platinum:   e (NF: difficult!) (see e.g. ISS physics working group report)  Other appearance:    (OPERA, NF?)  Neutral currents for new physics (e.g., Barger, Geer, Whisnant, 2004; MINOS, 2008)  31 =  m 31 2 L/(4E)

11. 11 Appearance channels (Cervera et al. 2000; Freund, Huber, Lindner, 2000; Huber, Winter, 2003; Akhmedov et al, 2004)  Antineutrinos:  Magic baseline:  Silver:  Superbeams, Plat.:

12. 12 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  -beam,  -beam, anti- Iso-probability curves

13. 13 Degeneracy resolution  Matter effects (sign- degeneracy) – long baseline, high E  Different beam energies or better energy resolution in detector  Second baseline  Good enough statistics  Other channels  Other experiment classes Talk: Thomas Schwetz WBB FNAL-DUSEL, T2KK, NF@long L, … Monochromatic beam, Beta beam with different isotopes, WBB, … T2KK, magic baseline ~ 7500 km, SuperNOvA Neutrino factory, beta beam, Mton WC SB+BB CERN-Frejus, silver/platinum @ NF Atmospheric, … (many many authors, see e.g. ISS physics WG report) (Minakata, Nunokawa, 2001; Parke)

14. 14 On-axis WBB versus off-axis NBB Example: NuMI-like beam  100kt liquid argon  CP =-  /2  CP =+  /2 sin 2 2  13 CP violationMass hierarchy (Barger et al, hep-ph/0703029) Constraint from NuMI beam FNAL- DUSEL WBB Ash River OA, NOvA* Off-axis technology may not be necessary if the detector is good enough, i.e., has good BG rejection and good energy resolution! WC good enough??? On axis C

15. 15 Quantification of performance Commonly used performance indicators: IndicatorDescription+-  13 sensitivity (limit) New  13 limit if no signal Does not depend on (true)  CP, MH Strongly affected by degs (corresponds to worst case discovery reach)  13, CPV, MH discovery reach Range of (true)  13 and  CP for which  13, CPV, or MH can be discovered Comprehensive picture of parameter space Difficult to visualize: Depends on two true parameters Sensitivity to octant Range of (true)  13,  23 (and  CP ) for which the  23 octant can be established Comprehensive picture of parameter space Many true parameter dependencies …

16. 16 Example: Discovery reaches … and the “Fraction of  CP ” Sensitive region as function of true  13 and  CP  CP values now stacked for each  13 Read: If sin 2 2  13 =0.04, we expect a discovery for 20% of all values of  CP Worst case  13 reach Best case  13 reach “Typical”  CP : CP fraction 50% Sometimes: Band for risk wrt  CP Simplifications: Sometimes: choose specifc  CP, e.g. 3  /2 (worst/best case) A B C D E F G

17. Experiment choice and optimization (some thoughts)

18. 18  Small  13 : Optimize  13, MH, and CPV discovery reaches in  13 direction  Large  13 : Optimize  13, MH, and CPV discovery reaches in (true)  CP direction  What defines “large  13 ”? A Double Chooz, Day Bay, T2K, … discovery? When? Optimization of exps (3  m 31 2 =0.0022 eV 2  Optimization for small  13 Optimization for large  13 T2KK Beta beam NuFact B

19. 19 Timescale for  13 discovery? (Huber, Kopp, Lindner, Rolinec, Winter, 2006)  Assume: Decision on future experiments made after some LHC running and next- generation experiments  Two examples:  ~ 2011: sin 2 2  13 > 0.04?  ~ 2015: sin 2 2  13 > 0.01? D

20. 20 Large  13 strategy  Assume that Double Chooz finds  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 For any (true)  13 in 90% CL D-Chooz allowed range!  What is the minimal effort (minimal cost) for that?  NB: Such a minimum wish list is non-trivial for small  13  NB: CP fraction 80% comes from comparison with IDS-NF baseline etc. (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.)

21. 21 Example: Minimal beta beam  Minimal effort =  One baseline only  Minimal   Minimal luminosity  Any L (green-field!)  Example: Optimize L-  for fixed Lumi:   as large as 350 may not even be necessary! (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 More on beta beams: Mezzetto‘s talk!

22. 22 Small  13 strategy  Assume that Double Chooz … do not find  13  Minimum wish list:   discovery of  13 > 0  3  mass hierarchy determination  3  CP violation determination For as small as possible (true)  13  Two unknowns here:  For what fraction of (true)  CP ? One has to make a choice (e.g. max. CP violation, for 80% of all  CP, for 50%, …)  How small  13 is actually good enough?  Minimal effort is a matter of cost!  Maybe the physics case will be defined otherwise?

23. 23 Connection to high-E frontier?

24. 24 Optimal strategy vs. regional interests? So far: purely conceptual … … however, the optimal strategy depends on regional boundary conditions! CERN-INO? JHF-INO? Talk: Goswami Talks: Goodman (US) Evans (MINOS) Kurimoto (SciBooNE) Talks: Ronga (Gran Sasso) Scott-Lavina (OPERA) Sala (CNGS) Talks: Kakuno (T2K) Dufour (T2KK)

25. Physics potential of the neutrino factory: what can we expect?

26. 26 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 Talks: Long (IDS-NF) Bonesini (R&D)

27. 27 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/) More by Ken Long

28. 28 Physics potential 33 BB B  Excellent  13, MH, CPV discovery reaches  About 10% full width error (3  ) on log 10 (sin 2 2  13 ) for sin 2 2  13 = 0.001 (Gandhi, Winter, hep-ph/0612158, Fig. 6)  About 20-60 degree full width error (3  ) on  CP for sin 2 2  13 = 0.001 (Huber, Lindner, Winter, hep-ph/0412199, Fig. 7) But what does that mean? Cabibbo angle-precision (  C ~ 13 deg.)! Why is that relevant? Can be another feature of nontrivial QLC models: E.g. from specific texture+QLC-type assumptions: (  : model parameter) (Niehage, Winter, 2008) (IDS-NF, 2007)

29. 29 Two-baseline optim. revisited  Robust optimum for ~ 4000 + 7500 km  Optimization even robust under non- standard physics (dashed curves) (Kopp, Ota, Winter, 2008) C C

30. 30 Matter density measurement  Assume that only one parameter measured: Constant reference density  Ref or lower mantle density  LM (Minakata, Uchinami, 2007; Gandhi, Winter, 2007) True  =0

31. 31  Solar term: Note that i.e., effect (initially) increases with baseline (  ~ L)! MSW effect sensitivity even for  13 =0! MSW effect in Earth matter (hep-ph/0411309) 55 C

32. 32 Octant degeneracy  4000 km alone: Problems with degs for intermediate  13  7200 km alone: No sensitivity for small  13  4000 km + 7200 km: Good for all  13 (Gandhi, Winter, 2007) Similar performance to Gold+Silver* @ 4000km Meloni, arXiv:0802.0086

33. The unexpected!?

34. 34 ~ current bound Neutrino osc. framework incomplete?  Example: non-standard interactions (NSI) from effective four-fermion interactions:  Discovery potential for NSI-CP violation 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  Talk by T. Ota See also talk by D. Meloni

35. 35 Help from other experiments?  Physics scenario: Double Chooz finds  13 and ~ a total of 100 muon tracks from astrophysical sources observed (ratio of muon tracks to showers), only m 1 stable on extragalatic distances  Double Chooz alone and this information could establish CPV  Other sources of information: Supernovae, atmospheric, LHC, 0   Talks: Petcov, Schwetz, Sigl, … (Maltoni, Winter, 2008)

36. 36 Outlook: How to design the optimal experiment Future LBL experiment Physics Politics Theory  Performance indicators:  13, CP violation, MH, … Correlations+ Degeneracies  Resolution strategies New physics?  Inclusive strategies (more channels, etc.) Potitical boundary conditions (e.g., Obama vs. McCain) Same measurement by other experiment (e.g., MH from supernova) Regional interests (e.g., DUSEL, T2KK, …) LHC (e.g.,connection to high-E frontier)