1. Neutrino phenomenology Lecture 2: Precision physics with neutrinos Winter school Schladming 2010 “Masses and constants” 01.03.2010 Walter Winter Universität Würzburg TexPoint fonts used in EMF: AAAAA A A A

2. 2 Contents (overall)  Lecture 1: Testing neutrino mass and flavor mixing  Lecture 2: Precision physics with neutrinos  Lecture 3: Aspects of neutrino astrophysics

3. 3 Contents (lecture 2)  Repetition  Matter effects in neutrino oscillations  CP violation phenomenology  Mass hierarchy measurement  Experiments: The near future  Experiments for precision. Example: Neutrino factory  New physics searches (some examples)  Summary

4. Repetition … from yesterday

5. 5  With three flavors: six parameters (three mixing angles, one phase, two mass squared differences)  Established by two flavor subsector measurements  In the future: measure unknown  13 and  CP, MH Three flavor oscillation summary 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)

6. 6 Global fits Schwetz, Tortola, Valle, 2008 11 90%CL, 3 

7. A new ingredient: Matter effects in neutrino oscillations

8. 8 Matter effect (MSW)  Ordinary matter: electrons, but no ,   Coherent forward scattering in matter: Net effect on electron flavor  Matter effects proportional to electron density n e and baseline  Hamiltonian in matter (matrix form, flavor space): Y: electron fraction ~ 0.5 (electrons per nucleon) (Wolfenstein, 1978; Mikheyev, Smirnov, 1985)

9. 9 Numerical evaluation  Evolution operator method: H(  j ) is the Hamiltonian in constant density  Note that in general  Additional information by interference effects compared to pure absorption phenomena

10. 10 Matter profile of the Earth … as seen by a neutrino (PREM: Preliminary Reference Earth Model) Core Inner core

11. 11 Two flavor limit (  =const.)  Multiplied out, two flavors, global phase substracted:  Compare to vacuum  Idea: write matter Hamiltonian in same form as in vacuum with effective parameters

12. 12 Parameter mapping  Oscillation probabilities in vacuum: matter: Matter resonance: In this case: - Effective mixing maximal - Effective osc. frequency minimal  ~ 4.5 g/cm 3 (Earth’s mantle) Solar osc.: E ~ 100 MeV !!! Atm osc.: E ~ 6.5 GeV Resonance energy:

13. 13 Mass hierarchy  Matter resonance for  Will be used in the future to determine the mass ordering: 8 8 Normal  m 31 2 >0 Inverted  m 31 2 <0 NormalInverted NeutrinosResonanceSuppression AntineutrinosSuppressionResonance Neutrinos/Antineutrinos

14. Three flavor effects: CPV phenomenology

15. 15 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 Why interesting? Lecture Xing!

16. 16 Three flavor effects (Cervera et al. 2000; Freund, Huber, Lindner, 2000; Huber, Winter, 2003; Akhmedov et al, 2004)  Antineutrinos:  Magic baseline:  Silver:  Platinum, T-inv.:

17. 17 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

18. 18 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

19. 19 The „magic“ baseline

20. 20 CP violation discovery … 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)

21. Mass hierarchy measurement

22. 22 Motivation  Specific models typically come together with specific MH prediction (e.g. textures are very different)  Good model discriminator (Albright, Chen, hep-ph/0608137) 8 8 NormalInverted

23. 23  Magic baseline:  Restore two flavor limit (  ~ 1 – A for small  13 )  Resonance: 1-A  0 (NH:, IH: anti- ) Damping: sign(A)=-1 (NH: anti-, IH: )  Energy close to resonance energy helps (~ 7 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)

24. 24 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 Peak neutrino energy ~ 14 GeV

25. Experiments: The near future

26. 26 There are three possibilities to artificially produce neutrinos  Beta decay:  Example: Nuclear reactors  Pion decay:  From accelerators:  Muon decay:  Muons produced by pion decays! Muons, neutrinos Artificial neutrino sources Protonen TargetSelection, focusing Pions Decay tunnel Absorber Neutrinos

27. 27 New reactor experiments Examples: Double Chooz, Daya Bay Identical detectors, L ~ 1.1 km (Quelle: S. Peeters, NOW 2008)

28. 28  Idea: The event rate N close to the reactor is high,  ~ 1/R 2  A few thousand events/day for “small” detector ~ 25 m away from reactor core  Anticipated precision: ~ O(10) kg for extraction of radioactive material Spin-off: Nuclear monitoring? (Adam Bernstein, LLNL)

29. 29 Narrow band superbeams  Off-axis technology to suppress backgrounds  Beam spectrum more narrow  Examples: T2K NO A T2K beam OA 1 degree OA 2 degrees OA 3 degrees (hep-ex/0106019)

30. 30 GLoBES AEDL „Abstract Experiment Definition Language“ Define and modify experiments AEDL files User Interface C library, reads 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, 2007) Application software linked with user interface Calculate sensitivities … Comes with a 180 pages manual with step-by-step intro!

31. 31 Calculation of event rates In practice: Secondary particles integrated out  Detector response R(E,E´) EE´

32. 32 Next generation CPV reach  Includes Double Chooz, Daya Bay, T2K, NOvA (Huber, Lindner, Schwetz, Winter, a rXiv:0907.1896 ) 90% CL

33. Experiments for precision Example: Neutrino factory

34. 34 Neutrino factory: International Design Study (IDS-NF) 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

35. 35 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/)

36. 36 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)

37. 37 Steve Geer‘s vision

38. 38 Science fiction or science fact? http://www.fnal.gov/pub/muon_collider/

39. New physics searches (some examples, using neutrino factory near detectors)

40. 40  Effective operator picture if mediators integrated out: Describes additions to the SM in a gauge-inv. way!  Example: 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  Interesting dimension six operators Fermion-mediated  Non-unitarity (NU) Scalar or vector mediated  Non-standard int. (NSI) New physics from heavy mediators mass d=6, 8, 10,...: NSI, NU, CLFV, …

41. 41 Example 1: Non-standard interactions  Typically described by effective four fermion interactions (here with leptons)  May lead to matter NSI (for  =  =e)  May also lead to source/detector NSI (e.g. NuFact:   s for  =  =e,  =  ) These source/det.NSI are process-dep.!

42. 42 Lepton flavor violation … and the story of SU(2) gauge invariance  Strong bounds ee e  NSI (FCNC) ee e  CLFV e  4 -NSI (FCNC) Ex.: e e  Affects neutrino oscillations in matter (or neutrino production)  Affects environments with high densities (supernovae) BUT: These phenomena are connected by SU(2) gauge invariance  Difficult to construct large leptonic matter NSI with d=6 operators (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!

43. 43 On current NSI bounds (Source NSI for NuFact)  The bounds for the d=6 (e.g. scalar-mediated) operators are strong (CLFV, Lept. univ., etc.) (Antusch, Baumann, Fernandez-Martinez, arXiv:0807.1003)  The model-independent bounds are much weaker (Biggio, Blennow, Fernandez-Martinez, arXiv:0907.0097)  However: note that here the NSI have to come from d=8 (or loop d=6?) operators   ~ (v/  ) 4 ~ 10 -4 natural?  „NSI hierarchy problem“?

44. 44 Source NSI with  at a NuFact  Probably most interesting for near detectors:  e  s,   s (no intrinsic beam BG)  Near detectors measure zero-distance effect ~ |  s | 2  Helps to resolve correlations (Tang, Winter, arXiv:0903.3039) ND5: OPERA-like ND at d=1 km, 90% CL This correlation is always present if: - NSI from d=6 operators - No CLFV (Gavela et al, arXiv:0809.3451; see also Schwetz, Ohlsson, Zhang, arXiv:0909.0455 for a particular model)

45. 45 Example 2: Non-unitarity of mixing matrix  Integrating out heavy fermion fields (such as in a type-I TeV see-saw), one obtains neutrino mass and the d=6 operator (here: fermion singlets)  Re-diagonalizing and re-normalizing the kinetic terms of the neutrinos, one has  This can be described by an effective (non-unitary) mixing matrix  with N=(1+  ) U  Similar effect to NSI, but source, detector, and matter NSI are correlated in a particular, fundamental way (i.e., process- independent) also: „MUV“

46. 46 Impact of near detector  Example: (Antusch, Blennow, Fernandez-Martinez, Lopez-Pavon, arXiv:0903.3986)   near detector important to detect zero-distance effect Curves: 10kt, 1 kt, 100 t, no ND

47. 47 Example 3: Search for sterile neutrinos  3+S schemes of neutrinos include (light) sterile states, i.e., neutral fermion states light enough to be produced  The mixing with the active states must be small, the mass squared difference can be very different  The effects on different oscillation channels depend on the model  test all possible two- flavor short baseline (SBL) cases, which are standard oscillation-free  Example: e disappearance

48. 48 SBL e disappearance  Averaging over straight important (dashed versus solid curves)  Location matters: Depends on  m 2 (Giunti, Laveder, Winter, arXiv:0907.5487) 90% CL, 2 d.o.f., No systematics, m=200 kg Two baseline setup? d=50 m d~2 km (as long as possible)

49. 49 SBL systematics  Systematics similar to reactor experiments: Use two detectors to cancel X-Sec errors (Giunti, Laveder, Winter, arXiv:0907.5487) 10% shape error arXiv:0907.3145

50. 50 Summary  Matter effects key ingredient to measure the mass ordering How do neutrinos behave in environments with strongly varying matter density (Sun, Supernovae)?  Man-made terrestrial sources can measure all of the remaining standard neutrino oscillation properties (  13, CPV, MH) even for very small  13 Are all parameters best measured using terrestrial sources? Where did the „solar sector“ get its name from?  Some new physics „neutrino properties“ can be tested as well Are there neutrino properties which are best tested using astrophysical environments? Lecture 3

51. 51  Transition amplitude in matrix form: For instance,  in = (1,0,0) T for e With, we have or Matrix form in flavor space