1. Perspectives for neutrino oscillations.
Walter Winter
DESY, 10./

2. Contents Introduction to neutrino oscillations
Current knowledge of neutrino oscillations
The future:
Measurement of dCP
Determination of the neutrino mass ordering
Summary and conclusions

3. Introduction to neutrino oscillations

4. Neutrinos from the atmosphere
The rate of neutrinos should be the same from below and above
But: About 50% missing from below
Neutrino change their flavor on the path from production to detection: Neutrino oscillations
Neutrinos are massive! (Super-Kamiokande: “Evidence for oscillations of atmospheric neutrinos”, 1998)

5. Neutrino production/detection
Neutrinos are only produced and detected by the weak interaction:
The dilemma: One cannot assign a mass to the flavor states ne, nm, nt!
Interaction with SU(2) symmetry partner only
Electron  electron neutrino ne Muon  muon neutrino nm Tau  Tau neutrino nt
e, m, t
ne, nm, nt
W exchange particle (interaction)
Production as flavor state

6. Which mass do the neutrinos have?
There is a set of neutrinos n1, n2, n3, for which a mass can be assigned.
Mixture of flavor states:
Not unusual, know from the Standard Model for quarks
However, the mixings of the neutrinos are much larger!
sin22q13=0.1, d=p/2

7. Neutrino oscillation probability
Standard derivation N active, S sterile (not weakly interacting) flavors
Mixing of flavor states
Time evolution of mass state
Transition amplitude
Transition probability
“quartic re-phasing invariant“

8. Further simplifications
Ultrarelativistic approximations: L: baseline (distance source-detector)
Plus some manipulations: “Master formula“ “mass squared difference“ F(L,E)=L/E “spectral dependence“
For antineutrinos: U  U*

9. Lower limit for neutrino mass!
Two flavor limit: N=2, S=0
Only two parameters:
From the master formula: Disappearance or survival probability Appearance probability
Lower limit for neutrino mass!

10. Three flavors: Mixings
Use same parameterization as for CKM matrix
Pontecorvo-Maki-Nakagawa-Sakata matrix
Neutrinos  Anti-neutrinos: U  U* (neutrino oscillations)
If neutrinos are their own anti-particles (Majorana neutrinos): U  U diag(1,eia,eib) do enter 0nbb, but not neutrino oscillations
Potential CP violation ~ q13
(sij = sin qij cij = cos qij)
( ) ( ) ( ) = x

11. Three active flavors: Masses
Two independent mass squared splittings, typically (solar) (atmospheric) Will be relevant for neutrino oscillations!
The third is given by
The (atmospheric) mass ordering (hierarchy) is unknown (normal or inverted)
The absolute neutrino mass scale is unknown (< eV) 8 8
Normal
Inverted

12. Current knowledge of neutrino oscillations

13. Three flavors: Simplified
What we know (qualitatively):
Hierarchy of mass splittings
Two mixing angles large, one (q13) small ~ 0?
From the “master formula“, we have

14. Select sensitive term by choice of L/E!
Two flavor limits
Two flavor limits by selection of frequency:
Atmospheric frequency: D31 ~ p/2  D21 << 1
Solar frequency: D21 ~ p/2  D31 >> 1
averages out
Select sensitive term by choice of L/E!
0.5

15. Atmospheric neutrinos
Super-Kamiokande
Measures ne, nm
From and q13 small
we have: Pee ~ 1, Pem ~ Pme ~ 0 and
 Two flavor limit with particular parameters q23,

16. Double Chooz Daya Bay RENO
Reactor neutrinos
In the presence of q13:
atmospheric
solar
K. Heeger
New idea:
Identical detectors, L ~ 1-2 km to control systematics (Minakata, Sugiyama, Yasuda, Inoue, Suekane, 2003; Huber, Lindner, Schwetz, Winter, 2003)
Chooz
Double Chooz Daya Bay RENO
KamLAND

17. (short distance)
(also: T2K, Double Chooz, RENO)

18. Three flavors: Summary
Three flavors: 6 params (3 angles, one phase; 2 x Dm2)
Describes solar and atmospheric neutrino anomalies, as well as reactor antineutrino disappearance!
Solar oscillations: Amplitude: q12 Frequency: Dm212
Atmospheric oscillations: Amplitude: q23 Frequency: Dm312
Coupling: q13
(Super-K, 1998; Chooz, 1999; SNO ; KamLAND 2002; Daya Bay, RENO 2012; MINOS, T2K …)
Suppressed effect: dCP

19. Precision of parameters?
± 2%
± 4%
(or better)
± 4%
± 3%
± 3%
Age of the precision flavor physics of the lepton sector
Open issues: - Degeneracies (mass ordering, octant) - CP phase
Gonzalez-Garcia, Maltoni, Salvado, Schwetz, JHEP 1212 (2012) 123

20. Current status and perspectives for existing equipment
Indication for dCP, no evidence for mass hierarchy
Potential of existing equipment
Capozzi, Fogli, Lisi, Marrone, Montanino, Palazzo, arXiv:
Main difference: NOvA data!
T2K, NOvA, Double Chooz, Daya Bay; 5 years each
CP cons.
High CL determination requires new equipment
NH simulated
IH simulated
Huber, Lindner, Schwetz, Winter, JHEP 0911 (2009) 044

21. Largest, bi-annual conference of the neutrino community, 550 participants
Highlights:
Discovery of cosmic neutrinos, by IceCube
First direct high-CL evidence for nm to ne flavor transitions, by T2K
First atmospheric measurement of leading atmospheric parameters comparable with long-baseline experiments, by IceCube-DeepCore (analysis done by DESY-Zeuthen group)
q13 central value shifts down (Daya Bay), tension with T2K increased; may strengthen hint for maximal leptonic CP violation dCP~-p/2
P5 prioritisation of Long Baseline Neutrino Oscillation Experiment at Fermilab
DESY with three plenary talks one of the strongest represented institutions in the program (after INFN, before Fermilab)
Juan-Pablo Neutrino 2014

22. The future: measurement of dCP

23. CKM-like correction leading to non-zero q13?
Why is dCP interesting?
CP violation Necessary condition for successful baryogenesis (dynamical mechanism to create matter-antimatter asymmetry of the universe)  thermal leptogenesis by decay of heavy see-saw partner?
Model building e.g. TBM sum rule: q12 = 35 + q13 cosd (Antusch, King; Masina …)
Need performance which is equally good for all dCP
sind
cosd
CKM-like correction leading to non-zero q13?
Symmetry e.g. TBM, BM, …?

24. Necessary conditions for the observation of CP violation
Since  need spectral info!
Since for a=b  need to observe flavor transitions
Need (at least) three flavors (actually conclusion in quark sector by Kobayashi, Maskawa, Nobel Prize 2008)  No CP violation in two flavor subspaces!  Need to be sensitive to (at least) two mass squared splittings at the same time!
~ Jarlskog invariant

25. Electron-muon neutrino flavor transitions
Antineutrinos:
Silver:
Platinum, T-inv.:
(Cervera et al. 2000; Freund, Huber, Lindner, 2000; Akhmedov et al, 2004)

26. Possible experimental setups (future)
+ Daya Bay
(Coloma, Huber, Kopp, Winter, arXiv: )

27. Performance Comparison at default systematics: ~ LBNE/LBNO
(Coloma, Huber, Kopp, Winter, arXiv: )

28. Example: Neutrino Factory International Design Study (IDS-NF)
(Geer, 1997; de Rujula, Gavela, Hernandez, 1998; Cervera et al, 2000)
Signal prop. sin22q13
Contamination  magnetized detector!
Muons decay in straight sections of a storage ring
IDS-NF: Initiative from ~ to present a design report, schedule, cost estimate, risk assessment for a neutrino factory

29. Steve Geer‘s vision
Paul Soler

30. Systematics: Main challenges for dCP
Robust wrt systematics
Main impact: Matter density uncertainty
Neutrino Factory
Operate in statistics- limited regime Exposure more important than near detector
High-E superbeam (e. g. LBNE)
QE ne X-sec critical: cannot be measured in near detector Theory: ne/nm ratio? Experiment:
Low-E (QE!) superbeam
(Coloma, Huber, Kopp, Winter, arXiv: )

31. Mass hierarchy determination

32. Why would one like to measure the mass ordering?8 8
Normal
Inverted
Specific models typically come together with specific MH prediction (e.g. textures are very different)
Good model discriminator
(Albright, Chen, hep-ph/ )

33. Method 1: Matter effects in neutrino oscillations
Ordinary matter: electrons, but no m, t
Coherent forward scattering in matter: Net effect on electron flavor
Hamiltonian in matter (matrix form, flavor space):
(Wolfenstein, 1978; Mikheyev, Smirnov, 1985)
Y: electron fraction ~ 0.5
(electrons per nucleon)

34. Parameter mapping … for two flavors, constant matter density
Oscillation probabilities in vacuum: matter:
Enhancement condition 8 8
Normal Dm312 >0
Inverted Dm312 <0
Normal
Inverted
Neutrinos
Resonance
Suppression
Antineutrinos

35. Long baseline experiments (up to first vacuum osc. maximum)
Best-fit values from arXiv: (first octant)
Matter effect
L=1300 km
~ sin22q13 sin2q23
+ dCP modulation
Vacuum oscillation maximum

36. Long-Baseline Neutrino Oscillation Experiment (LBNE)
Bob Neutrino 2014
Particle Physics Project Prioritization Panel (P5) in the US; Report May ‘14

37. Matter profile of the Earth … as seen by a neutrino
(Preliminary Reference Earth Model)
Core
For nm appearance, Dm312: - r ~ 4.7 g/cm3 (Earth’s mantle): Eres ~ 6.4 GeV - r ~ 10.8 g/cm3 (Earth’s outer core): Eres ~ 2.8 GeV
Resonance energy (from ):

38. Mantle-core-mantle profile
(Parametric enhancement: Akhmedov, 1998; Akhmedov, Lipari, Smirnov, 1998; Petcov, 1998)
Probability for L=11810 km
Best-fit values from arXiv: (first octant) !
Oscillation length ~ mantle-core-mantle structure Parametric enhancement.
Core resonance energy
Mantle resonance energy
Naive L/E scaling does not apply!
Threshold effects expected at:
2 GeV
4-5 GeV

39. Emerging technologies: Atmospheric ns
Example: PINGU (“Precision IceCube Next Generation Upgrade“)
40 additional strings, 60 optical modules each
Lower threshold, few Mtons at a few GeV
ORCA, INO: similar methods
Mantle resonance energy
(PINGU LOI, arXiv: )

40. Method 2: Disappearance probabilities
Works in vacuum, and even for q13=0
Just flipping the sign of Dm2 is not sufficient
Example: Reactor experiment, L=53 km Probabilities apparently different (unphysical effect!)

41. Method 2: Disappearance probabilities
The disappearance Dm2 depends on the channel. Consequence e. g.
Now first oscillation maxima match. Discrimination by higher osc. Maxima. Need energy resolution!
de Gouvea, Jenkins, Kayser, hep-ph/ ;
Nunokawa, Parke, Zukanovich, hep-ph/
Zoom-in
3% (E/MeV)0.5

42. Emerging technologies: Reactor experiments
Jiangmen Underground Neutrino Observatory (JUNO) [formerly Daya Bay-II]
L=53 km
Excellent energy resoluton (3% (E/MeV)0.5) requires O(100%) PMT coverage
Talk by Liangian Wen Posters?
Yu-Feng Li, arXiv:
3% (E/MeV)0.5

43. Global context
LBNE 10kt if q23 varied as well  Fig. 9 in arXiv: ; see also arXiv: v2
Bands: risk wrt q23 (PINGU, INO), dCP (NOvA, LBNE), energy resolution (JUNO)
LBNE and sensitivity also scales with q23!
True NO
POF III Matter and the Universe
(version from PINGU LOI, arXiv: , based on Blennow, Coloma, Huber, Schwetz, arXiv: )

44. Summary and conclusions
Mass hierarchy: may be tested in beginning of 2020s by “emerging technologies“, such as PINGU or JUNO PINGU has a good chance to be the first experiment to measure the mass hierarchy if timely; DESY involved
CP violation: requires a new long-baseline experiment, such as LBNE, T2HK, NuFact; P5 recognition milestone towards such a program at Fermilab
Other issues: q23 maximal? Octant? Sun and Earth tomography? New physics?
Light sterile neutrinos - best candidate for physics BnSM? Test short-baseline anomalies, measure neutrino X-secs, …
Perspectives for neutrino oscillations? Fantastic!