1. September 24, 2007 Walter Winter
Phenomenology of q13
q13 half-day meeting
Oxford, UK
September 24, Walter Winter
Universität Würzburg

2. Contents Introduction
The measurement of q13: Reactor versus beam experiments
Performance indicators for q13 … and comparison of experiments
The “farer” future: what if q13 is very small?
Beyond q13: Mass hierarchy and CP violation
Summary
Sept. 24, 2007
Oxford Walter Winter

3. Neutrino mixing ( ) ( ) ( )
Use standard parameterization - as for CKM matrix:
(sij = sin qij cij = cos qij)
( ) ( ) ( ) = x
Three mixing angles q13, q12, q23; one CP phase dCP
Difference to quarks: Two mixing angles large: q12, q23
Sept. 24, 2007
Oxford Walter Winter

4. Neutrino mass Mass hierarchy: Normal or inverted?
Theory: Dirac or Majorana mass terms?
To independent mass squared differences relevant for oscillations: |Dm212 | << |Dm312| |a| = Dm212/|Dm312| ~ 3% 8 8
Mass spectra: Difference to origin? Degenerate masses?
Sept. 24, 2007
Oxford Walter Winter

5. Neutrino oscillations with two flavors
Mixing and mass squared difference: na “disappearance”: nb “appearance”:
~Frequency
Amplitude
Baseline: Source - Detector
Energy
Sept. 24, 2007
Oxford Walter Winter

6. Picture of three-flavor oscillations
Atmospheric oscillation: Amplitude: q23 Frequency: Dm312
Solar oscillation: Amplitude: q12 Frequency: Dm212
Sub-leading effect: dCP
Coupling strength: q13
Use ne transitions on atmospheric oscillation scale
(“Oscillation maximum”)
Magnitude of q13 is key to
“subleading” effects:
Mass hierarchy determination
CP violation
Sept. 24, 2007
Oxford Walter Winter

7. Matter effects in n-oscillations (MSW)
Ordinary matter contains electrons, but no m, t
Coherent forward scattering in matter has net effect on electron flavor because of CC (rel. phase shift)
Matter effects proportional to electron density and baseline
Hamiltonian in matter:
The matter potential is not CP-inv.! Source of many problems!
(Wolfenstein, 1978; Mikheyev, Smirnov, 1985)
Y: electron fraction ~ 0.5
(electrons per nucleon)
Sept. 24, 2007
Oxford Walter Winter

8. The measurement of q13
Experiment classes

9. Experiment classes by source
Production … and Detection
Limitations L
<E>
Reactor
Systematics
1-2 km
~4 MeV
Super-beam
Intrinsic beam BG, systematics
100-2,500 km
0.5 – 5 GeV
Neutrino factory
Charge identification, NC BG
700-7,500 km
5-50 GeV
b-beam
Source luminosity
100-2,000 km
0.3 – 10 GeV
For leading atm. params
Signal prop. sin22q13
Contamination
Sept. 24, 2007
Oxford Walter Winter

10. Disappearance measurements
Use expansions in small parameters:
Short baseline reactor experiments: nd term small for sin22q13 >> 10-3!
Long baseline accelerator experiments:
D31 = Dm312 L/(4E)
No dCP, No mass hierarchy!
(see e.g. Akhmedov et al., hep-ph/ )
Sept. 24, 2007
Oxford Walter Winter

11. A multi-detector reactor experiment … for a “clean” measurement of q13
See also Lisa Falk-Harris‘ talk!
Identical detectors, L ~ km
Daya Bay size
Unknown systematics important for large luminosity
NB: No sensitivity to dCP and mass hierarchy!
Double Chooz size
(Minakata et al, 2002; Huber, Lindner, Schwetz, Winter, 2003)
Sept. 24, 2007
Oxford Walter Winter

12. Appearance channels: nm ne
Antineutrinos
(Cervera et al. 2000; Freund, Huber, Lindner, 2000; Freund, 2001)
Complicated, but all interesting information there: q13, dCP, mass hierarchy (via A)
Sept. 24, 2007
Oxford Walter Winter

13. Neutrino beams nb? Accelerator-based neutrino source na Far detector
See also Dave Wark‘s talk!
nb?
Accelerator-based neutrino source na
Far detector
Often: near detector (measures flux times cross sections)
Baseline:
L ~ E/Dm312
(Osc. length)
Sept. 24, 2007
Oxford Walter Winter

14. Running example: MINOS
Measurement of atmospheric parameters with high precision
Flavor conversion ?
Fermilab - Soudan L ~ 735 km
Beam line
Near detector: 980 t
Far detector: 5400 t
735 km
Sept. 24, 2007
Oxford Walter Winter

15. q13 performance indicators …and comparison of experiments
q13 exclusion/sensitivity limit q13 discovery potential

16. Predictions for future experiments
Existing experiments:
Future experiments: ?
Simulated data
Fit parameters to data: Precision of quantity of interest
Input parameters
Data
Fit parameters to data: Precision of quantity of interest
Performance indicators depend on input param. hypothesis!
Sept. 24, 2007
Oxford Walter Winter

17. Simulated versus fit parameters
Simulated/true params
Represent the values implemented by nature
Known within current limits
Change the event rates, top.
Have to be interpreted like “If the value of … is …, then the performance will be …” - Luck or not luck?
Used for risk minimization!
Determine the precision of the quantity of interest
“Unused” parameteres are usually marginalized over (projection onto axis/plane of interest)
Source of correlations!
Sept. 24, 2007
Oxford Walter Winter

18. q13 exclusion/sensitivity limit (1)
Describes the new q13 limit for the simulation of no signal (q13=0)
Define as largest fit value of q13, which fits true q13=0
Straightforward inclusion of correlations and degeneracies
Does not depend on the simulated dCP and mass hierarchy!
(from hep-ph/ , App. C)
Sept. 24, 2007
Oxford Walter Winter

19. q13 exclusion/sensitivity limit (2)
Simulated parameters: q13=0, dCP meaningless
Relatively “simple” parameter dependencies
No dependence on dCP, mass hierarchy
Fit parameters: All six parameters
Correlations and degeneracies affect this performance indicator
Look for any combination of parameters which “fake” the smallest rate
Small for T2K etc.; Rate ~ 0
Sept. 24, 2007
Oxford Walter Winter

20. q13 exclusion: Problems with degeneracies
Connected (green) or disconnected (yellow) degenerate solutions in parameter space
Affect measurements Example: q13-sensitivity (exclusion limit)
Discrete degeneracies: (d,q13)-degeneracy (Burguet-Castell et al, 2001) sgn-degeneracy (Minakata, Nunokawa, 2001) (q23,p/2-q23)-degeneracy (Fogli, Lisi, 1996)
(Huber, Lindner, Winter, 2002)
Degeneracy resolution important topic in recent years! Example: Neutrino factory (later)
Sept. 24, 2007
Oxford Walter Winter

21. q13 discovery limit
Simulated parameters: Hypothesis: Certain q13>0, dCP, mass hierarchy
Can we establish q13>0 for this hypothesis?
Maximize parameter space for discovery
Fit parameters: Relatively simple as long as “solar term” negligible
Small impact of correlations
Simulated rate depends on all parameters
Small for NOvA etc.; Rate ~ 0
Sept. 24, 2007
Oxford Walter Winter

22. q13 discovery: CP fraction plots
Read: For sin22q13=0.04, we expect a discovery for 20% of all values of dCP
Sensitive region as function of true q13 and dCP
“Typical dCP”: CP fraction 50%
Fraction of dCP for successful discovery
dCP values now stacked for each q13
Sept. 24, 2007
Oxford Walter Winter

23. Evolution of q13 discovery limit?
Specific scenario
Bands reflect dependence on dCP
GLoBES 2005
(NOvA)
(from: FNAL Proton Driver Study)
Sept. 24, 2007
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24. Discovery versus exclusion power
(Huber, Kopp, Lindner, Rolinec, Winter, 2006)
Beams: discovery machines? Reactor experiments: Exclusion instruments?
Sept. 24, 2007
Oxford Walter Winter

25. Experiments for very small q13
The „farer“ future?
Experiments for very small q13

26. Superbeam upgrades: Examples
Bands reflect variation of systematical errors: 2%-5%-10%
Dots: Nominal L
Typical dCP, 3s
Discovery of sin22q13 downto ~10-3
discovery
(Barger, Huber, Marfatia, Winter, hep-ph/ , hep-ph/ )
Sept. 24, 2007
Oxford Walter Winter

27. Neutrino factory Ultimate “high precision” instrument!?
Muon decays in straight sections of storage ring
Technical challenges: Target power, muon cooling, charge identification, maybe steep decay tunnels
Decays
Target
Cooling
m-Accelerator m n p
p, K m
“Wrong sign”
“Right sign”
“Wrong sign”
“Right sign”
(from: CERN Yellow Report )
(Geer, 1997; de Rujula, Gavela, Hernandez, 1998; Cervera et al, 2000)
Sept. 24, 2007
Oxford Walter Winter

28. Ken Long (Imperial, RAL)
IDS-NF launched at NuFact 07 International design study for a neutrino factory
Successor of the International Scoping Study for a „future neutrino factory and superbeam facility“: Physics case made in physics WG report (~368 pp)
Initiative from ~ to present a design report, schedule, cost estimate, risk assessment for a neutrino factory
In Europe: Close connection to „Euronus“ proposal within the FP 07; currently ranked #1, negotiating contract
In the US: „Muon collider task force“ How can a neutrino factory be „upgraded“ to a muon collider?
Ken Long (Imperial, RAL)
Sept. 24, 2007
Oxford Walter Winter

29. Resolving degeneracies Example: „Magic“ baseline for NF
L= ~ 4000 km (CP) + ~7500 km (degs) today baseline configuration of a neutrino factory (ISS study, 2006)
(Huber, Winter, 2003)
Sept. 24, 2007
Oxford Walter Winter

30. Mass hierarchy and CP violation Precision measurements
Beyond q13 discovery
Mass hierarchy and CP violation Precision measurements

31. Perspectives for MH and dCP for the coming 5 to 10 years?
A mass hierarchy or CP violation measurement will be unlikely or impossible from
Beams+Reactor experiments
Any other source alone (supernova etc.)
(from: Huber, Lindner, Rolinec, Schwetz, Winter, 2004)
Sept. 24, 2007
Oxford Walter Winter

32. Help from outer space?
Astrophysical neutrino sources produce certain flavor ratios of neutrinos (ne:nm:nt): Neutron decays: (1:0:0) Muon damped sources: (0:1:0) Pion decays: (1:2:0)
These ratios are changed at Earth through averaged neutrino oscillations:
Measure muon track to shower ratio at neutrino telescope: R = fm/(fe+ft) (conservative, since in future also flavors!?)
~ cosd
Sept. 24, 2007
Oxford Walter Winter

33. Complementarity to beams
Use R to obtain information on osc. parameters? Difficult, since
Low statistics
No spectral info
(Serpico, Kachelriess, 2005; Serpico, 2005)
But: Complementary dependence on dCP
Combine the information from multiple low statistics exps?
Total Rates R
(Winter, 2006)
Sept. 24, 2007
Oxford Walter Winter

34. Early measurement of dCP ... using Double Chooz?
(Winter, 2006)
Double Chooz might be the first experiment to observe dCP
If more information: possibly even CP violation measurement:
(Blum, Nir, Waxman, 2007)
Sept. 24, 2007
Oxford Walter Winter

35. Future discovery of MH and dCP
Mass hierarchy discovery
CP violation discovery
Left end of band: Optimistic setup Right end of band: Conservative setup
(ISS study)
Sept. 24, 2007
Oxford Walter Winter

36. Beyond discovery: Precision measurements at a NF
dCP precision
q13 precision 3s
dCP dep.
(Huber, Lindner, Winter, 2004)
(Gandhi, Winter, 2006)
Sept. 24, 2007
Oxford Walter Winter

37. Summary
q13 will be tested in the near future by reactor experiments and superbeams
Reactor experiments provide very good limits on q13, while a discovery may be more likely at a beam experiment
If not found, neutrino factories may probe sin22q13 down to the level of 10-4 or 10-5
The measurements of the mass hierarchy and dCP will require the next generation of experiments
Sept. 24, 2007
Oxford Walter Winter

38. Backup

39. Matter effects (two flavors, r const.)
Parameter mapping (same form): Vacuum: Matter:
Describes ne – nm transitions to 0th order in a: q  q13 Dm2  Dm312 (except factor 0.5)
“Matter resonance”: In this case: - Effective mixing maximal - Effective osc. frequency min. r ~ 4.5 g/cm3 (Earth’s mantle) LBL osc.: E ~ 6.5 GeV
Resonance energy:
Sept. 24, 2007
Oxford Walter Winter

40. Early mass hierarchy measurement?
Fake solution is running in dCP as function of q13
Astrophysical source may help mass hierarchy measurement by constraining this running
Curves: Errors on R 5% 10% 20% No constraint
MINOS+Double Chooz+T2K+NOvA
(Winter, 2006)
Sept. 24, 2007
Oxford Walter Winter