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

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

5. Connection to measurement
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 (MR)+18 (MD)+18 (Ml) = 45 parameters
At low E: 6 (masses) + 3 (mixing angles) + 3 (phases) = 12 parameters
LBL accessible CPV: d If  UPMNS real  CP conserved
CPV in 0nbb decay
Extremely difficult! (Pascoli, Petcov, Rodejohann, hep-ph/ )
There is no specific connection between low- and high-E CPV!
But: that‘s not true for special (restrictive) assumptions!

6. ~ MD (in basis where Ml and MR diagonal)
Why is CPV interesting?
Leptogenesis: CPV from Nc decays
If special assumptions (such as hier. MR, NH light neutrinos, …) it is possible that dCP is the only source of CPV for leptogensis!
(Nc)i
(Nc)i
~ MD (in basis where Ml and MR diagonal)
Different curves: different assumptions for q13, …
(Pascoli, Petcov, Riotto, hep-ph/ )

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 Ml) The QLC-type assumptions lead to deviations O(qC) ~ 13
Can also be seen in sum rules for certain assumptions, such as (F: model parameter)
This talk: Want Cabibbo-angle order precision for dCP!
(arXiv: )
(Niehage, Winter, arXiv: )

8. CPV phenomenology

9. Terminology Any value of dCP (except for 0 and p) violates CP
Sensitivity to CPV: Exclude CP-conserving solutions and p for any choice of the other oscillation parameters in their allowed ranges

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

11. Iso-probability curves
Degeneracies
Iso-probability curves
CP asymmetry (vacuum) suggests the use of neutrinos and antineutrinos
One discrete deg. remains in (q13,d)-plane (Burguet-Castell et al, 2001)
Additional degeneracies: (Barger, Marfatia, Whisnant, 2001)
Sign-degeneracy (Minakata, Nunokawa, 2001)
Octant degeneracy (Fogli, Lisi, 1996)
Neutrinos
Antineutrinos
Best-fit

12. Intrinsic vs. extrinsic CPV
The dilemma: Strong matter effects (high E, long L), but Earth matter violates CP
Intrinsic CPV (dCP) has to be disentangled from extrinsic CPV (from matter effects)
Example: p-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
Critical range
True dCP (violates CP maximally)
NuFact, L=3000 km
Degeneracy above 2s (excluded)
Fit
True
(Huber, Lindner, Winter, hep-ph/ )

13. The magic baseline

14. CPV discovery reach … in (true) sin22q13 and dCP
Best performance close to max. CPV (dCP = p/2 or 3p/2)
Sensitive region as a function of true q13 and dCP
dCP values now stacked for each q13
No CPV discovery if dCP too close to 0 or p
No CPV discovery for all values of dCP 3s
~ Cabibbo-angle precision at 2s BENCHMARK!
Read: If sin22q13=10-3, we expect a discovery for 80% of all values of dCP

15. The experiments

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

17. Current status: A variety of ideas
“Classical” beta beams:
“Medium” gamma options (150 < g < ~350)
Alternative to superbeam! Possible at SPS (+ upgrades)
Usually: Water Cherenkov detector (for Ne/He)
(Burguet-Castell et al, ; Huber et al, 2005; Donini, Fernandez-Martinez, 2006; Coloma et al, 2007; Winter, 2008)
“High” gamma options (g >> 350)
Require large accelerator (Tevatron or LHC-size)
Water Cherenkov detector or TASD or MID? (dep. on g, 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. Neutrino factory: International design study
(Geer, 1997; de Rujula, Gavela, Hernandez, 1998; Cervera et al, 2000)
Signal prop. sin22q13
Contamination
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
In Europe: Close connection to „Euronus“ proposal within the FP 07
In the US: „Muon collider task force“
ISS

19. IDS-NF baseline setup 1.0 Two decay rings Em=25 GeV
5x1020 useful muon decays per baseline (both polarities!)
Two baselines: ~ km
Two MIND, 50kt each
Currently: MECC at shorter baseline (

20. NF physics potential Excellent q13, MH, CPV discovery reaches
(IDS-NF, 2007)
Robust optimum for ~ km
Optimization even robust under non-standard physics (dashed curves)
(Kopp, Ota, Winter, arXiv: ; see also: Gandhi, Winter, 2007)

21. Optimization for CPV

22. Optimization for CPV
Small q13: Optimize discovery reach in q13 direction
Large q13: Optimize discovery reach in (true) dCP direction ~ Precision!
What defines “small” vs “large q13”? A Double Chooz, Day Bay, T2K, … discovery?
Optimization for large q13
Optimization for small q13

23. Large q13 strategy Assume e.g. that Double Chooz discovers q13
Minimum wish list easy to define:
5s independent confirmation of q13 > 0
3s mass hierarchy determination for any (true) dCP
3s CP violation determination for 80% (true) dCP (~ 2s sensitvity to a Cabibbo angle-size CP violation)
For any (true) q13 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 q13
(arXiv: ; Sim. from hep-ph/ ; 1.5 yr far det yr both det.)

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

25. Small q13 strategy Example: Beta beams
Assume that Double Chooz … do not find q13
Example: Beta beam in q13-direction (for max. CPV)
„Minimal effort“ is a matter of cost!
LSF ~ 2
50 kt MID L=400 km
(LSF)
(Huber et al, hep-ph/ )
(Agarwalla et al, arXiv: )

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: , Fig. 105)

27. CP precision measurement

28. Why is that interesting?
Theoretical example Large mixings from CL and n sectors? Example: q23l = q12n = p/4, perturbations from CL sector (can be connected with textures) (Niehage, Winter, arXiv: ; see also Masina, 2005; Antusch, King 2005 for similar sum rules)
The value of dCP is interesting (even if there is no CPV)
Phenomenological example Staging scenarios: Build one baseline first, and then decide depending on the outcome
Is dCP in the „good“ (0 < dCP < p) or „evil“ (p < dCP < 2p) range? (signal for neutrinos ~ +sin dCP)
q12l dominates
q13l dominates
q12 ~ p/4 + q13 cos dCP
q12 ~ p/4 – q13 cos dCP
 q13 > 0.1, dCP ~ p
 q13 > 0.1, dCP ~ 0
q23 ~ p/4 – (q13)2/2
q23 ~ p/4 + (q13)2/2
dCP and octant discriminate these examples!

29. Performance indicator: CP coverage
Problem: dCP is a phase (cyclic)
Define CP coverage (CPC): Allowed range for dCP which fits a chosen true value
Depends on true q13 and true dCP
Range: 0 < CPC <= 360
Small CPC limit: Precision of dCP
Large CPC limit: 360 - CPC is excluded range

30. CP pattern Performance as a function of dCP (true)
Example: Staging. If km baseline operates first, one can use this information to determine if a second baseline is needed
Precision limit
Exclusion limit
(Huber, Lindner, Winter, hep-ph/ )

31. CPV from non-standard physics?

32. 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?
~ current bound
IDS-NF baseline 1.0
(arXiv: ) 3s

33. CPV discovery for large NSI
If both q13 and |eetm| 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/ ; Fernandez-Martinez et al, hep-ph/ ; Altarelli, Meloni, ; Antusch et al, )
IDS-NF baseline 1.0
(arXiv: )

34. Models for large NSI?
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 ettm, maybe) (Bergmann, Grossman, Pierce, hep-ph/ ; Antusch, Baumann, Fernandez-Martinez, arXiv: ; Gavela, Hernandez, Ota, Winter,arXiv: )
Need d=8 effective operators!
Finding a model with large NSI is not trivial!
n mass
d=6, 8, 10, ...: NSI

35. Systematic analysis for d=8
Feynman diagrams
Basis (Berezhiani, Rossi, 2001)
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: )
Need at least two mediator fields plus a number of cancellation conditions (Gavela, Hernandez, Ota, Winter, arXiv: )
Avoid CLFV at d=8: C1LEH=C3LEH
Combine different basis elements C1LEH, C3LEH
Cancel d=8 CLFV
But these mediators cause d=6 effects  Additional cancellation condition (Buchmüller/Wyler – basis)

36. Mass hierarchy (MH)

37. Motivation 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-h/ )

38. Matter effects Magic baseline:
(Cervera et al. 2000; Freund, Huber, Lindner, 2000; Huber, Winter, 2003; Akhmedov et al, 2004)
Magic baseline:
Removes all degeneracy issues (and is long!)
Resonance: 1-A  0 (NH: n, IH: anti-n) Damping: sign(A)=-1 (NH: anti-n, IH: n)
Energy close to resonance energy helps (~ 8 GeV)
To first approximation: Pem ~ L2 (e.g. at resonance)
Baseline length helps (compensates 1/L2 flux drop)

39. Baseline dependence Comparison matter (solid) and vacuum (dashed)
Event rates (A.U.)
Comparison matter (solid) and vacuum (dashed)
Matter effects (hierarchy dependent) increase with L
Event rate (n, NH) hardly drops with L
Go to long L!
(Dm212  0)
NH matter effect
Vacuum, NH or IH
NH matter effect
(Freund, Lindner, Petcov, Romanino, 1999)

40. Mass hierarchy sensitivity
For a given set of true q13 and dCP: Find the sgn-deg. solution
Repeat that for all true true q and dCP (for this plot)

41. Small q13 optimization: NF
Em-L (single baseline)
L1-L2 (two baselines)
(Kopp, Ota, Winter, 2008)
(Huber, Lindner, Rolinec, Winter, 2006)
Magic baseline good choice for MH
Em ~ 15 GeV sufficient (peaks at 8 GeV)

42. Small q13 optimization: BB
(Agarwalla, Choubey, Raychaudhuri, Winter, 2008)
Only B-Li offers high enough energies for „moderately high“ g
Magic baseline global optimum if g>=350 (B-Li)
Recently two-baseline setups discussed (Coloma, Donini, Fernandez-Martinez, Lopez-Pavon, 2007; Agarwalla, Choubey, Raychaudhuri, 2008)

43. Optimization for large q13
(arXiv: )
Performance as defined before (incl. 3s MH)
L > 500 km necessary
Large enough luminosity needed
High enough g necessary
Ne-He: limited to g > 120
B-Li: in principle, smaller g possible
High g = high E = stronger matter effects!

44. Physics case for CERN-India? (neutrino factory)
MH measurement if q13 small (see before; also de Gouvea, Winter, 2006)
Degeneracy resolution for ≤ sin22q13 ≤ 10-2 (Huber, Winter, 2003)
Risk minimization (e.g., q13 precision measurement) (Gandhi, Winter, 2007)
Compementary measurement (e.g. in presence of NSI) (Ribeiro et al, 2007)
MSW effect verification (even for q13=0) (Winter, 2005)
Fancy stuff (e.g. matter density measurement) (Gandhi, Winter, 2007)

45. Summary
The Dirac phase dCP is probably the only realistically observable CP phase in the lepton sector
Maybe the only observable CPV evidence for leptogenesis
This and f1, f2: the only completely model-inpendent parameterization of CPV
What precision do we want for it? Cabibbo-angle precision?  Relates to fraction of „dCP“ ~ 80-85%
For a BB or NF, the experiment optimization/choice depends on q13 large or small
Other interesting aspects in connection with CPV: CP precision measurement, NSI-CPV
MH for small q13 requires magic baseline