CP Violation in Neutrino
Oscillations
without Antineutrinos:
Energy Dependence
Jose Bernabeu
U. Valencia and IFIC
XIII International Workshop on
Neutrino Telescopes
March 2009
Programme
 What is known, what is unknown in Neutrino Oscillations
 Third Generation of Neutrino Experiments: CP Violation
 The CP phase with neutrinos only: Energy Dependence
 A combined BB and EC experiment for the same ion Ytterbium
 Comparison between
i) low energy (Ep(SPS) ≤ 450 GeV, Frejus and Canfranc)
ii) high energy (Ep(SPS) ≤ 1000 GeV, Canfranc and Boulby)
 CP-Violation Discovery Potential and Mass Hierarchy
Determination
 Conclusions
What is known,
what is unknown

Neutrino flavour oscillations
 m 23  2.4  10 eV
 2
m 12  7.65  10 5 eV 2
 13  10o , A hint ?

2
3
2
sin 2  23  0.50
sin 2 12  0.304
 ?
Absolute neutrino masses ?  3 H beta, Cosmology
Form of the mass spectrum
 Matter effect in neutrino
propagation
Majorana neutrinos?  0: masses and phases
The Pontecorvo MNS Matrix
 e 
 1 
 
 
    U  2 
 
 
 
 3
After diagonalization of the neutrino mass matrix,
 For Flavour oscillations
U: 3 mixings, 1 phase
0   c13
1 0



U  0 c23 s23   0
i

0  s23 c23    s13e
 Atmospheric
 KEK, MINOS,
OPERA
Even if they
are Majorana
i 
0 s13e   c12 s12 0


1
0    s12 c12 0
0 c13   0
0 1
•Appearance e!
•Reactors
•Matter effects
Solar
KAMLAND
Borexino
Three Generations
of Experiments


0. Only three?  MiniBoone
I. Solar Sector, Atmospheric Sector 
Δm2
Δ

12,
θ12
Borexino
MINOS, OPERA
II. Connection between both Sectors 
θ13,
Sign
θ (Δm223)

│Δm223│, θ23
Double CHOOZ, Daya Bay, T2K, NOVA, …
III. CP-Violating Interference  δ
Super-Beams? Beta/ EC Beams? Neutrino Factory?
Third Generation Experiments:
CP Violation





European Strategy Plan demands
for ~ 2012 a CDR with the
alternatives: SuperBeams,
Beta/EC Beams, Neutrino
Factory.
SuperBeam: no pure Flavour,
uncertain continuous Spectrum.
Beta Beam: pure Flavour, known
continuous Spectrum.
EC Beam: pure Flavour, known
single Monochromatic Beam.
Neutrino Factory: pure Flavour
iff detector with charge
discrimination, known continuous
Spectrum.
Frejus
• CPV can be observed either by an Asymmetry between
Neutrinos and Antineutrinos or by Energy Dependence (CP
phase as a phase shift) in the Neutrino channel, or both.
Why Energy Dependence ?
A theorem
CP violation:
P( e    )  P( e    )
CPT invariance + CP violation = T non-invariance
P( e    )  P(    e )
No Absorptive part  Hermitian Hamiltonian 
CP odd = T odd = P (   )  P (   )
e

e

is an odd function of time = L !
In vacuum neutrino oscillations for relativistic
neutrinos L/E dependence, so
CP-even (odd) terms in the appearance probability
 Even (odd) functions of energy. Then ENERGY DEPENDENCE
disentangles the CP-even and CP-odd terms
Interest of energy dependence in
suppressed neutrino oscillations
• CP violation accessible in suppressed appearance
experiments, in order to have access to the interference
between the atmospheric and solar probability amplitudes
• Appearance probability:
2
m13
L
P ( e    )  s sin 213 sin (
)
4 E


2
23
2
2
Atmospheric
2
m12
L
c sin 212 sin (
)
4 E


2
23
2
2
Solar
2
2
2
m13
L m12
m13
L
L
~
J cos( 
)
sin(
)
4
E
4
E
4
E

|Ue3| gives the
strength of P(νe→νμ)
•
δ gives the interference
pattern: CP odd term is
odd in E/L
• δ acts as a phase shift
•
Interferen ce
This suggests the idea of either a monochromatic neutrino beam
to separate δ and |Ue3| by energy dependence with different
boosts, or a combination of channels with different neutrino
energies in the same boost

Neutrinos from electron capture
How can we obtain a monochromatic neutrino beam?
Electron capture:
J. B., C. E. et al
boost
Z protons
N neutrons
●
Z-1 protons
N+1 neutrons
Forward direction
2 body decay!  In the CM , a single discrete energy
if a single final nuclear level is populated
Eν
From the single energy e--capture neutrino spectrum, we can get a
pure and monochromatic beam by accelerating ec-unstable ions
and choosing forward ν’s  One can concentrate all the
intensity at the most appropriate energy for extracting the
neutrino parameters
A combined beta-beam and
156
EC neutrino experiment ( Yb)
• Suppressed appearance
probabilities for the CERN-Frejus
(130 Km, red line) and
CERN-Canfranc (650 Km, blue
line) baselines. The unoscillated
neutrino flux is shown for γ=166
• Suppressed appearance
probabilities for the CERNCanfranc (650 Km, blue line) and
CERN-Boulby (1050 Km, red line)
baselines. The unoscillated
neutrino flux is shown for γ=369
Similarities and Differences between
Beta beam and EC neutrinos
In proton rich nuclei (to restore the same orbital angular momentum
for protons and neutrons )
-
 Superallowed Gamow-Teller transition
The “breakthrough” came thanks
to the recent discovery of
isotopes with small half-lives of
one minute or less, which decay
in neutrino channels near 100%
to a SINGLE Gamow-Teller
resonance.
●
Nuclear
• A Facility with an EC channel would require a different approach to
acceleration and storage of the ion beam compared to the standard betabeam, as the atomic electrons of the ions cannot be fully stripped
• Partly charged ions have a short vacuum life-time against collisions. The
interesting isotopes have to have
half-life < vacuum half-life ~ few min.
Electron neutrino fluxes
from EC and BB

Distribution of neutrino energy per unit surface at the
detector in the forward direction:
EC:
BB:
d 2 N N iones  2 2
2
2

y
(
1

y
)
(
1

y
)

y
e
dSdE L2 g ( y e )
E
me
0 y
 1  y 2 , ye  

2E0
E0
• Notice:
and
E0  Q   me  QEC  me


ye
1 


2
2
4
4


g ( ye ) 
1

y
(
2

9
y

8
y
)

15
y
log


e
e
e
e
60 
1  1  y e2  


i) All Nuclear Physics input is under control
ii) The Intensity increases like γ2 with the Lorentz factor.
iii) The Monochromatic line E=2γE0 is higher by 2γ MeV to the end point of
the β+ spectrum
Experimental Setups for the
combined experiment

Appearance Experiment : Electron Neutrino Flux × Oscillation
Probability to muon neutrinos × CC Cross Section for muon production.
• I: CERN-Frejus (130 Km), γ=166
 SPS
• II: CERN-Canfranc (650 Km), γ=166
 SPS
• III and III-WC: CERN-Canfranc (650 Km), γ=369  Upgraded SPS
• IV and IV-WC: CERN-Boulby (1050 Km), γ=369
 Upgraded SPS
Detectors:
• LAr or TASD, 50 kton
 Neutrino spectral information from CC muon events
• Water Cerenkov, 0.5 Mton  Neutrino energy from QE events only + inelastic events
in a single bin, with 70% efficience
• The separation between the energy of the EC spike and the end point energy
of the beta-spectrum is possible: if Eν(QE)>2γEo(β), since E ν(true)> E ν(QE),
the event must be attributed to the EC flux and hence, it is not necessary to
reconstruct the true energy
Comparing baselines I and II

For the combined BB + EC fluxes with θ13=10 and δ=900
• The BB channel contributes very little to the overall sensitivity of the
setup, due to the γ2 dependence. The bulk of the sensitivity is due to the EC
channel placed on the first oscillation maximum
Comparing energies II and
III with the same baseline

Combination of BB and EC fluxes for θ13=10 and δ=900
γ=166
γ=369
• The sensitivity is better with the upgraded SPS energy
• The relative role of the two BB and EC components is exchanged when
going from II to III
Setup III: The virtues of
combining energies from BB and EC
• Setup
BB
III: θ13=30, δ=900
EC
BB+EC
• The power of the combination of the two channels is in the difference in phase and in
amplitude between the two fake sinusoidal solutions, selecting a narrow allowed region
in the parameter space
Set up III-WC : Disentangling
θ13 and δ
• Solutions, from discrete degeneracies included, for θ13=10 , 30 and for different
values of the CP phase
•
• The increase in event rates improves the results substantially with respect to those results
for Setup III, although not as much as the size factor between the two detectors.
• The effects of the hierarchy clon solution are taken into account. The mass ordering can be
determined for large values of the mixing angle.
• The hierarchy degeneracy worsen the ability to measure δ for negative true values of δ.
Comparing III-WC and IV-WC

Boulby provides a longer baseline L=1050 km than Canfranc L=650 km. This has
two contrasting effects on the sensitivity to measure CP violation: i) Sufficient
matter effects to resolve the hierarchy degeneracy for small values of θ13;
ii) It decreases the available statistics
• The smaller count rate results in a poorer resolution.
• The longer baseline allows for a good determination of the mass ordering,
eliminating more degenerate solutions.
CP Discovery Potential
for WC
Canfranc

Boulby
Comparing the two locations of the WC detector, the
Canfranc baseline has a significally (slightly) better
reach for CP violation at negative (positive) values of δ
than the Boulby baseline.
Mass hierarchy determination

Fraction of δ for which the neutrino mass
hierarchy can be determined
• III-WC with
present priors
in the known
parameters
• III-WC with
negligible errors
in the known
parameters
• IV-WC with
present priors
in the known
parameters
• The Boulby baseline, with its larger matter effect, is better for the determination
of the mass hierarchy
Conclusions




The two separate channels BB and EC have a limited overlap of the
allowed regions in the (θ13, δ) plane, resulting in a good resolution on the
intrinsic degeneracy.
The CP phase sensitivity is obtained by only using neutrinos, thanks to the
Energy Dependence of the oscillation probability with the combination of
the two BB and EC channels.
THE SPS UPGRADE TO HIGHER ENERGY (Ep = 1000 GeV) IS CRUCIAL
TO HAVE A BETTER SENSITIVITY TO CP VIOLATION (the main
objective of the third generation neutrino oscillation experiments) IFF
ACCOMPANIED BY A LONGER BASELINE ( Canfranc or Boulby).
THE BEST E/L FOR HIGHER SENSITIVITY TO THE MIXING U(e3) IS
NOT THE SAME THAN THAT FOR THE CP PHASE. Like the phaseshifts, the effect of δ is easier to observe by going to the region of the
second oscillation.
Conclusions



Setups III and III-WC, with the Canfranc baseline, have
larger counting rates and a better tuning of the beam to the
oscillatory pattern, resulting in a very good ability to measure
the parameters. These setups provide the best sensitivity to
CP violation for positive values of δ.
For negative δ, the type of hierarchy cannot be resolved in
some cases for these setups.
Setups IV and IV-WC, with the Boulby baseline, provide a
better determination of the hierarchy and a good reach to CP
violation for negative δ, even if the mass ordering is unknown.
THE COMBINATION OF THE TWO BB AND EC BEAMS
FROM A SINGLE DECAYING ION AND A FIXED γ
BOOST
ACHIEVES REMARKABLE RESULTS
Acknowledgements


Thanks to many colleagues and, particularly,
to my collaborators:
J. Burguet-Castell, C. Espinoza, M. Lindroos,
C. Orme, S. Palomares-Ruiz and S. Pascoli.
Thank you very much for
your attention…