Optimization studies for CP violation

1
Optimization studies for CP violation

• A.Bueno, M.Campanelli, A.Rubbia
• ETH-Zurich

Neutrino masses and mixings Les Houches, June 2001
2
Layout

• Oscillation probability for complex mixing
• Fluxes in a Neutrino Factory
• Scaled probabilities
• Correlation CP-?13
• Matter propagation
• L/E? scaling
• Determination of oscillation probabilities
• Electron charge
• T-violation
• Conclusions

3
Introduction

• Optimizing the search for a complex phase in the
  leptonic mixing matrix far from trivial
• A priori, the effect depends on L and E in a
  complicated way (In vacuum, the scaling of the
  effect with L/E can help an intuitive
  understanding of the oscillation behavior)
• Measurement precision depends on practical limits
  on machine power, maximal energy/flux, detector
  mass

The choice of the baseline is critical at the
time of the Neutrino Factory, there will be
already experiments located at a distance of 250
km from JHF and 730 km from CERN and FNAL if new
sites are really needed, due to physics
considerations, that would require major new
investments
4
?e??? oscillation probability
Following the conventional formalism for leptonic
mixing, CP-violating effects are observed in
appearance transitions involving the first
family. Experimentally, ????e is clearly
favored. This probability is composed of three
terms
Independent of ?
P(?e???)P(????e) 4c213sin2 ?23s212s213c212(sin
2?13s213s223sin2?12s212(1-(1s213)s223))
-1/2c213sin2?12s13sin2?23cos?cos2?13-
cos2?23-2cos2?12sin2?12 1/2c213sin?sin2?12s13sin
2?23sin2?12-sin2?13sin2?23
CP-even
CP-odd
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L/E regimes
?m221 (L/4En)gt1 ?m232 (L/4En )gt1 ?L/E of solar
?m221 (L/4En)ltlt1 ?m232 (L/4En )gt1 ?L/E of
atmospherics
?m221 (L/4En)ltlt1 ?m232 (L/4En )ltlt1
f ? ?m212 (L/4En) ? sin2(?m223 L/4En)
f ? ?m212 (?m223 )2(L/4En)3
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Observable quantities

• ??? P(?e?????/2)- P(?e????0)
• Compares oscillation probabilities as a function
  of E? measured with wrong-sign muon event
  spectra, to MonteCarlo predictions of the
  spectrum in absence of CP violation
• ?CP(?)? P(?e????)- P(?e????)
• Compares oscillation probabilities measured using
  the appearance of ?? and ??, running the storage
  ring with a beam of stored ? and ?-,
  respectively. Matter effects are dominant at
  large distances
• ?T(?)? P(?e??? ?)- P(????e ?)
• Compares the appearance of ?? and ?e in a beam of
  stored ? and ?-. As opposite to the previous
  case, matter effects are the same, thus cancel
  out in the difference
• ?T(?)? P(?e??? ?)- P(????e ?)
• Same as previous case, but with antineutrinos.
  This effect is usually matter-suppressed with
  respect to the neutrino case.

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Measuring ?T
The comparison of ??? ?e and ?e? ?? oscillation
probabilities offers a direct way to highlight a
complex component in the mixing matrix,
independent of matter and other oscillation
parameters.
This measurement is not directly accessible at a
Neutrino Factory with a conventional detector due
to the large ?e background in the beam. It would
add a considerable improvement to the physics
reach of a Neutrino Factory

• Two methods have been proposed to solve the
  problem of beam ?e background
• Beam polarization (not very effective see
  A.Blondel, A.Bueno, M.Campanelli, A.Rubbia,
  Monterey proceedings)
• Electron charge (discussed later in this talk)

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Oscillation probabilities
For a complex mixing matrix (in vacuum)
?CP?T
Complex term in matrix
Need LA MSW
Oscillation P goes like sin2?13
1
hence, DCP/vP independent of q13
2 cos?13 sin? sin2?12 sin2?13 sin2?23 ?
sin(?m212 L/4En) sin(?m213 L/4En) sin(?m223
L/4En)
Oscillating term only depends on L/E
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Neutrino Factory fluxes
P. Lipari, hep-ph/0102046
Forward neutrino spectrum fixed by m decay
kinematics Only scales with energy
Em5, 10, 20, 40 GeV
Integrating
Flux scales as E2m/L2
? En 2
Total event rate scales as E3m/L2
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Scaled probabilities
We define
n in matter
probability
Approximate En-dependence of NF n-spectrum
Flux attentuation with distance
n in matter
1. p?const when En ?? 2. It correctly weighs
the probabilities with the En dependence of the
NF n spectrum 3. p can be directly compared at
different baselines
in vacuum
En
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CP violation at high energy?
See also P. Lipari, hep-ph/0102046
L730 km
1. The En2 term takes into account that the NF
likes to go to high energy ? damps the part ?m221
(L/4En)1 2. At high energy, i.e. ?m221
(L/4En)ltlt1 ?m232 (L/4En)ltlt1, there is no more
oscillation ? change of d change of q13 !!! 3.
At high energy, the CP-effect goes like cosd,
as pointed out by Lipari ? cannot measure sign of
d
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Looking for a compromise
We must compromise at medium energy to 1. This
means ?m221 (L/4En)ltlt1 ?m232 (L/4En)1 2. To
gain from the Em3 behavior of the NF 3. To
guarantee the possibility to disentangle d from
q13
L2900 km
Position of first maximum!

• En,MAX 2 GeV for L732 km
• En,MAX 8 GeV for L2900 km
• En,MAX 20 GeV for L7400 km

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Matter affects L/E scaling
for neutrinos for antineutrinos
where
For example, for neutrinos
Resonance
Suppression
Mixing in matter smaller than in vacuum
Effect tends to become visible for L gt 1000 km
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Maximal length for L/E scaling
The magnitude of the CP effect (given by J) is
known to be unaffected by matter
J cos?13 sin? sin2?12 sin2?13 sin2?23/8
Our choice-point for CP is at the fixed
L/En,max given by
When the neutrino energy becomes close to the MSW
resonance, the effective oscillation wavelength
increases, hence the CP effect at a fixed
distance L becomes less visible.
Hence, we gain until the MSW resonance region and
then lose
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Effect of matter on L/E scaling
MSW resonance position EMSW 12 GeV
When E?,max gt EMSW, the oscillation gets
suppressed
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CP- and T-violation in matter
Scaled ?T
Scaled ?CP
Experimental observables for both ?CP and ?T,
the difference between ??/2 and ?-?/2 is
suppressed at L7400 km (E?,MAX 20 GeV gt EMSW)
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Effects of matter on ?T
The cut-off of the scaled T-violating term in
matter for L4000 km destroys L/E scaling. It is
useless to go above this distance for T-and CP-
violation studies
vacuum
The above considerations have nothing to do with
the necessity of subtracting fake-CP violation
due to matter ?-? asymmetry
matter
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Electron charge
In a granular detector (?x 100 ?m) with a
magnetic field of about 1T, bending of low-energy
(Ee lt 5 GeV) electrons can be observed before
the start of the shower
e
Fully simulated 2.5 GeV electron in LAr with 1T
external field
Hard bremsstrahlung
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Energy-baseline considerations
For CP violation, L/E scaling breaks down for
L4000 km due to matter effects. The measurement
is performed measuring the charge of muons, and
detector efficiency is approximately constant
over a wide energy range
For T-violation, the electron charge has to be
measured. This is only practically conceivable
for energies lt 5 GeV ?low energies/short
baselines needed!
Radiation length of a light material (ex. LAr)
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MC simulation for electron charge
MC simulations of electrons in a magnetic field
have been performed, assuming the following
magnet parameters
Purities obtained (for 10 efficiency) are
encouraging, but clearly require high fields
Magnetic and electric fields are perpendicular to
exploit the better resolution along drift (O(300
?m) vs O(3mm) wire pitch)
E
For a practical implementation of a magnetized
LAr TPC see talk from F.Sergiampietri
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A practical example
In order to prove L/E scaling, and explore the
physical reach in practical examples, we have
studied in detail two cases

• L 732 km, E? 7.5 GeV, 1021 ? decays for ?CP
  and ?T (also higher flux considered)
• L2900 km, E? 30 GeV, 2.51020 ? decays for ?CP
  only

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Event rates

1021 muon decays 10 kton detector
?- beam
Assume BG rejection factor for electrons O(10-3)
for 20 efficiency
? beam
??e background another reason to require low
energies!
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L/E scaling
Also the number of oscillated events around the
oscillation maximum depends on L/E
??/2
?0
The integral below the maximum goes like E3/L2,
so it is linear in L for a given L/E
L2900 km, E?30 GeV
However, for constant machine power, N?E?
const, so CP-violating effects only depend on L/
E?.
L732 km, E?7.5 GeV
Wrong-sign electrons
Wrong-sign muons
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Direct measurement of oscillation
In addition to the MonteCarlo-based fit to the
observed spectra, information about ?CP and ?T
can be directly extracted from the oscillation
probability
_
Observed WSL events
Background

?
Oscillation probability
Non-oscillated
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Measuring CP violation
The ?e??? and ?e??? oscillation probabilities
obtained from wrong-sign muons.
L732 km
?CP P(?e???)-P(?e???), Will be different from
zero due to matter effects, even for ?0
L2900 km
At L732 km, matter effects are smaller, and
large negative values of ? can reverse the sign
of ?CP
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L/E? scaling at work
90 contours in the ?m212-? plane, obtained
translating the probability differences into ??2
The sensitivity for the two cases is similar,
proving the validity of the L/E? scaling at
constant machine power. Actually, the shorter
distance is even better due to the smaller
influence of matter effects
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Measured probabilities for T-violation

• ?m2233.5?10-3 eV2
• ?m2121.?10-4 eV2
• sin22?130.05
• sin22?231.
• sin22?121.
• ?13?/2
• 1021 ? decays
• 10 kton detector
• 20 e charge eff.

E?5 GeV, L732 km
Direct comparison of oscillation probabilities
for neutrinos and antineutrinos
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Measuring ?T
The difference in probability for wrong-sign
muons and wrong-sign electrons is a direct proof
of T-violation. Matter effects are the same, and
cancel out in the difference.
This measurement has a 3? significance for ???/2
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Efficiency-purity dependence
Due to the large background from the beam, a
large purity is needed from the charge
identification. However, charge confusion at 1
level does not spoil the measurement
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?T exclusion
CP violation and T-violation L732 km E? 7.5 GeV
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Conclusions

• In neutrino factory experiments, most of the
  sensitivity to CP-violation will come from events
  close to the first oscillation maximum
• Given the scaling laws for the number of events,
  for a given L/E? and a fixed flux, the
  sensitivity grows linearly with L until Llt4000 km
• For fixed machine power, all energy/baseline
  combinations with same L/E? are equal. Baselines
  of 730 km, where existing facilities and
  experiments will be located at the time of the
  start of a neutrino factory can be used with an
  intense, low energy neutrino beam
• Matter effects are creating fake CP violation,
  but they are small for baselines lt1000 km
• Matter effects can be fully eliminated searching
  for T-violation
• A detector with electron charge identification
  capabilities can provide a clean and
  model-independent evidence for a complex phase in
  the leptonic mixing matrix