Neutrino Factory for Pedestrians II

1
Neutrino Factory for PedestriansII

• J.J. Gómez-Cadenas
• IFIC-Valencia

2
Lecture II

• Matter matters
• Degenerate physics
• Design your experiment

3
Matter matters
4
Recall In a NuF, rates grow with muon energy
(flux cross sections increase with E) To work
at the oscillation peak one needs long baselines
(5000 km at 10 GeV) This implies that the
neutrino beam travels through Earth But Earth is
less transparent to ?e than to ??, ??!
5
The fact that ?e and ?e have charged current
elastic scattering interactions on the Earth
electrons introduce effective masses for the
electron neutrinos ? 2E?A, where A is the
matter parameter
Matter effects may be important if A is
comparable of bigger than ?ij for a given mass
split and E?
6
(No Transcript)
7
At L300 Km (E700 MeV) matter does not matter
8
At L1000 Km (E2.4 GeV) atmospheric term starts
to see matter
9
At L3000 Km (E10GeV) atmospheric term shows
strong effect, solar term starts to see effect
10
At L10000 Km (E30GeV) matter effects are also
important for solar term and will mask completely
any oscillation effect
11
At L300 Km (E700 MeV) no fake CP effect from
matter
12
At L1000 Km (E2.4 GeV) fake CP smaller than
true CP
13
At L3500 Km (E10 GeV) fake CP same order than
true CP
14
At L10000 Km (E30 GeV) fake CP much larger than
true CP
15
The bad news Matter effects are large at large
distances. For a high energy neutrino factory one
is prevented to go to the oscillation peak and
has to work in the lineal region where one is
less sensitive to ACP. The good news Because
matter effects are large, one can use them to
find out the mass hierarchy, that is the
so-called, sign of matter.
B changes sign depending on whether the sign of
matter is positive or negative.
16
(No Transcript)
17
(No Transcript)
18
Homework

• You are the owner of a tunable beta-beam
  facility.
• Choose a neutrino beam energy
• Choose baseline
• Choose detector tecnology (explain your reasons)
• Explain your physics program
• Repeat the game for a tunable neutrino-factory.
• Compare both facilities
• Since matter matters. What is your criteria now
  to choose a baseline?

19
Significance of the interference term, for
different Nufact energies in presence of matter.
One cannot go much beyond 3000 km to measure CP.

20
Significance of the CP asymmetry after
subtracting matter effects for a nufact of 50
GeV. Thick line is the integral asymmetry, red
lines spectral analysis
21
Degenerate physics
22
Suppose you make an experiment with a fixed
polarity (neutrinos) and fixed energy and
baseline. The outcome of your experiment is a
measurement of P(?,E,L). Your goal is to find the
true value (chosen by Nature) of ? and ?13.
23
Curve of equiprobability in the plane (?13, ?).
The true solution is one of a continuous set and
cannot be obtained if we fix polarity, baseline
and energy. But one can now repeat the experiment
using antineutrinos!
24
But one can now repeat the experiment using
antineutrinos! In this case we obtain two curves
which cross at the true point. But, alas, these
are periodic equations. If they cross in one
point, they cross in a second point! Thus the
outcome of the experiment is a true solution and
a clone! That is we find a degeneration in the
solution, which is called the intrinsic
degeneracy.
25
But (fortunately!) our beam is not monocromatic.
If we have good energy resolution, we can
approximate our beam as a set of monocromatic
beams. All monocromatic beam cross in the true
point, but each one of them gives a different
clone. Therefore, spectral analysis allows
solving the degeneracy!
26
Golden Silver channels at NUFACT
27
If one has a tau-capable detector (Opera like)
then the combination of golden and silver
channels, helps further the spectral analysis.
Golden and Silver solutions cross in the true
value and each one has a clone, but these are
different clones! Thus one can solve the system
and eliminate degeneracy.
28
Discrete degeneracies

• Two other sources of degeneracy.
• Ignorance of the sign of ?m232
• Ignorance of the octant of ?23

These two discrete values assume the value 1
29
Eightfold degeneracy
Experimental measurement. Number of observed
charged leptons Nb Integrate P over Fn, s, and
detector efficiencies.
Since satm soct not known, one should consider
also 2 other equations which result in an 8-fold
degeneracy
30
Correlation and degeneracies

• Discrete degeneracies

2 intrinsic degeneracies
x 2 possible ? hierarchies
d
x 2 possible q23 octants
p-d
1 true solution 7 clones!!
q13

• Each color belongs to a different parameter
  space.
• Intrinsic fake solution and its clones
  depend strongly on E/L ratio (unlike the
  clones of the true solution ).
• greatly increase the errors,
  particularly for ?.

31
How to solve degeneracies

• Use spectral information on oscillation signals?
  experiment with energy resolution
• Combine experiments differing in E/L (and/or
  matter effects) ? need two experiments
• Include other flavor channels silver channel ne
  ? nt. Need a tau-capable detector

Burguet et al, Nucl.Phys.B608301-318,2001
32
Homework

• Starting from equation
• Write a computer program to ilustrate graphically
  the existence of degeneracies and the way to
  solve them
• Find the analytical solutions for the case of
  neutrino and anti-neutrino equations in the solar
  and atmospheric regime.
• Digest Thomas Schwetz lecture on degenerations
  with the whole works in it!