Neutrino physics today, important issues and the future Page: 4 of 5
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Therefore CP violation is maximum when A32
(2n + 1)4 and grows as n grows. Notice also, that
for this term to be non-zero the kinematical phase
A32 cannot be nor. This is the neutrino counter
part to the non-zero strong phase requirement for
CP violation in the quark sector.
The asymmetry between P(vN -> ve) and
P(vN -> ie) is a maximum when Patm Ps,,.
At the first oscillation maximum, A31 7r/2, this
occurs when sin2 2013 0.002 in vacuum. For val-
ues of sin2 2013 < 0.002 the oscillation probabilities
are dominated by Po0 and thus observing the ef-
fects of non-zero sin2 2013 become increasing more
challenging.oo2-o
00B(e
E (eV)Vro'pii -soir 1 -'i2
o--d 5=3'2
05 X10 2 3 0
E (c.Figure 7: The left panel shows the two components Patm
and Ps0 in matter for the normal and inverted hierarchies
for sin2 2013 = 0.04 and a baseline of 1200 km. The right
panel shows the total probability including the interference
term between the two components for various values of the
CP phase 6 for the neutrino. Notice that the coherent sum
of two amplitudes shows a rich structure depending on the
hierarchy and value of CP phase. These curves can also be
interpreted as anti-neutrino probabilities if one interchanges
the hierarchy AND the values of the CP phase.
3.3. Comparing the results from Reactor and LBL
experiments
A direct comparison can be made between the re-
actor and the long baseline experiments by compar-
ing [P(v -> ve)+P(v -> Pe)]A31=- from the long
baseline experiments and 1 - P(c -> e)]iA 1
from the reactor experiments. Since
[P(vA -> ve) + P(VA - Ve)]A3=2=
2 sin2 023 sin2 2013 + O[(aL) sin (] (8)
and
1 - P(ve -> v)] A31=2 sin2 2013 (9)
then this comparison is a way to measure by how
much sin2 023 differs from z including the sign, so
is a way to determine the quadrant of 023. Fig. 80.10
0.08
p 0.06
V
^0.04
a 0.02
VNOvA (<E>=2.OGeV and L=810km)
0.00
0.000.02 0.04 0.06
sin 2G010.08 0.10
Figure 8: The sum of the ve and ve appearance probabil-
ities for the NOvA experiment verses sin2 2013. The re-
gions between the dotted lines give the allowed ranges for
sin2 2023 = 0.6 and sin2 2023 = 0.4 which are well separated
for large values of sin2 2013 and some what insenitive to the
mass hierarchy.
shows that this comparison works reasonable well
even when the long baseline experiment is not ex-
actly at the vacuum oscillation extremuum.
4. Beyond Superbeams: /-Beams and p1-
Storage Rings
To access the physics for small values of sin2 2013,
approximately <0.01, one requires neutrino beams
with small (1%) contamination of the appear-
ance flavor of neutrinos. Two possibilities are under
intense investigation:
(I) 3-Beams, where the neutrinos are produced
by the -decay of a nucleus,N -> N' + e - (e+) + Pc(ve).
(10)
Two pairs of nuclei are under investigation 6He and
18Ne as well as 8B and 'Li. These ions are acceler-
ated to high energy, -y 0 (100)), with a resulting
neutrino energy of order of 1 GeV or less and there-
fore correspondingly baselines of <1000km. The de-
tectors for this setup must be optimized to separate
electron events from muon events. Neutrino beams
produced by this technique are better suited to in-
vestigating CP violation than the neutrino mass hi-
erarchy, see E. Wildner this proceedings.
(II) Another possibility is to produce the neutri-
nos from a muon storage ring, this option has been4, J~--
4Ix <-
A-
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Parke, Stephen J. Neutrino physics today, important issues and the future, article, October 1, 2010; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc834312/m1/4/: accessed March 28, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.