360
21. CP Violation and Oscillation Phenomena
Another long baseline accelerator experiment is MINOS at Fermilab. Neutrinos are produced by the Neutrinos at the Main Injector facility (NuMI),
using 120 GeV protons from the Fermilab main injector. The detector is a
5.4 kton iron-scintillator tracking calorimeter with a toroidal magnetic field,
situated underground in the Soudan mine, 735 km from Fermilab. The neutrino energy spectrum from a wide-band beam is horn-focused to be en2
hanced in the 1-5 GeV range. The current MINOS results yield |Δm 31 | =
(2.32
+0.12 ) × 10
−3 eV
2 , and sin
2 2θ μ3 > 0.90 at 90 % CL (Adamson et al.
−0.08
2011).
A second reactor experiment, KamLAND at Kamioka, was designed to
2
be sensitive to the smaller squared mass difference Δm , and thus to θ e2 .
21
The Kamioka Liquid scintillator AntiNeutrino Detector is at the site of the
former Kamioka experiment. The detector is essentially one kiloton of highly
purified liquid scintillator surrounded by photomultiplier tubes. ν ¯ e s are detected as usual via the inverse β-decay reaction ¯
ν e + p → e
+ + n. KamLAND
is surrounded by 55 nuclear power units, each an isotropic ¯
ν e source. The
flux-weighted average path length is L ∼ 180 km, and the energy E ranges
from about 2 MeV to about 8 MeV. For E = 3 MeV, 2λ 21 (E) ∼ 30 km, which
allows for more than one oscillation. In this case (21.119) reduces to
P (¯ ν e → ν ¯ e ; L, E) = 1 − 4|U e1 |
2
|U e2 |
2 sin
2 (L/2λ 21 (E))
(21.135)
assuming |U e3 | ≈ 0. In a parametrization of the form (20.166), this becomes
P (¯ ν e → ν ¯ e ; L, E) = 1 − sin
2 2θ e2 sin
2 (L/2λ 21 (E)),
(21.136)
again a simple 2-state mixing result. Data shown in figure 21.11 (Abe et al.
2008) gives
2
|Δm 21 | = 7.58
+0.14+0.15
(21.137)
−0.13−0.15 × 10
−5 eV
2
= 0.56
+0.10+0.10
tan
2 θ e2
−0.70−0.06 .
(21.138)
The KamLAND data showed for the first time the periodic behaviour of the
ν ¯ e survival probability.
We now return to the solar neutrino problem, taking up the story after
Davis’ results. Some doubts remained as to whether the solar calculations
could be absolutely relied upon, for example because of the extreme sensitivity
to the core temperature (∝ T
18 ). One particular class of ν e could, however,
be reliably calculated, namely those associated with the initial reaction pp →
2
H+e
+ + ν e of the pp cycle. Whereas the Davis experiments allowed detection
of the higher energy ν e s (threshold 814 keV) from the B and Be stages of
the cycle, the energy of the ν e s from the pp stage cuts off at around 400
−
keV. Detectors using the reaction ν e +
71 Ga → e +
71 Ge, which has a 233
keV energy threshold, were built (GALLEX, GNO and SAGE); their results
(Altman et al. 2005, Abdurashitov et al. 2009) are in agreement, and again
much smaller than the (updated) Bahcall et al. (2005) prediction.
21. CP Violation and Oscillation Phenomena
Another long baseline accelerator experiment is MINOS at Fermilab. Neutrinos are produced by the Neutrinos at the Main Injector facility (NuMI),
using 120 GeV protons from the Fermilab main injector. The detector is a
5.4 kton iron-scintillator tracking calorimeter with a toroidal magnetic field,
situated underground in the Soudan mine, 735 km from Fermilab. The neutrino energy spectrum from a wide-band beam is horn-focused to be en2
hanced in the 1-5 GeV range. The current MINOS results yield |Δm 31 | =
(2.32
+0.12 ) × 10
−3 eV
2 , and sin
2 2θ μ3 > 0.90 at 90 % CL (Adamson et al.
−0.08
2011).
A second reactor experiment, KamLAND at Kamioka, was designed to
2
be sensitive to the smaller squared mass difference Δm , and thus to θ e2 .
21
The Kamioka Liquid scintillator AntiNeutrino Detector is at the site of the
former Kamioka experiment. The detector is essentially one kiloton of highly
purified liquid scintillator surrounded by photomultiplier tubes. ν ¯ e s are detected as usual via the inverse β-decay reaction ¯
ν e + p → e
+ + n. KamLAND
is surrounded by 55 nuclear power units, each an isotropic ¯
ν e source. The
flux-weighted average path length is L ∼ 180 km, and the energy E ranges
from about 2 MeV to about 8 MeV. For E = 3 MeV, 2λ 21 (E) ∼ 30 km, which
allows for more than one oscillation. In this case (21.119) reduces to
P (¯ ν e → ν ¯ e ; L, E) = 1 − 4|U e1 |
2
|U e2 |
2 sin
2 (L/2λ 21 (E))
(21.135)
assuming |U e3 | ≈ 0. In a parametrization of the form (20.166), this becomes
P (¯ ν e → ν ¯ e ; L, E) = 1 − sin
2 2θ e2 sin
2 (L/2λ 21 (E)),
(21.136)
again a simple 2-state mixing result. Data shown in figure 21.11 (Abe et al.
2008) gives
2
|Δm 21 | = 7.58
+0.14+0.15
(21.137)
−0.13−0.15 × 10
−5 eV
2
= 0.56
+0.10+0.10
tan
2 θ e2
−0.70−0.06 .
(21.138)
The KamLAND data showed for the first time the periodic behaviour of the
ν ¯ e survival probability.
We now return to the solar neutrino problem, taking up the story after
Davis’ results. Some doubts remained as to whether the solar calculations
could be absolutely relied upon, for example because of the extreme sensitivity
to the core temperature (∝ T
18 ). One particular class of ν e could, however,
be reliably calculated, namely those associated with the initial reaction pp →
2
H+e
+ + ν e of the pp cycle. Whereas the Davis experiments allowed detection
of the higher energy ν e s (threshold 814 keV) from the B and Be stages of
the cycle, the energy of the ν e s from the pp stage cuts off at around 400
−
keV. Detectors using the reaction ν e +
71 Ga → e +
71 Ge, which has a 233
keV energy threshold, were built (GALLEX, GNO and SAGE); their results
(Altman et al. 2005, Abdurashitov et al. 2009) are in agreement, and again
much smaller than the (updated) Bahcall et al. (2005) prediction.