359
21.4. Neutrino mixing and oscillations
We begin with the CHOOZ experiment, which was the first experiment to
limit the value of θ e3 (Apollonio et al. 1999, 2003). CHOOZ is the name of
a nuclear power station situated near the French village of the same name.
The experiment was designed to detect reactor ¯
ν e s via the inverse β-decay
+
reaction ¯
ν e + p → e + n. The signature was a delayed coincidence between
the prompt e
+ signal, and the signal from the neutron capture. The detector was located in an underground laboratory about 1 km from the neutrino
source. It consisted of a central 5-ton target filled with 0.09 % Gd-doped
liquid scintillator; Gd-doping was chosen to maximize the capture of the neutrons. The neutrino energy E was a few MeV, and L was 1 km. For these
values 2λ 21 (E) is greater than about 10 km, while 2λ 31 (E) is about 0.3 km.
The neglect of sin
2 L/2λ 21 (E) is justified, and formula (21.127) can be used
for the ¯
ν e survival probability. The experiment found no evidence for ¯
ν e disappearance, and reported the 90% CL upper limit of sin
2 2θ e3 < 0.19, for
2
|Δm 31 | = 2 × 10
−3 eV
2 . We shall for the moment set θ e3 to zero, and return
to discuss its value at the end of the chapter.
2
The mass squared range Δm > 2×10
−3 eV
2 can be explored by acceleratorbased long-baseline experiments, with typically E ∼ 1 GeV and L ∼ several hundred kilometres. The K2K (KEK-to-Kamioka) experiment was the
first accelerator-based experiment with a neutrino path length extending hundreds of kilometres. A horn-focused wide-band ν μ beam with mean energy
1.3 GeV and path length 250 km was produced by 12 GeV protons from
the KEK-PS and directed to the Super-Kamiokande detector. In this case,
L/2λ 21 (E) ∼ 10
−2 , which may be neglected. Then formulae (21.128) and
(21.129) may be used, in the approximation U e3 ≈ 0. The K2K data showed
2
(Ahn et al. 2006) that sin
2 2θ μ3 ≈ 1(θ μ3 ≈ π/4), and that |Δm 31 | had a value
consistent with (21.125).
The first evidence for the appearance of ν e in a ν μ beam was obtained by
the T2K collaboration (Abe et al. 2011). The ν μ beam is produced using
the high intensity proton accelerator at J-PARC, located in Tokai, Japan.
The beam was directed 2.5
◦ off-axis to the Super-Kamiokande detector at
Kamioka, 295 km away. This configuration produces a narrow-band ν μ beam,
2
tuned at the first oscillation maximum E ν = |Δm |L/2π ≈ 0.6 MeV, so
31
as to reduce background from higher energy neutrino interactions. In the
vacuum, the probability of the appearance of a ν e in a ν μ beam is given (in
our customary effective 2-state mixing approximation) by (21.126) as
2
31
P (ν μ → ν e ; L, E) = sin
2 θ μ3 sin
2 2θ e3 sin
2 Δm L;
(21.134)
4E
2
P (¯ ν μ → ν ¯ e ; L, E) is given by the same expression. Taking |Δm 31 | = 2.4 ×
10
−3 eV
2 and sin
2 2θ μ3 = 1, the number of expected ν e events was 1.5 ±
0.3(syst.) for sin
2 2θ e3 = 0, and 5.5 ± 1.0 events if sin
2 θ e3 = 0.1. Six events
were observed which passed all the ν e selection criteria. As we will see in the
following section, the value of sin
2 2θ e3 = 0.1 is entirely consistent with direct
measurements of this quantity reported in 2012.
21.4. Neutrino mixing and oscillations
We begin with the CHOOZ experiment, which was the first experiment to
limit the value of θ e3 (Apollonio et al. 1999, 2003). CHOOZ is the name of
a nuclear power station situated near the French village of the same name.
The experiment was designed to detect reactor ¯
ν e s via the inverse β-decay
+
reaction ¯
ν e + p → e + n. The signature was a delayed coincidence between
the prompt e
+ signal, and the signal from the neutron capture. The detector was located in an underground laboratory about 1 km from the neutrino
source. It consisted of a central 5-ton target filled with 0.09 % Gd-doped
liquid scintillator; Gd-doping was chosen to maximize the capture of the neutrons. The neutrino energy E was a few MeV, and L was 1 km. For these
values 2λ 21 (E) is greater than about 10 km, while 2λ 31 (E) is about 0.3 km.
The neglect of sin
2 L/2λ 21 (E) is justified, and formula (21.127) can be used
for the ¯
ν e survival probability. The experiment found no evidence for ¯
ν e disappearance, and reported the 90% CL upper limit of sin
2 2θ e3 < 0.19, for
2
|Δm 31 | = 2 × 10
−3 eV
2 . We shall for the moment set θ e3 to zero, and return
to discuss its value at the end of the chapter.
2
The mass squared range Δm > 2×10
−3 eV
2 can be explored by acceleratorbased long-baseline experiments, with typically E ∼ 1 GeV and L ∼ several hundred kilometres. The K2K (KEK-to-Kamioka) experiment was the
first accelerator-based experiment with a neutrino path length extending hundreds of kilometres. A horn-focused wide-band ν μ beam with mean energy
1.3 GeV and path length 250 km was produced by 12 GeV protons from
the KEK-PS and directed to the Super-Kamiokande detector. In this case,
L/2λ 21 (E) ∼ 10
−2 , which may be neglected. Then formulae (21.128) and
(21.129) may be used, in the approximation U e3 ≈ 0. The K2K data showed
2
(Ahn et al. 2006) that sin
2 2θ μ3 ≈ 1(θ μ3 ≈ π/4), and that |Δm 31 | had a value
consistent with (21.125).
The first evidence for the appearance of ν e in a ν μ beam was obtained by
the T2K collaboration (Abe et al. 2011). The ν μ beam is produced using
the high intensity proton accelerator at J-PARC, located in Tokai, Japan.
The beam was directed 2.5
◦ off-axis to the Super-Kamiokande detector at
Kamioka, 295 km away. This configuration produces a narrow-band ν μ beam,
2
tuned at the first oscillation maximum E ν = |Δm |L/2π ≈ 0.6 MeV, so
31
as to reduce background from higher energy neutrino interactions. In the
vacuum, the probability of the appearance of a ν e in a ν μ beam is given (in
our customary effective 2-state mixing approximation) by (21.126) as
2
31
P (ν μ → ν e ; L, E) = sin
2 θ μ3 sin
2 2θ e3 sin
2 Δm L;
(21.134)
4E
2
P (¯ ν μ → ν ¯ e ; L, E) is given by the same expression. Taking |Δm 31 | = 2.4 ×
10
−3 eV
2 and sin
2 2θ μ3 = 1, the number of expected ν e events was 1.5 ±
0.3(syst.) for sin
2 2θ e3 = 0, and 5.5 ± 1.0 events if sin
2 θ e3 = 0.1. Six events
were observed which passed all the ν e selection criteria. As we will see in the
following section, the value of sin
2 2θ e3 = 0.1 is entirely consistent with direct
measurements of this quantity reported in 2012.