364
21. CP Violation and Oscillation Phenomena
push the bound on half-lives up to 10
26 –10
27 years, and the upper bound on
‹m› down to magnitudes of the order of a few times 10
−2 eV.
A second crucial question concerns the magnitude of CP-violation effects
in neutrino oscillations. We recall from (20.172) that this vanishes if sin θ e3 =
0. As we saw earlier, CHOOZ set a 90% CL limit sin
2 2θ e3 < 0.17. A non-zero
value of sin
2 2θ e3 has now been observed by two groups, both ν ¯ e disappearance
experiments: the Daya Bay collaboration (An et al. 2012) and the RENO
collaboration (Ahn et al. 2012). Their reported results were
sin
2 2θ e3 = 0.092 ± 0.016 ± 0.005 (Daya Bay)
(21.143)
sin
2 2θ e3 = 0.113 ± 0.013 ± 0.019 (RENO),
(21.144)
in a 3-neutrino framework. For this value of sin θ e3 , it should be possible to
detect a CP-violating difference in the probabilities for ν μ → ν e and ν ¯ μ → ν ¯ e ,
and it may be enough to sustain leptogenesis models.
The value of sin θ e3 is also relevant to the determination of the sign of
2
Δm we shall mention just one possibility. We have seen that the MSW effect
31 ;
for solar neutrinos implies that m 2 > m 1 (using the fact that cos θ e2 > 0), but
the mass spectrum (for 3-neutrino mixing) could be ordered as m 1 < m 2 < m 3
(‘normal spectrum’) or as m 3 < m 1 < m 2 (‘inverted spectrum’). We have
ignored the terrestrial MSW effect, but it can be significant in long-baseline
accelerator-based experiments, and could be exploited to determine the sign
of m 3 − m 1 . In the vacuum, the probability of the appearance of a ν e in
a ν μ beam is given by (21.134) (in our customary effective 2-state mixing
approximation). As in the solar case, these probabilities will be modified by
the MSW effect, which will enhance (suppress) the appearance probability for
neutrinos (antineutrinos) in the case of the normal spectrum, and vice versa
for the inverted spectrum. Clearly if θ e3 were too small, the effect would be
very hard to see, but the value in (21.143) and (21.144) makes this a realistic
experiment; it formed part of the physics motivation for the NOνA experiment
at Fermilab (Ayres et al. 2005). NOνA is a long-baseline neutrino oscillation
experiment now under construction, which aims to detect the appearance of
ν e and ¯
ν e in the NuMI muon neutrino beam. The beam from Fermilab is
directed 14 mrad off-axis to a detector 810 kn away; the neutrino energy is
narrowly peaked around 2.2 GeV. NOνA will also have sensitivity to leptonic
CP-violation.
Problems
21.1 Verify equation (21.34).
21.2 Verify equations (21.46) and (21.47).
20.3 Verify equations (21.48) and (21.49).
21. CP Violation and Oscillation Phenomena
push the bound on half-lives up to 10
26 –10
27 years, and the upper bound on
‹m› down to magnitudes of the order of a few times 10
−2 eV.
A second crucial question concerns the magnitude of CP-violation effects
in neutrino oscillations. We recall from (20.172) that this vanishes if sin θ e3 =
0. As we saw earlier, CHOOZ set a 90% CL limit sin
2 2θ e3 < 0.17. A non-zero
value of sin
2 2θ e3 has now been observed by two groups, both ν ¯ e disappearance
experiments: the Daya Bay collaboration (An et al. 2012) and the RENO
collaboration (Ahn et al. 2012). Their reported results were
sin
2 2θ e3 = 0.092 ± 0.016 ± 0.005 (Daya Bay)
(21.143)
sin
2 2θ e3 = 0.113 ± 0.013 ± 0.019 (RENO),
(21.144)
in a 3-neutrino framework. For this value of sin θ e3 , it should be possible to
detect a CP-violating difference in the probabilities for ν μ → ν e and ν ¯ μ → ν ¯ e ,
and it may be enough to sustain leptogenesis models.
The value of sin θ e3 is also relevant to the determination of the sign of
2
Δm we shall mention just one possibility. We have seen that the MSW effect
31 ;
for solar neutrinos implies that m 2 > m 1 (using the fact that cos θ e2 > 0), but
the mass spectrum (for 3-neutrino mixing) could be ordered as m 1 < m 2 < m 3
(‘normal spectrum’) or as m 3 < m 1 < m 2 (‘inverted spectrum’). We have
ignored the terrestrial MSW effect, but it can be significant in long-baseline
accelerator-based experiments, and could be exploited to determine the sign
of m 3 − m 1 . In the vacuum, the probability of the appearance of a ν e in
a ν μ beam is given by (21.134) (in our customary effective 2-state mixing
approximation). As in the solar case, these probabilities will be modified by
the MSW effect, which will enhance (suppress) the appearance probability for
neutrinos (antineutrinos) in the case of the normal spectrum, and vice versa
for the inverted spectrum. Clearly if θ e3 were too small, the effect would be
very hard to see, but the value in (21.143) and (21.144) makes this a realistic
experiment; it formed part of the physics motivation for the NOνA experiment
at Fermilab (Ayres et al. 2005). NOνA is a long-baseline neutrino oscillation
experiment now under construction, which aims to detect the appearance of
ν e and ¯
ν e in the NuMI muon neutrino beam. The beam from Fermilab is
directed 14 mrad off-axis to a detector 810 kn away; the neutrino energy is
narrowly peaked around 2.2 GeV. NOνA will also have sensitivity to leptonic
CP-violation.
Problems
21.1 Verify equation (21.34).
21.2 Verify equations (21.46) and (21.47).
20.3 Verify equations (21.48) and (21.49).