2.3 Neutrino Oscillations
2.3.6 Measurements
After the initial discovery of neutrino oscillations in 1998 by Super-Kamiokande, new experiments began to come online which could make precise measurements of neutrino mixing. There are six parameters that can be measured in neutrino oscillation experiments: θ12,∆m212, θ23,∆m223, θ13, δ.
The first four parameters have been measured10 with precision, an upper limit has been placed on the fifth, and the sixth is not yet constrained.
The earliest solar neutrino experiments, the Homestake experiment discussed above [48] and the Kamiokande water Cherenkov experiment in Japan [60], were sensitive only to the highest energy solar neutrinos coming from the decay of8B,
8B→8Be∗+e++νe(≈10 MeV), (2.151) but these neutrinos are only a tiny fraction of the solar neutrino flux and their rate is model- dependent. They observed solar neutrino rates that were 28%±5% and 46%±8%, respectively, of those predicted by the standard solar model. The later radiochemical experiments, SAGE in Soviet
10With the notable exception of the sign of ∆m223, which remains unknown.
Union [61] and GALLEX-GNO in Italy [62], used the reaction
νe+71Ga→e−+71Ge (2.152)
to observe solar neutrinos, which has a significantly lower threshold of 0.223 MeV. Consequently, these experiments were sensitive to the pp neutrinos produced in the beginning of the main solar fusion reaction
p+p→d+e++νe(≈0.3 MeV), (2.153) which are lower in energy but make up the bulk of the solar neutrino flux. Their rate, unlike that of the8B neutrinos, is mostly model-independent. The standard solar model predicts a rate of 128 SNU on Gallium but Sage and Gallex measured rates of 70.8+6.5−6.1SNU and 77.5+7.5−7.8 SNU respectively.11 However, even when the results from all these experiments were combined, the oscillation parameters could not be constrained to a single region of ∆m212-θ12 parameter space (the 12 sector is believed to be responsible for transitions fromνe to νµ andντ). The isolation of a single pair of oscillation parameters came when the results of the SNO experiment were released [63], isolating the Large Mixing Angle (LMA) solution with MSW matter effects. The combined best oscillation fit to all solar neutrino data, circa 2005, gives [64]
∆m212= 6.5+4.4−2.3
×10−5eV2, tan2θ12= 0.45+0.09−0.08. (2.154) Additionally, by measuring the sign of the MSW effect, it was established thatm2> m1 [35].
Final confirmation of neutrino oscillations in the ‘solar sector’ (where the 12 oscillations are dominant) came from the KamLAND experiment. KamLAND is a ¯νe detector situated in the Kamioka mine in Japan which uses 1 kTon of liquid scintillator surrounded by non-scintillating buffer oil and is instrumented with approximately 1,900 phototubes. It detects neutrinos via inverse beta decay with the prompt-delayed double coincidence used in the earliest neutrino experiments.
It is exposed to a flux of ¯νe’s from 55 commercial nuclear reactors, which are an average of 180 km from the detector. KamLAND saw significant ¯νedisappearance [65] which, when fit for oscillations, gave
∆m212= 7.66+0.22−0.20
×10−5eV2, tan2θ12= 0.52+0.16−0.10 (2.155) which are clearly consistent with the parameters measured by the solar experiments in Equa- tion 2.154. The contours from KamLAND and the combined solar experiments can be seen in Figure 2.7. This independent measurement of similar oscillation parameters in a completely different experimental set up (¯νevs. νe, different energy and oscillation length, different detector technology) significantly increased confidence in neutrino oscillations. When the solar and KamLAND results
11SNU denotes a Solar Neutrino Unit which is defined as 10−36events/atom/second.
36 Physics of Neutrinos and Antineutrinos
32 Neutrino Physics
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Figure 2.7: Prompt event energy spectrum ofνe candidate events (top) and allowed re- gion for neutrino oscillation parameters from KamLAND and solar neutrino experiments (bottom). All histograms corresponding to reactor spectra and expected backgrounds incor- porate the energy-dependent selection efficiency shown on the top. For the bottom plot, the side panels show the ∆χ2-profiles for KamLAND (dashed) and solar experiments (dotted) individually, as well as their combination (solid). Images obtained from [54].
Figure 2.7: The oscillation parameter regions allowed by the KamLAND experiment (solid colors) and the combined solar experiments (black lines). The side plots show the two one-dimensional profiles for KamLAND (dashed), solar (dotted), and combined (solid). The consistency between the solar and reactor measurements lends significant support to the oscillation model of neutrino disappearance. Figure taken from [65].
are combined, the resulting measurement has a precision of better than 3.5% [35]:
∆m212= (7.59±0.20)×10−5eV2, tan2θ12= 0.47+0.06−0.05. (2.156)
After the initial discovery of oscillations, Super-Kamiokande continued to run and improve its measurements of oscillations in atmospheric neutrinos. The most recent result, based on data from phases SK-I, SK-II, and SK-III and including the possibility of sub-leading (θ13) oscillation effects, find at 90% confidence assumingm3> m1,2 (the ‘normal hierarchy’) [66],
1.9×10−3≤ |∆m2atm| ≤2.6×10−3eV2 0.407≤sin2θ23≤0.583 (2.157) with central values ∆m2atm= 2.1×10−3eV212 and sin2θ23= 0.5.
The atmospheric oscillations were confirmed by experiments usingνµ’s from terrestrial accelera- tors, just as the solar results were confirmed by the KamLAND reactor experiment. The experiments were designed with neutrino sources and detectors separated by approximately a quarter of the at- mospheric oscillation length, the distance over which a neutrino with energy E will oscillate back to its original state. In a sense the oscillation length is the ‘wavelength’ of the oscillation, and it is
12The atmospheric mass-splitting is referred to as ∆m2atmsince it is, in fact, a combination of ∆m223and ∆m213 which are too close to each other to be easily distinguished.
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