Subatomic Physics

11.12. Massive Neutrinos 363
11.12 Massive Neutrinos
In our treatment so far we have assumed massless neutrinos. In Section 11.2, we
pointed out that the high energy end of the beta spectrum can be used to search
for a finite electron neutrino mass and yields a limit of m(νe)c 2 < 2.2 eV. Similarly,
searches for masses of νµ and ντ give m(νµ)c 2 ≤ 0.19 MeV and m(ντ)c 2 ≤ 18.2MeV.
Because the masses of neutrinos are so much smaller than the masses of the other
particles, they were assumed to carry no mass in the Standard Model (Chapter 13.)
Here the mystery story starts with two experiments that were not motivated
by measuring neutrino masses: one was the IMB-collaboration detector that was
mounted to search for proton decay and the other was the Homestake-mine Cl detector
set up to detect neutrinos from the Sun and confirm the mechanisms for
production of solar energy (the intensity of light produced by the Sun is directly
related to the intensity of neutrinos, see Problem 11.46.) The IMB-collaboration
detector did not find any evidence for proton decay but proved able to detect and
identify the flavor of neutrinos that are produced in the upper atmosphere (called
atmospheric neutrinos). Both detectors found something unexpected: the IMB detector
(28) determined that the ratio of muon neutrinos to electron neutrinos from
the upper atmosphere was approximately a factor of 2 too small compared to expectations
and the Homestake-mine Cl detector found only ≈ 1/3 of the electron
neutrinos expected from the Sun. (29) For many years it was thought that the solutions
to these problems were unrelated. (30) Many scientists thought, for example,
that the solar neutrino problem was due to lack of proper understanding of the solar
physics. Other detectors were built to confirm the findings and better understand
them and eventually it became clear that neutrinos do have mass and undergo flavor
oscillations. A detector built in Japan, Super-Kamiokande, showed clear evidence
for atmospheric neutrino oscillations (31) and a Canadian-American collaboration,
the SNO detector, showed clear evidence for solar neutrino oscillations. (32)
Assuming that there are 3 kinds of neutrinos, ν1, ν2, andν3 with corresponding
masses m1, m2 and m3, and that weak decays produce neutrinos not in a pure mass
eigenstate, but in a general linear combination of all possible states, we have:
⎛
⎝
νe
νµ
ντ
⎞
⎠ =
⎛
⎝
Ve1 Ve2 Ve3
Vµ1 Vµ2 Vµ3
Vτ 1 Vτ 2 Vτ 3
⎞
⎠
⎛
⎝
ν1
ν2
ν3
⎞
⎠ . (11.79)
This should be reminiscent of Eq. 11.59 but here the matrix is called the Pontecorvo-
Maki-Nakagawa-Sakata matrix. (33) To simplify our equations we assume only two
28 D. Casper et al., Phys. Rev. Lett. 66, 2561 (1991).
29 J.N. Bahcall and R. Davis, jr. Science 191, 264 (1976).
30 For a very nice description of the history see J.N. Bahcall, posted at the Nobel prize web site:
http://nobelprize.org/physics/articles/bahcall/index.html .
31 Y. Fukuda et al., Phys. Rev. Lett. 81, 1562 (1998).
32 Q.R. Ahmad et al. Phys. Rev. Lett. 89, 011301 (2002).
33 V.N. Gribov and B.M. Pontecorvo, Phys. Lett. B28, 493 (1969); Z. Maki, M. Nakagawa, and