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The neutrino is one of nature's most peculiar particles. It has 1/2 unit of spin but no electric charge, a near-zero rest-mass, and it interacts with other particles only through gravity and the weak interaction. It can pass through light years of lead without an interaction. There is good experimental evidence that the Earth receives only about 1/3 of the neutrinos that the Sun should be producing and sending in our direction.

I've written several previous columns about neutrinos. One discussed the then-current evidence for a neutrino with a huge 17 keV rest-mass (see Analog, December, 1991). Several other columns considered the possibility that the electron neutrino might have an imaginary rest-mass characteristic of faster-than-light tachyon particles (see Analog, September, 1992 and October, 1993). I will start this column by saying that from new experimental results, it is now clear that neutrinos do not have a 17 keV mass (that was a detector artifact) and are not tachyons (that was a subtle artifact of the physics and chemistry of the tritium sources used). We now understand much more about neutrinos, and this column will present some of that understanding.

Let me start by reviewing the Standard Model of particle physics as it applies to neutrinos. There are two classes of fundamental spin 1/2 particles, the strongly-interacting quarks and the weakly-interacting leptons. Three of the leptons (e, m, and t) have significant masses, and all three have the same electric charge. The other three leptons (n_e, n_m, and n_t) have zero charge and are called neutrinos. The simplest form of the Standard Model assumes that neutrinos, like photons and gluons, have zero rest-mass. However, we have had to change that assumption, based on new experimental evidence. Neutrinos have very small masses (probably a few hundredths of an electron-volt), they usually travel at nearly (but not quite) the speed of light, and they rarely interact with anything.

Our sun is a giant thermonuclear reactor that burns hydrogen into helium, making lots of neutrinos in the process. You can think of the Sun's thermonuclear reaction as applying heat and pressure that forces hydrogen nuclei to "eat" their orbiting electron and change their charges to become neutrons, spitting out the neutrino "lepton seeds" that are left over. About 61 billion neutrinos per second made in the Sun pass through each square centimeter of area on the surface of the Earth. If your body presents an area to the sum of a square meter, this means that 610 trillion neutrinos are passing right through your body in the second it takes to read this line. But you don't notice this because there are no interactions.

Neutrinos pass through your body and through the Earth as if neither was there. As you might imagine, this makes neutrinos very difficult to detect... but not impossible. Over the last quarter of the twentieth century, a succession of large underground neutrino detectors has demonstrated that (a) the neutrinos from the Sun can be detected and that (b) there is a discrepancy of a factor of three between the number of neutrinos predicted by astrophysical theories and the number of neutrinos actually detected. This is known as the Solar Neutrino Problem. At the end of the twentieth century, it was number five on my list of the top ten things that we do not understand about physics (see Analog, July/August, 1999). However, in the past few years, important new information about neutrinos has come from observations by the SNO, KamLAND and WMAP detectors, and the Solar Neutrino Problem has essentially been solved.

• SNO ( Sudbury Neutrino Observatory)

Some years ago, the Canadian government began a program for developing and selling nuclear power reactors, called CANDU reactors. These were fueled with natural uranium and moderated with "heavy water," that is, with water made with deuterium instead of hydrogen. This made economic sense, because Canada had lots of natural uranium and a great deal of hydroelectric power, and during off-peak times this surplus electricity could be used to separate deuterium from hydrogen by electrolysis to make heavy water. However, after the market for nuclear power reactors diminished because of misguided environmentalism and after India used a CANDU reactor in developing its nuclear bomb, sales of the CANDU units dried up and Canada was left with a sizable quantity of surplus heavy water.

Physicists are opportunists. The large reservoir of Canadian heavy water represented an experimental opportunity that could not be overlooked. After years of proposal writing and some delicate negotiations between the US and Canadian governments, a consortium of US and Canadian physicists built the SNO detector (Sudbury Neutrino Observatory), a large acrylic vessel filled with $300,000,000 worth of Canadian heavy water and housed miles deep in a mine in Sudbury , Ontario . The acrylic vessel is suspended in a tank of normal water and surrounded by photomultiplier tubes that record light flashes from the vessel.

When neutrinos pass through heavy water, they can interact in several ways. In the first process, which is called a "charged-current interaction," the incoming neutrino can convert the deuterium nucleus into two protons and an electron. Essentially, a neutron and neutrino change charges through a W boson to become a proton and electron. The electron carries off most of the original neutrino's energy and will make a flash of Cerenkov light in the heavy water.

In the second process, which is called a "neutral-current interaction," the in-coming neutrino breaks up the deuterium nucleus into a proton and a neutron. Essentially, a neutron and neutrino interact through a Z boson. The neutron subsequently is captured by another nucleus, producing a gamma ray that can be detected from the flash of Cerenkov light by a photo-electron.

In the third process, which is called a "neutrino elastic scattering," the incoming neutrino bounces off the electron of a deuterium atom. Here, the electron and neutrino interact through a either a Z or W boson. The electron carries off part of the neutrino's energy and will make a flash of Cerenkov light in the heavy water. These three types of interactions generate somewhat different signals and are distinguishable in the SNO detector.

The SNO detector is selectively sensitive to electron neutrinos (n_e) through the charged-current interactions, and is unselectively sensitive to all three neutrino species (n_e, n_m, and n_t), through the neutral and elastic interactions. Therefore, if the missing 2/3 of the neutrinos from the Sun are absent because they have "oscillated" from n_e to n_m and n_t, they should contribute to the neutral and elastic interactions, but not the charged-current interactions.

And sure enough, when the SNO data was analyzed, the solar neutrinos missing in the charged-current interactions turned up in the neutral and elastic interactions. The Solar Neutrino Problem occurs because all three neutrino species have small and slightly different rest-masses. As they propagate through space, the small mass differences modify the quantum interference between species, and n_e are transformed into n_m and n_t (and back again).  Before SNO operated, there were several alternative theories for how neutrinos might oscillate.  The SNO results are consistent with only one of these theories, the so-called LMA (Large Mixing Angle) solution, and indicate that the electron neutrinos are oscillating into another neutrino species (presumably n_m) that has a difference in mass-squared |m(n_e)² – m(n_m)²| of 8 ´ 10^-5 electron-volts².

• KamLAND  (Kamioka liquid-scintillator Anti-Neutrino Detector)

The neutrinos detected by SNO travel 150 million kilometers, so there is a very long path length over which the oscillations between neutrino species can occur. Rather surprisingly, the SNO data suggests that the path distance over which significant neutrino oscillations occur is fairly short, only a few hundred kilometers.

This rather short oscillation length has been tested by the KamLAND experiment conducted in Japan . In the old Kamioka cavity inside a Japanese mountain, where the predecessor of the Super Kamiokande detector was housed, a new detector has been built, a stainless-steel tank containing a spherical balloon holding one kiloton of liquid scintillator. About 180 km from the Kamiokande site are several Japanese nuclear power reactors. In the nuclear fission process that occurs in these reactors, neutron-rich fission-fragment nuclei are produced, and these undergo radioactive decays in which the excess neutrons are converted to protons, emitting an electron and an anti-neutrino in the process. KamLAND is designed to detect these anti-neutrinos as they convert protons in the detector into a neutron and a positron. The signal of such an anti-neutrino event is the detection of gamma rays from the positron annihilation, followed by the detection of a 2.2-MeV gamma ray from the capture of the neutron by hydrogen.

The KamLAND detector will continue to operate for some time with improving statistics, but in the initial period of its operation the consortium has reported evidence for neutrino oscillations consistent with the LMA solution, with a difference in mass-squared |m(n_e)² – m(n_m)²| of about 7 ´ 10^-5 electron-volts². Thus, neutrino oscillations have been detected for both neutrinos from the Sun and anti-neutrinos from nuclear power reactors and give consistent results.

• WMAP  (Wilkinson Microwave Anisotropy Probe)

The problem with the new SNO and KamLAND results is that they measure |m(n_e)² – m(n_m)²| rather than m(n_e) and m(n_m).  In a column published in the October 2003 issue of Analog, I described the results of the WMAP satellite probe, which mapped the small angle fluctuations of the cosmic microwave background, the reverberating "sound of the Big Bang" when our universe was about 380,000 years old.

It turns out that the WMAP data also has something to say about the rest-mass of neutrino species. This is because massive neutrinos fall into the general cosmological category of "hot dark matter," which tends to smear out the "clumpiness" of the early universe.  The WMAP data, because it views this initial clumpiness, places fairly stringent limits on how much hot dark matter could have existed in the early universe.  The data indicate that the mass density of neutrinos in the universe cannot be larger than about 2% of critical density.  This translates to 1.0 electron-volts as the sum of the rest-masses of all three neutrino species.

Assuming that the electron neutrino (n_e) is no more massive than the other two neutrino types, this result limits its mass to no more than 0.33 electron-volts. This is to be compared with laboratory measurements of tritium beta decay, which place a corresponding upper limit of 2.2 electron-volts.  Thus, cosmology has beaten laboratory physics in placing a limit on the rest-mass of the electron neutrino by almost an order of magnitude.

• Conclusion

The results from SNO, KamLAND, and WMAP are not the final word on neutrino physics, but they have answered some outstanding questions. We know that about 2/3 of the neutrinos reaching the Earth from the Sun are in the form of n_m or n_t. We know that neutrinos are not tachyons and have positive mass-squared values with differences that suggest (but do not prove) that the masses are around 0.01 electron-volts.  We know from WMAP that in no case can the electron neutrino have more mass than around 0.33 electron-volts.  We also know that about 93% of the universe's mass-energy is in the form of some mysterious dark energy and cold dark matter, with only 7% left for ordinary matter including neutrinos.  We now know that we live in a very peculiar universe.

References

Neutrino Physics

"Neutrino Physics: an Update," Wick C. Haxton and Barry R. Holstein, American Journal of Physics 72, 18-24 (2004), preprint hep-ph/0306282.

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