Each "cycle" of nuclear fusion in a star, such as the proton-proton cycle or the CNO cycle, can be represented as a "chain" of reactions, proceeding one after the other. Sometimes only one such chain is involved in a particular reaction, but usually there are several ways in which particles can combine, resulting in different end or intermediate results. In such a case the chain which occurs most of the time (and usually produces the most overall energy) is the main chain, and those which occur less frequently are side chains.
     As an example, let's break the proton-proton cycle, the way in which the Sun gets the majority of its energy, into its components. The start of this series of reactions is the collision of two protons, creating a deuteron (a hydrogen nucleus with one proton, which is what makes it a hydrogen nucleus, but with a neutron as well, which is relatively uncommon for hydrogen). Since there are two positive charges on the two protons (one each) and only one on the deuteron, a positive charge must be removed from the two protons to make the deuteron. That happens through the emission of a particle of antimatter which is called a positron or anti-electron. The reaction also produces a nearly massless particle called an electron neutrino (ν_e) with an energy of 0.42 MeV, as shown here:

     The positron produced in this reaction almost immediately collides with one of the host of normal electrons in the vicinity of the reaction, resulting in the annihilation of the electron and positron and the creation of a gamma-ray photon with an energy of 1.02 MeV, as shown here:

     Occasionally, however (about once for every 400 proton-proton reactions in the Sun), the collision of two protons occurs simultaneously with a collision with an electron. In this case the positron emission and annihilation is unnecessary, as the negative charge on the electron cancels out the positive charge that needed to be removed. However, the energy created by the more common electron-positron annihilation is still produced; it just isn't produced in the form of gamma rays, but as an increase in the energy of the electron neutrino produced by the reaction:

     We can show the two possibilities side-by-side, at the beginning of the series of reactions involved in the proton-proton cycle, as shown here:

Main Chain (probability 99 3/4%) p+ + p+ → p+n + e+ + νe (of energy 0.42 MeV) e+ + e- → γ (of energy 1.02 MeV) (another step) (another step) (etc etc etc)

Side Chain (probability 1/4%) p+ + p+ + e- → p+n + νe (of energy 1.44 MeV) (another step) (another step) (etc etc etc)

     As shown by the label at the top of each column, the chain on the left, which occurs 400 times more often, is the main chain, while the one on the right, which hardly occurs at all, is a side chain. In this case the two chains produce the same amount of energy, but in different forms: in the main chain more energy is produced as photons of "light" (the gamma-rays) and is available to help heat up and hold up the Sun, while in the side chain the extra 1.02 MeV zips out of the Sun at the speed of light, and is lost in space (since neutrinos do not normally interact with matter, once created in the core of a star they almost immediately escape).

Consequences of Side Chains: The Solar Neutrino Problem
     Suppose you were examining neutrinos coming out of the Sun with a device which could only detect neutrinos with an energy greater than 1 MeV. The neutrinos produced by the main proton-proton chain only have 0.42 MeV of energy and would not be detectable, while the neutrinos produced by the side chain shown above have an energy of 1.44 MeV and would be detectable. In other words, only one neutrino in 400 would be detectable. You could correct for this by multiplying the number of neutrinos detected by 400, but that assumes that the ratio involved is always the same. What if it weren't?
     Suppose that the main chain has a temperature sensitivity of 3% higher energy production for a 1% increase in temperature (which is about right), while the side chain has a temperature sensitivity of a 30% higher energy production for a 1% increase in temperature (which may not be right for the particular reaction involved, but is not unusual). If our temperature estimate for the core of the Sun were off by 3%, the energy production of the main chain would only be affected by about 10%, while the energy production of the side chain would be off by a factor of two. This would change the ratio of low and high energy neutrinos by nearly a factor of two as well. In other words, if a side chain has a much greater temperature sensitivity than a main chain, the ratio of particles produced by the chains can be very different from what we expect it to be.
     Many years ago it was thought that the Sun's core was hotter than we now believe it to be. This meant that certain side chains which produced easily detectable high energy neutrinos were thought to be much more important than we now believe them to be, and high-energy solar neutrinos were expected to be sufficiently common to be more or less easily detectable. Solar neutrino detectors soon showed that the flux of high-energy neutrinos was essentially zero, and that the Sun's core must therefore be too cool to produce a significant number of such neutrinos. To solve the problem models of the Sun's core had to be adjusted to a slightly lower temperature and a slightly higher density. The lower temperature slightly reduced the energy production expected, but the higher density slightly increased it, balancing the overall energy production to match the observed energy production of the Sun. But while the lower temperature only slightly decreased the production of lower-energy neutrinos (by the main chain), it practically eliminated the production of higher-energy neutrinos (by various side chains), "explaining" the lack of high-energy neutrinos in the observations. Warning: The production of high-energy neutrinos, although partly due to the side chain shown above, was primarily thought to be due to other side chains not currently shown on this page (hence the use of the phrase "by various side chains" in the previous sentence). So although the concepts involved are properly described, the details are wrong. A more accurate description of the "solar neutrino problem" and its solution will be posted at a later date.