• 251 Prologue: The Rise of the Sigmas The standard deviation of a distribution is represented by the Greek letter sigma (σ), where σ = (√(1/(N − 1)))Σi = 1 i = N(xi − xave)2. N is the number of measurements and i is the ith measurement. In discussing the significance of an experimental result scientists often refer to it as a three-standard-deviation effect or as a three-sigma effect. In the episodes discussed, the signal is seen in either one bin of a graph or possibly in a few bins. For a single bin the number of standard deviations is usually given by NS/√NB, where NS is the number of signal events and NB is the number of background events. The larger the number of standard deviations the less likely it is that the signal is a fluctuation of the background, and the more significant the signal is. For a very readable account of the use of statistics in particle physics see Lyons (2012). 1. Abe et al. (1994b) contained a longer and much more detailed account of the analysis procedures used in the experiment than is allowed in a letters journal. 2. In the Standard Model, the currently accepted theory of elementary particles, particles that interact by the strong interaction, the interaction that holds the atomic nucleus together, are made up of either three quarks or a quark-antiquark pair and held together by the whimsically named gluons. The quarks are named up, down, strange, charm, top, and bottom. The top quark was the last to be discovered. The names of elementary particles are merely labels, and nothing of significant importance in this discussion depends on knowing the properties of these particles. 3. For a detailed discussion of how the decision about the claim was made, see Staley (2004). 4. The statement from the editors was in a private communication. There are, for example, no criteria for papers titled “Measurement of,” and this seems quite reasonable because a measurement will contain a stated uncertainty. There are occasions when even a rough measurement can be useful. For example, an experiment may demonstrate that a certain phenomenon can be measured. 5. Scientists also prefer to publish in letters journal, which are regarded as more prestigious than archival journals. The initial publication is usually, although not always, followed by a longer, more detailed publication in an archival journal. 6. D0 refers to the location of the detector on the Fermilab Tevatron ring. The location is specified by a letter and a number. 7. I have been told that some high-energy physicists considered publishing their results in Physics Letters, the European equivalent of Physical Review Letters, because it does not have a five-sigma rule. As discussed below, if Physics Letters has such a rule, it is not as stringently enforced as it is in Physical Review Letters. 8. In this section, unlike the remainder of the book, I will, primarily, be using papers Notes published in Physical Review Letters, the journal in which the most important results are published, as my source of information. 9. High-energy physicists use the terms “resonances” and “particles” interchangeably. Resonances are very short-lived particles and are often first observed by a peak in an invariant mass plot. 10. An interesting application of χ2 analysis occurred in the history of genetics. In 1936, the distinguished British statistician and geneticist R. A. Fisher (1936) analyzed Gregor Mendel’s data on pea plants, the experiments that founded modern genetics, and found that the fit to Mendel’s theoretical expectations was “too good.” Using χ2 analysis Fisher found that the probability of obtaining a fit as good as Mendel’s was only 7 in 100,000. The χ2 was 41.6056 for 84 degrees of freedom. Since 1964 there has been a controversy concerning Fisher’s analysis. (Fisher’s work, like that of Mendel, was neglected for a considerable period of time.) Contemporary scholarship has argued that Fisher’s accusation is unjust. For details, see Franklin et al. (2008). 11. Using the old method of calculation in effect at the time, the standard deviation is 6, which gives 24/6 or 4 standard deviations. Using the current method, the standard deviation would be √12 = 3.46, which would give 24/3.46 or 6.9 standard deviations. 12. In this section, and throughout the book, I will be presenting many graphs that show the experimental results. This is also an important part of the presentation of experimental results...