Rational trigonometry

2014-02-03T18:33:32Z

78.147.177.220: Move sections 'Spread polynomials' & 'Spread Periodicity Theorem' from end of article to between 'Spread' & 'Laws of rational trigonometry'

[[Image:E288 1976 ee Oops-Leon.png|thumb|200px|right|A plot counting the rate of production of [[electron]]–[[positron]] pairs as a function of [[invariant mass]] (in [[GeV]]). The apparent peak around 6 GeV was initially identified as a new particle,<ref name="Oops"/> but named '''Oops-Leon''' when it turned out not to exist.]]

'''Oops-Leon''' is the name given by [[particle physicist]]s to what was thought to be a new [[subatomic particle]] "discovered" at [[Fermilab]] in 1976. The E288 collaboration, a group of physicists led by [[Leon Lederman]] who worked on the E288 [[particle detector]], announced that a particle with a [[mass]] of about 6.0 [[GeV]], which decayed into an [[electron]] and a [[positron]], was being produced by the Fermilab [[particle accelerator]].<ref name="Oops"/> The particle's initial name was the [[greek letter]] [[Upsilon]] (<math>\Upsilon\,</math>). After taking further data, the group discovered that this particle did not actually exist, and the "discovery" was named "Oops-Leon" as a [[pun]] on the original name ([[English pronunciation of Greek letters|mispronounced]] {{IPAc-en|ˈ|juː|p|s|ɨ|l|ɒ|n}}) and the first name of the E288 collaboration leader.<ref name="Yoh">
{{cite journal
|author=J. Yoh
|year=1998
|title=The Discovery of the ''b'' Quark at Fermilab in 1977: The Experiment Coordinator's Story
|url=http://lss.fnal.gov/archive/1997/conf/Conf-97-432-E.pdf
|journal=[[AIP Conference Proceedings]]
|volume=424 |pages=29–42
|doi=
}}</ref>

The original publication was based on an apparent peak ([[resonance#Quantum_field_theory|resonance]]) in a [[histogram]] of the [[invariant mass]] of electron-positron pairs produced by [[proton]]s colliding with a stationary [[beryllium]] target, implying the existence of a particle with a mass of 6 GeV which was being produced and decaying into two leptons. An analysis showed that there was "less than one chance in fifty" that the apparent resonance was simply the result of a coincidence.<ref name="Oops">
{{cite journal
|author=D.C. Hom ''et al''.
|year=1976
|title=Observation of High Mass Dilepton Pairs in Hadron Collisions at 400 GeV
|url=http://lss.fnal.gov/archive/1976/pub/Pub-76-019-E.pdf
|journal=[[Physical Review Letters]]
|volume=36 |pages=1236–1239
|doi=10.1103/PhysRevLett.36.1236
|bibcode=1976PhRvL..36.1236H
|issue=21
}}</ref> Subsequent data collected by the same experiment in 1977 revealed that the resonance had been such a coincidence after all.<ref name="Yoh"/> However, a new resonance at 9.5 GeV was discovered using the same basic logic and greater statistical certainty,<ref>
{{cite journal
|author=D.C. Hom ''et al''.
|year=1977
|title=Observation of a Dimuon Resonance at 9.5 Gev in 400-GeV Proton-Nucleus Collisions
|url=http://lss.fnal.gov/archive/1977/pub/Pub-77-058-E.pdf
|journal=[[Physical Review Letters]]
|volume=39 |pages=252–255
|doi=10.1103/PhysRevLett.39.252
|bibcode=1977PhRvL..39..252H
|issue=5
}}</ref> and the name was reused (see [[Upsilon particle]]).

Today's commonly accepted standard for announcing the discovery of a particle is that the number of observed events is 5 [[standard deviation]]s (σ) above the expected level of the background.<ref>
{{cite journal
|author=C. Seife
|year=2000
|title=Scientific Priority: CERN's Gamble Shows Perils, Rewards of Playing the Odds
|journal=[[Science (journal)|Science]]
|volume=289 |pages=2260–2262
|doi=10.1126/science.289.5488.2260
|issue=5488
}}</ref> Since for a normal distribution of data, the measured number of events will [[Standard deviation#Rules for normally distributed data|fall within 5σ over 99.9999% of the time]], this means a less than one in a million chance that a statistical fluctuation would cause the apparent resonance. Using this standard, the Oops-Leon "discovery" would never have been published.

==References==
{{reflist}}

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Rational trigonometry