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Could someone please refer me to the paper that ruled out Peccei-Quinn axions experimentally. Most literature mentions this happening but doesn't refer to the original paper where it was proven so.

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Usually, individual experimental papers don't decisively "rule out" a model, because there are usually multiple ways to set up the model, but a combination of experiments can. For a review of the experimental situation circa 1978, see Peccei's contribution to the Proceedings of the 19th International Conference on High Energy Physics.

Peccei describes several ways to search for axions.

  1. The decay $K \to \pi a$. This is too rare to be ruled out by 1978, but Peccei mentions that a similar decay may soon be testable. OP links a related paper along these lines released in 1982.
  2. Production and subsequent detection in reactor neutrino events. Performing a post-hoc analysis of data collected in the mid 1970s gives a picture that is "surely very bad for axions", according to Peccei. However, it is not definitive because the rate depends on the axion couplings.
  3. Production of axions in beam dump experiments at SLAC, CERN, and BNL, where they give rise to hadronic showers. These bounds are similar to (2), and Peccei concludes that "the above analyses are quite discouraging for the axion idea".

Note that Peccei and Quinn's original paper was released in 1977, so this is quite early, but already the experimental pressure is strong. "Invisible axion" models that evaded these bounds appeared in 1980. I believe the original axion model was regarded as completely dead by the early 1980s.

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