# Synopsis: Testing the Weak Interaction with Potassium

Potassium-37 is one of several isotopes that could be used to directly test the standard model weak interaction.

The weak interaction is responsible for radioactive decay, so the half-lives of certain isotopes can be used to test the interaction’s description in the standard model. A new way of doing this test could come from a measurement of the half-life of potassium-37 (${}^{37}\text{K}$), which has been determined with its greatest precision to date by researchers at the Cyclotron Institute at Texas A&M University.

${}^{37}\text{K}$’s decay to argon-37, which occurs by positron emission, is known as a “mirror” transition. The half-life of a mirror decay has a simple mathematical dependence on the standard model parameter ${V}_{u\phantom{\rule{0}{0ex}}d}$, which gives the probability of a down quark decaying into an up quark. So far, the most precise ${V}_{u\phantom{\rule{0}{0ex}}d}$ value comes from the family of so-called superallowed pure Fermi transitions. But determining ${V}_{u\phantom{\rule{0}{0ex}}d}$ from mirror transitions, including ${}^{37}\text{K}$, would provide an independent check on its value.

The authors prepared a high-purity beam of ${}^{37}\text{K}$ ions by colliding argon-36 with cooled hydrogen gas. After capturing the ions in a strip of Mylar tape, they determined the ${}^{37}\text{K}$ half-life by recording the exponential falloff in the number of emitted positrons. The reported value (1.23651 seconds) has an uncertainty of $0.08%$—an order of magnitude improvement compared to previous results. The newly measured half-life value won’t immediately give a more precise ${V}_{u\phantom{\rule{0}{0ex}}d}$ value, as the two quantities are related by another parameter that has to be determined with greater precision. But the value of ${V}_{u\phantom{\rule{0}{0ex}}d}$ derived from the new result is about $0.5%$ lower than the one based on previous measures of the ${}^{37}\text{K}$ half-life, and agrees better with the one derived from other mirror nuclei and pure Fermi transitions.

This research is published as a Rapid Communication in Physical Review C.

–Jessica Thomas

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