We present simple derivations of nuclear β-decay correlations with an emphasis on the special role of helicity. This topic provides a good opportunity to teach students about helicity and chirality in particle physics with exercises that use simple aspects of quantum mechanics. In addition, this paper serves as an introduction to nuclear β-decay correlations from both a theoretical and experimental perspective. This article can be used to introduce students to ongoing experiments searching for hints of new physics in the low-energy precision frontier.

1.

In this paper, we use “e-ν correlation” to represent both electron-antineutrino and positron-neutrino correlations.

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This formula can also be derived by considering a spin-1/2 particle moving through two Stern-Gerlach devices, the first one oriented along the direction of polarization (corresponding to the angular momentum defined by the nuclei) and the second one in a random polar direction (corresponding to the emission of the left-handed electron in a particular direction).

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We emphasize again this “unnatural” relationship between chirality and helicity for antiparticles. Explanations can be found in  Appendix A.

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In pure Fermi transitions, only vector and scalar currents are involved. In pure GT transitions, only axial-vector and tensor currents are involved. Check  Appendix C for further explanations.

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