"Little" a

What is "little" a?

The weak interaction is one of the four basic forces which physicists have described. It is most commonly seen in beta decays. The simplest of beta decays is the splitting of a neutron into a proton, electron, and a neutrino. Despite being abundant in nature, neutrons are unstable outside of nuclear matter. In its rest frame a neutron has a half life of roughly 10 minutes.

"Little" a is one of the experimentally determined parameters in the formula predicting neutron decay probabiltiy. The formula was derived by Jackson, Treiman and Wyld in a 1957 paper. Among the four parameters "little" a is the least precisely measured. It quantifies the correlation between the electron and anti-neutrino following the decay. The present accepted value is a= -.103 +/- .004 (Particle Data Group, 2004).

In a mathematical sense, "little" a is the parameter that measures the dependence of the neutron decay on the angular relationship between the electron and neutrino momentum. For instance, if a was negative the decay would favor the electron being emitted in the opposite direction of the neutrino. Likewise, if a was identically 0 the electron's initial momentum would be independent of the neutrinos.

Previous experiments (Grigor'ev et al., 1967; Stratowa et al., 1978; Byrne et al., 2002) determined "little" a from the shape of the recoil proton energy spectrum. This approach is statistically most advantagous because it does not require a coincidence measurement. However low energy proton spectroscopy is difficult, and these experiments were systematics limited at the 5% level. We plan to improve the fractional precision to less than 1%.