Method For Boson Spin Determination

Abstract

The reaction $K\left(\pi \right)+P\to Y+B$ is considered, in which $Y$ is a spin-½ hyperon and $B$ is a spin-$\ell$ boson which decays into two spin-zero bosons. Taking into account the consequences of parity conservation in the production process, the structure of the joint decay distribution of $Y$ and $B$ is defined for arbitrary spin $\ell$. It is shown that, at given production angle and total center-of-mass energy, there are $2\ell (2\mathrm{}\ell -1)$ constraints on the complete set of moments of the joint decay distribution. These constraints may be utilized to test for the compatibility of a set of data with each hypothesized value of $\ell$. The structure of the joint distribution may also be used to define the forbidden moments, whose absence may be experimentally verified in order to rule out distortion of the distribution due to interference effects, final-state interaction, or experimental biases. The absence of the forbidden moments is also important in cases where the spin of $B$ is known and the data are used to determine the production parameters.