Measurement of the $\alpha$ asymmetry parameter for the ${\Omega }^{-}\to \Lambda K^{-}$ Decay

We have measured the $\alpha$ parameter of the ${\Omega }^{-}\to \Lambda K^{-}$ decay using data collected with the HyperCP spectrometer during the 1997 fixed-target run at Fermilab. Analyzing a sample of $0.96\times {10}^6$ ${\Omega }^{-}\to \Lambda K^{-}$, $\Lambda \to p{\pi }^{-}$ decays, we obtain ${\alpha }_{\Omega }{\alpha }_{\Lambda }=[1.33\pm 0.33(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.52(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})]\times {10}^{-2}$. With the accepted value of ${\alpha }_{\Lambda }$, ${\alpha }_{\Omega }$ is found to be $[2.07\pm 0.51(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.81(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})]\times {10}^{-2}$.

Figure 1

Definition of the Lambda Helicity Frame.

Figure 2

Plan view of the HyperCP spectrometer.

Figure 3

Distribution of the $p{\pi }^{-}{K}^{-}$ invariant mass with third-degree polynomial background fit superimposed.

Figure 4

Comparison of the real-proton and weighted-HMC-proton $\cos \theta$ distributions in the Lambda Helicity Frame, where the number of events in each plot has been normalized to one (top). The bottom plot is the ratio of the real-proton to weighted-HMC-proton $\cos \theta$ distributions.