Measurement of the Spin of the ${\Omega }^{-}$ Hyperon

A measurement of the spin of the ${\Omega }^{-}$ hyperon produced through the exclusive process ${\Xi }_c^0\to {\Omega }^{-}{K}^{+}$ is presented using a total integrated luminosity of $116{\mathrm{fb}}^{-1}$ recorded with the BABAR detector at the $e^{+}{e}^{-}$ asymmetric-energy $B$ factory at SLAC. Under the assumption that the ${\Xi }_c^0$ has spin $1/2$, the angular distribution of the $\Lambda$ from ${\Omega }^{-}\to \Lambda K^{-}$ decay is inconsistent with all half-integer ${\Omega }^{-}$ spin values other than $3/2$. Lower statistics data for the process ${\Omega }_c^0\to {\Omega }^{-}{\pi }^{+}$ from a $230{\mathrm{fb}}^{-1}$ sample are also found to be consistent with ${\Omega }^{-}$ spin $3/2$. If the ${\Xi }_c^0$ spin were $3/2$, an ${\Omega }^{-}$ spin of $5/2$ could not be excluded.

Figure 1

Schematic definition of the helicity angle ${\theta }_h$ in the decay chain ${\Xi }_c^0\to {\Omega }^{-}{K}^{+}$, ${\Omega }^{-}\to \Lambda K^{-}$; as shown in (b) ${\theta }_h$ is the angle between the $\Lambda$ direction in the ${\Omega }^{-}$ rest frame and the ${\Omega }^{-}$ direction in the ${\Xi }_c^0$ rest frame (the quantization axis).

Figure 2

The uncorrected ${\Omega }^{-}{K}^{+}$ (a) and ${\Omega }^{-}{\pi }^{+}$ (b) invariant mass spectra in data. The curves result from the fits described in the text.

Figure 3

The efficiency-corrected $\cos {\theta }_h(\Lambda )$ distribution for ${\Xi }_c^0\to {\Omega }^{-}{K}^{+}$ data. The dashed curve shows the $J_{\Omega }=3/2$ fit using Eq. (4), in which $\beta$ allows for possible asymmetry. The solid curve represents the corresponding fit with $\beta =0$.

Figure 4

The efficiency-corrected $\cos {\theta }_h(\Lambda )$ distribution for ${\Xi }_c^0\to {\Omega }^{-}{K}^{+}$ data. The dotted line represents the expected distribution for $J_{\Omega }=1/2$, while the dashed curve corresponds to $J_{\Omega }=5/2$. In each case, $\beta =0$.

Figure 5

The efficiency-corrected $\cos {\theta }_h(\Lambda )$ distribution in data for ${\Omega }_c^0\to {\Omega }^{-}{\pi }^{+}$ events. The curve corresponds to $J_{{\Omega }_c}=1/2$ and $J_{{\Omega }^{-}}=3/2$ with $\beta =0$.