| Abstract |
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The properties of the $\Xi(1530)$ resonance are investigated in the $\Lambda_c^+\rightarrow \Xi^- \pi^+ K^+$ decay process.
The data sample was collected with the BaBar detector at the SLAC PEP-II asymmetric-energy $e^+ e^-$ collider operating at center
of mass energies 10.58 and 10.54 GeV. The corresponding integrated luminosity is approximately 230 fb$^{-1}$.
The spin of the $\Xi(1530)$ is established to be 3/2. The existence of an $S$-wave amplitude in the $\Xi^- \pi^+$ system is inferred,
and its interference with the $\Xi(1530)^0$ amplitude provides the first clear demonstration of the Breit-Wigner phase motion
expected for the $\Xi(1530)$. The $P_1(\rm cos\,\theta_{\Xi^-})$ Legendre polynomial moment indicates the presence of a significant
$S$-wave amplitude for $\Xi^- \pi^+$ mass values above 1.6 GeV/c$^2$, and a dip in the mass distribution at approximately 1.7 GeV/c$^2$
is interpreted as due to coherent addition of a $\Xi(1690)^0$ contribution to this amplitude. This would imply $J^P=1/2^-$ for the
$\Xi(1690)$. Attempts at fitting the $\Xi(1530)^0$ lineshape yield unsatisfactory results, and this failure is attributed to
interference effects associated with the amplitudes describing the $K^+ \pi^+$ and/or $\Xi^- K^+$ systems.
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