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The SU(3)-flavor violating decay $J/\psi\to\Xi(1530)^{-}\bar\Xi^{+}+c.c.$ isstudied using $(1310.6\pm7.0)\times 10^{6} ~J/\psi$ events collected with theBESIII detector at BEPCII and the branching fraction is measured to be  ${\cal{B}}(J/\psi\to\Xi(1530)^{-}\bar\Xi^{+}+c.c.)=(3.17\pm0.02_{\rmstat.}\pm0.08_{\rm syst.})\times10^{-4}$. This is consistent with previousmeasurements with an improved precision. The angular parameter for this decayis measured for the first time and is found to be $\alpha=-0.21\pm0.04_{\rmstat.}\pm0.06_{\rm syst.}$. In addition, we report evidence for the radiativedecay $\Xi(1530)^{-}\to\gamma\Xi^- $ with a significance of 3.9$\sigma$,including the systematic uncertainties. The 90\% confidence level upper limiton the branching fraction is determined to be$\mathcal{B}(\Xi(1530)^{-}\to\gamma\Xi^- )\leq3.7$\%.

Measurement of {\boldmath $J/\psi\to\Xi(1530)^{-}\bar\Xi^{+}$} and evidence for the radiative decay {\boldmath $\Xi(1530)^{-}\to\gamma\Xi^-$}