Abstract In this work, we study the $K^- p \to \gamma \Lambda$ reaction in an effective Lagrangian approach and isobar model. Compared to previous studies using an Regge-plus-resonance model, here we consider the contributions of the $t$-channel($K$ and $K^*$) and $u$-channel(proton) exchanges explicitly as the background contribution. To restore the gauge invariance of the amplitude violated by introducing the phenomenological form factors, we employ two different methods that adopted in literatures. Then we discuss the roles of possible resonance contributions in this reaction and present the predictions of $\Lambda$ polarization based on various models. We find that the contribution of the background terms play an important role in the present reaction. On the other hand, the $\Lambda(1520)$, $\Sigma(1660)$ and $\Sigma(1670)$ resonances may also contribute in this reaction. Due to the uncertainties of the present data and the relatively small contributions of the hyperon resonances, we can not identify the roles of various hyperon resonances in the present work. While, we show that the measurement of the spin polarization of the final $\Lambda$ will be helpful to verify various models.
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