Kaon production in the HADES experiment in Au+Au collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=2.4$ GeV

Within an isospin- and momentum-dependent transport model by including the kaon reaction channels, we study the kaon prodution in heavy-ion collisions (HICs) at SIS (Darmstadt Schwerionen Synchrotron, GSI) energies. Based on simulations of a centrality of 0-40% Au + Au collision at $\sqrt{s_{NN}}=2.4$ GeV, a typical reaction that has been carried out by the HADES Collaboration, we confirm that the medium modification of kaon masses plays a vital role in studying the kaon productions in HICs, and is also unavoidable for the successful interpretation of the HADES data on kaon rapidity distributions and transverse mass spectra. Moreover, it is shown that the directed flows of kaons are affected significantly by the kaon potential and slightly affected by the medium modification of kaon masses. Also, the rapidity-dependent inverse slope parameter $T_B$ of the kaon transverse mass spectra is shown to be affected considerably by both the kaon potential and medium modification of kaon masses. However, through checking the simulations of related reactions in FOPI and/or KaoS experiments, some of these regular effects do not seem to be obvious and appear to be the reaction system and/or beam energy dependent. Nevertheless, it can be confirmed that the medium modification of kaon masses is favored by observations from the inverse slope parameter $T_B$ and transverse mass spectra of kaons in both HADES Au + Au collisions at $\sqrt{s_{NN}}=2.4$ GeV and FOPI Ni + Ni collisions at 1.93$\mathit{\text{A}}$ GeV. Therefore, measurements of the inverse slope parameter $T_B$ of kaon transverse mass spectra and the kaon directed flows in HADES Au + Au collisions would be great benefit to detection of the kaon potential and the corresponding medium effects on kaon masses.