Examining the influence of hadronic interactions on the directed flow of identified particles in RHIC Beam Energy Scan energies using UrQMD model

The directed flow of identified particles can serve as a sensitive tool for investigating the interactions during initial and final states in heavy ion collisions. This study examines the rapidity distribution ($dN∕dy$), rapidity-odd directed flow ($v_1$) and its slope ($d{v}_1∕dy$) for ${\pi }^{\pm }$, $K^{\pm }$, p, and $\overline{\mathrm{\text{p}}}$ in Au+Au collisions at different collision centralities and beam energies ($\sqrt{s_{\mathrm{\text{NN}}}}=7.7$, 11.5, 14.5, 19.6, 27, and 39$$GeV) using the UrQMD model. We investigate the impact of late-stage hadronic interactions on charge-dependent $v_1(y)$ and its slope by modifying the duration of the hadronic cascade lifetime ($\tau$). The energy dependence of $d{v}_1∕dy$ for p ($\overline{\mathrm{\text{p}}}$) exhibits distinct pattern compared to ${\pi }^{\pm }$ and $K^{\pm }$. Notably, we observe a change in the sign reversal position of proton $d{v}_1∕dy$ at different beam energies with varying $\tau$ in central and mid-central collisions. Moreover, the difference in $d{v}_1∕dy$ between positively and negatively charged hadrons ($\mathrm{\Delta }d{v}_1∕dy$) demonstrates a stark centrality dependence for different particle species. The deuteron displays a significant increase in $d{v}_1∕dy$ with increasing $\tau$ compared to p and n. This investigation underscores the importance of considering the temporal evolution and duration of the hadronic phase when interpreting the sign reversal, charge splitting of $v_1$ and light nuclei formation at lower RHIC energies.