System size dependence of charged hadrons directed flow at $\sqrt{s_{NN}}$ = 200 GeV using a multi-phase transport model

The directed flow ($v_1$) of charged hadrons ($h^{\pm}$) in symmetric collision systems (O+O, Cu+Cu, Zr+Zr, Ru+Ru, Au+Au, and U+U) at $\sqrt{s_{\mathrm{NN}}} =$ 200 GeV using string-melting version of A Multiphase Transport (AMPT-SM) model is reported. The $v_1$ as a function of pseudo-rapidity ($\eta$) is obtained for transverse momentum ($p_{\mathrm{T}}$) ranges of 0.2-2.0 GeV/$c$ and 2.0-5.0 GeV/$c$. The dependence of $v_1$-slope ($dv_1/d\eta$) at mid-rapidity on $p_{\mathrm{T}}$ range, collision centrality, and system size are discussed particularly in the context of the hard-soft asymmetry in the flow profiles of produced particles. In the AMPT-SM model, a system size independence of the magnitude of $dv_1/d\eta$ between Cu+Cu and Au+Au collisions at low-$p_{\mathrm{T}}$ is observed, and this finding is similar to the observation from the STAR experiment at $\sqrt{s_{\mathrm{NN}}} =$ 200 GeV. In contrast, a strong centrality and system size dependence, with the opposite sign of $dv_1/d\eta$, is found for the high-$p_{\mathrm{T}}$ charged hadrons. The AMPT-SM model demonstrates a clear violation of the expected scaling of charged hadrons $(dv_1/d\eta)/A^{1/3}$ across different colliding systems.