Energy dependence study of directed flow in Au+Au collisions using an improved coalescence in AMPT model

The rapidity-odd component of directed flow ($v_{1}$) of identified hardons ($\pi^{\pm}$, $K^{\pm}$, $K^{0}_{S}$, p, $\bar{\rm p}$, $\phi$, $\Xi^{\pm}$, $\Lambda$, $\bar{\Lambda}$) and partons (u, $\bar{\rm u}$, d, $\bar{\rm d}$, s, $\bar{\rm s}$) in Au+Au collisions at various beam energies ($\sqrt{s_{NN}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 54.4, 62.4, 200 GeV) using a multi-phase transport model are analyzed. A data driven approach (inspired from the experimental analysis) is performed here to distinguish the transported and produced quarks which are found to have different directed flow values at various collision beam energies. The coalescence sum rule (Number of Constituent Quark scaling) violation is observed at lower energies where hadronic matters dominate. The strange quark (s) and $\phi$ meson slope (d$v_{1}$/dy) show a double sign change around 14.5 GeV unlike other partons and hadrons. It suggests that strange quark is more sensitive towards the softening of Equation of State (EoS).