The directed flow   observed in heavy-ion collisions is sensitive to the initial baryon density distribution, the equation of state of the produced medium, and electromagnetic fields.  In this article, we present the STAR measurements of   for  , and   as functions of rapidity, transverse momentum, and centrality in Au+Au collisions at   , and   GeV from the RHIC Beam Energy Scan Phase-II. These results provide unprecedented precision for constraining theoretical models aimed at understanding the initial conditions and the subsequent evolution of the medium in heavy-ion collisions.

List of Figures

Figure 1: Directed flow of pions as a function of rapidity in 0-10%, 10-40% and 40-80% centrality in Au+Au collisions at center of mass energy 7.7 - 200 GeV.

Figure 2: Directed flow of kaons as a function of rapidity in 0-10%, 10-40% and 40-80% centrality in Au+Au collisions at center of mass energy 7.7 - 200 GeV.

Figure 3: Directed flow of protons as a function of rapidity in 0-10%, 10-40% and 40-80% centrality in Au+Au collisions at center of mass energy 7.7 - 200 GeV.

Figure 4: Directed flow of lambdas as a function of rapidity in 0-10%, 10-40% and 40-80% centrality in Au+Au collisions at center of mass energy 7.7 - 200 GeV.

Figure 5: Deltav1 for pi/K/p/lambda as a function of rapidity in 50-80% centrality in Au+Au collisions at center of mass energy 7.7 - 200 GeV.

Figure 6: Directed flow of pions as a function of transverse momentum in 0-10%, 10-40% and 40-80% centrality in Au+Au collisions at center of mass energy 7.7 - 200 GeV.

Figure 7: Directed flow of kaons as a function of transverse momentum in 0-10%, 10-40% and 40-80% centrality in Au+Au collisions at center of mass energy 7.7 - 200 GeV.

Figure 8: Directed flow of protons as a function of transverse momentum in 0-10%, 10-40% and 40-80% centrality in Au+Au collisions at center of mass energy 7.7 - 200 GeV.

 
Figure 9: Directed flow of lambdas as a function of transverse momentum in 0-10%, 10-40% and 40-80% centrality in Au+Au collisions at center of mass energy 7.7 - 200 GeV.

Figure 10: Deltav1 for pi/K/p/lambda as a function of transverse momentum in 50-80% centrality in Au+Au collisions at center of mass energy 7.7 - 200 GeV.

Figure 11: dv1/dy of pions as a function of centrality  in Au+Au collisions at center of mass energy 7.7 - 200 GeV.

Figure 12: dv1/dy of kaons as a function of centrality  in Au+Au collisions at center of mass energy 7.7 - 200 GeV.

Figure 13: dv1/dy of protons as a function of centrality  in Au+Au collisions at center of mass energy 7.7 - 200 GeV.

Figure 14: dv1/dy of lambdas as a function of centrality  in Au+Au collisions at center of mass energy 7.7 - 200 GeV.

Figure 15: delta(dv1/dy) for pi/k/p/lambda as a function of centrality  in Au+Au collisions at center of mass energy 7.7 - 200 GeV.

Conclusion

In this article, we reported the STAR measurements of directed flow   for pions, kaons, protons and lambdas as functions of rapidity, transverse momentum, and centrality in Au+Au collisions at center of mass energy from 7.7-200 GeV from the RHIC Beam Energy Scan Phase-II. 

The directed flow slope difference delta(dv1/dy)  between positively and negatively charged particles exhibits a strong dependence on centrality and beam energy. The observed trends are consistent with expectations based on the dominance of the Faraday and Coulomb effects, which are more pronounced at lower collision energies.

As a function of p_T, deltav1 shows a non-monotonic trend, with the dip shifting to higher p_T  in peripheral collisions. In these peripheral events, deltav1 tends to become increasingly negative at higher  p_T, consistent with expectations from electromagnetic field effects.

These measurements can help constrain the equation of state, initial baryon deposition profile and electromagnetic properties of the quark gluon plasma phase of matter produced in heavy ion collisions and understand the medium evolution with different initial conditions.