Neutron-proton differential transverse flow in ${}^{132}$Sn + ${}^{124}$Sn collisions at 270 MeV/nucleon

Within a transport model, we study the neutron-proton differential transverse flow and its excitation function in central ${}^{132}$Sn + ${}^{124}$Sn collisions at 270 MeV/nucleon. To more accurately evaluate effects of the high-density behavior of symmetry energy \esym on this observable, we also consider the uncertainties of \esym around the saturation density ${\rho }_0$. It is shown that the neutron-proton differential transverse flow and its excitation function are mainly sensitive to the slope $L$ of \esym at ${\rho }_0$. However, the effects of low-density behavior of \esym on this observable should also be considered. Therefore, it is suggested that measurements of the neutron-proton differential transverse flow and its excitation function may provide useful complements to the constraints on $L$ extracted from the spectral pion ratio in S$\pi$RIT experiments.