Differential elliptic flow of identified hadrons and constituent quark number scaling at FAIR

Differential elliptic flow $v_2(p_{T})$ for identified hadrons has been investigated in the FAIR energy regime, employing a hadronic-string transport model (UrQMD) as well as a partonic transport model (AMPT). It has been observed that both the models show a mass ordering of $v_2$ at low $p_{T}$ and a switch over resulting a baryon-meson crossing at intermediate $p_{T}$. AMPT generates higher $v_2$ values compared to UrQMD. In addition, constituent quark number scaling behavior of elliptic flow has also been addressed. Scaling behavior in terms of the transverse momentum $p_T$ is found to absent for both the partonic as well as the hadronic model. However UrQMD and AMPT with string melting scenario do exhibit a NCQ scaling of $v_2$ at varying degree, with respect to transverse kinetic energy $KE_T$. But default AMPT, where partonic scatterings are not included, does not show any considerable scaling behavior. A variable $\alpha$ is defined to quantify the degree of $KE_T$ scaling. We found that UrQMD gives better scaling than AMPT at FAIR.