Investigating the scaling of higher-order flows in relativistic heavy-ion collisions

Relativistic heavy-ion collisions provide a useful way of studying the new phase which may exist at extreme high energy densities on earth. Collectivity is one of the main evidences of the produced dense matter, named as quarkgluon plasma (QGP), produced in relativistic heavy-ion collider (RHIC) [1–4]. Due to the almond shape of the produced QGP in non-central collisions, there are more freeze-out particles moving in-plane than out-plane, leading to the so-called elliptic flow (v2). Generally, the anisotropic flow is believed to be mostly produced at the early stages of the collision when the interaction is strongest. The number of constituent quark (NCQ) scaling law v2/nq ∼ pT /nq or v2/nq ∼ KET /nq [5–10], where pT and KET are respectively the transverse momentum and transverse kinetic energy, shows that the underlining mechanism for hadron elliptic flow is from partons as baryons and mesons are scaled by their number of constituent quark numbers nq. The NCQ scaling can be well explained by the coalescence model [11–15], typically by assuming that hadrons are formed from the combination of its constituent quarks whose distance in momentum space is small [16, 17]. The coalescence or recombination mechanism also automatically results in the relation v4 ∼ v 2 from the leading order [17], which originates actually from the partonic level [18]. Although the above coalescence picture works well at intermediate pT or KET , it has been observed that the collective flows of light and heavy hadrons obey the mass ordering at low pT showing the thermalization of different species of particles in the medium [6, 8, 9], and this can usually be explained by a blast wave model [19] or the Cooper-Frye freeze-out condition [20] in the hydrodynamic model.