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

The modified number of constituent quark (NCQ) scaling $v_{n}/n_{q}^{n/2} \sim KE_{T}/n_{q}$ for mesons and baryons and the scaling relation $v_{n} \sim v_{2}^{n/2}$ for higher-order anisotropic flows, which were observed experimentally, have been investigated at top RHIC energy. It has been found that the modified NCQ scaling can not be obtained from the naive coalescence even by taking into account event-by-event fluctuations but may be due to hadronic afterburner or thermal freeze-out. In addition, we observed that the behavior of the $v_{n}/v_{2}^{n/2}$ ratio is sensitive to the partonic interaction, and it is different for mesons and baryons from the naive coalescence but is expected to be almost the same experimentally.