Collective flows of $\alpha$-clustering $^{12}\mathrm{C}$ + $^{197}\mathrm{Au}$ by using different flow analysis methods

Recently the ratio of triangular flow to the elliptic flow ($v_3/v_2$) of hadrons was proposed as a probe to detect the pattern of $\alpha$-clustering $^{12}\mathrm{C}$ in $^{12}\mathrm{C}$+$^{197}\mathrm{Au}$ collisions at relativistic energy by a participant plane method (Phys. Rev. C 95, 064904 (2017)). In experimental event plane method, Q-cumulant method and two-particle correlation method with rapidity gap always were used for measurement of collective flow only by means of momentum space. By comparing collective flow through the different methods, the ratio of $v_3/v_2$ could be taken as an experimental probe to distinguish different $\alpha$-clustering structure of $^{12}\mathrm{C}$.