Number-of-constituent-quark scaling of elliptic flow: a quantitative study

The number-of-constituent-quark (NCQ) scaling behavior of the elliptic flow of identified particles produced in A+A collisions is studied quantitatively using an empirical function that fits the experimental $v_2$ data available from the RHIC and LHC. The most common approach for NCQ scaling involves (1) doing a scaling of the experimental $v_2$ data of an identified particle with its NCQ, (2) doing the same to its transverse momentum or energy, then (3) combining all the scaled data and identifying the NCQ behavior by intuitively looking (since the measured experimental data are discrete). We define two variables $(d_1, d_2)$ to describe NCQ scaling quantitatively and simultaneously, and identify the approximate region where the NCQ scaling holds. This approach could be applied to study NCQ or other scaling phenomena in future experiments.