Phenomenological study on correlation between flow harmonics and mean transverse momentum in nuclear collisions

To assess the properties of the quark-gluon plasma formed in nuclear collisions, the Pearson correlation coefficient between flow harmonics and mean transverse momentum, $\rho (v_n^2,\left[p_{\mathrm{T}}\right])$, reflecting the overlapped geometry of colliding atomic nuclei, is measured. $\rho (v_2^2,\left[p_{\mathrm{T}}\right])$ was found to be particularly sensitive to the quadrupole deformation of the nuclei. We study the influence of the nuclear quadrupole deformation on $\rho (v_n^2,\left[p_{\mathrm{T}}\right])$ in $\mathrm{A}\mathrm{u}+\mathrm{A}\mathrm{u}$ and $\mathrm{U}+\mathrm{U}$ collisions at RHIC energy using $\mathrm{A}\mathrm{M}\mathrm{P}\mathrm{T}$ transport model, and show that the $\rho (v_2^2,\left[p_{\mathrm{T}}\right])$ is reduced by the prolate deformation ${\beta }_2$ and turns to change sign in ultra-central collisions (UCC).