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Probing nuclear quadrupole deformation from correlation of elliptic flow and transverse momentum in heavy ion collisions

In heavy ion collisions, elliptic flow $v_2$ and radial flow, characterized by event-wise average transverse momentum $[p_{\mathrm{T}}]$, are related to the shape and size of the overlap region, which are sensitive to the shape of colliding atomic nuclei. The Pearson correlation coefficient between $v_2$ and $[p_{\mathrm{T}}]$, $ρ_2$, was found to be particularly sensitive to the quadrupole deformation parameter $β$ that is traditionally measured in low energy experiments. Built on earlier insight that the prolate deformation $β>0$ reduces the $ρ_2$ in ultra-central collisions (UCC), we show that the prolate deformation $β<0$ enhances the value of $ρ_2$. As $β>0$ and $β<0$ are the two extremes of triaxiality, the strength and sign of $v_2^2-[p_{\mathrm{T}}]$ correlation can be used to provide valuable information on the triaxiality of the nucleus. Our study provide further arguments for using the hydrodynamic flow as a precision tool to directly image the deformation of the atomic nuclei at extremely short time scale ($<10^{-24}$s).